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DERIVE Help File

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Main Menu

Line Editing commands
Functions and constants
Algebra window commands
2D-plot window commands
3D-plot window commands
Utility file functions
Current State of system


Line Editing Commands (Section 2.4)

Special key commands: Backspace delete character left of cursor Del delete character at the cursor Enter enter line of text Ctrl-Enter enter and simplify line of text Esc abort edit and return to menu Ins toggle text input mode (insert or overwrite) F1 display help on line-editing, functions, etc. F3 copy highlighted expression onto author line F4 copy highlighted expression in parentheses F6 toggle arrow key mode (line-edit or subexpression) Back to main menu, function menu or Derive Basics Cursor movement commands (arrow keys NOT available in subexpression mode): Ctrl-S or <-- move cursor left a character Ctrl-D or --> move cursor right a character Ctrl-A or Ctrl<-- move cursor left a word Ctrl-F or Ctrl--> move cursor right a word Ctrl-], Ctrl-Q S or Home move cursor to left end of line Ctrl-\, Ctrl-Q D or End move cursor to right end of line Text deletion commands: Ctrl-H or Backspace delete character left of cursor Ctrl-G or Del delete character at cursor Ctrl-T delete word beginning at cursor Ctrl-Y delete all text on line Ctrl-Q Y delete text at and to right of cursor Ctrl-Q H delete text to the left of cursor Miscellaneous commands: Ctrl-M or Enter enter line of text Ctrl-J or Ctrl-Enter enter and simplify line of text Ctrl-[ or Esc abort edit and return to menu Ctrl-V or Ins toggle insert/overwrite modes Ctrl-U insert previous line of text Ctrl-P insert control or special character Back to main menu, function menu or Derive Basics Expression highlighting commands (Section 3.3): Ctrl-E or Up arrow move up one expression Ctrl-X or Down arrow move down one expression Ctrl-R or PgUp move up one half screen Ctrl-C or PgDn move down one half screen Ctrl-PgUp or Ctrl-Home move up to first expression Ctrl-PgDn or Ctrl-End move down to last expression Ctrl-F or Ctrl--> scroll expression left one half screen Ctrl-A or Ctrl<-- scroll expression right one half screen Sub-expression highlighting commands (Section 3.3): --> move right an operand <-- move left an operand Home move to leftmost operand End move to rightmost operand Ctrl-E or Up arrow move up one level Ctrl-X or Down arrow move down one level
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Function Menu

Greek letters, special constants
Constants
Operators
All Functions
SOLVE
CALCULUS
VECTOR
Programming: ITERATES, IF, etc.



Entering Greek letters, special constants and operators (Section 4.1)

(Note: type English equivalent name or, on PC compatibles only, use Alt key): Alt-A alpha Alt-M mu Alt-B beta Alt-P pi Alt-G GAMMA Alt-S sigma Alt-D delta Alt-T tau Alt-N epsilon Alt-F phi Alt-H theta Alt-O omega Alt-E #e - base of natural logs Alt-I #i - square root of -1 Alt-P pi - area of a unit circle Alt-0 inf - plus infinity Alt - "+-" - plus-or-minus operator Alt-V SUB - subscript operator Alt-Q SQRT - square root operator Alt-G GAMMA - Gamma function Back to main menu, function menu or Derive Basics

Functions, Constants, and Operators

DERIVE can approximate and/or simplify the following functions, constants, and operators. Given numeric arguments in approximate mode, they are numerically approximated to the current precision. Otherwise they are algebraically simplified. Many transformations are applied automatically; some are applied only when requested by a Manage command:

Constants:

#e - base of natural logs (=2.71828...) (Alt-E) #i - square root of -1 (Alt-I) pi - area of unit circle (=3.14159...) (Alt-P) inf - plus infinity (Alt-0) deg - radians per degree (=pi/180) unit_circle - arbitrary point on unit circle euler_gamma := Euler's constant (=0.577215...)

Operators (Section 3.1):

u + v u plus v - u minus u u - v u minus v u * v u times v u v u times v u / v u divided by v u ^ v u raised to v u % u percent u ! u factorial Back to main menu, function menu or Derive Basics Relational operators (Section 4.13): u = v u equals v u /= v u not equal v u < v u less than v u <= v u less than or equal to v u > v u greater than v u >= v u greater than or equal to v Boolean operator and functions (Section 19.5): NOT p true iff p is false p AND q true iff both p and q are true p OR q true iff either p or q is true p XOR q true iff p or q is true but not both p IMP q true iff p is false or q is true If p and q are integers, bit-wise logical operations are performed TRUTH_TABLE (p,q,...,u,v,...) p,q,... are variables and u,v,.. are Booleans

Solving equations and relations (Section 4.14):

SOLVE (u,x) - solve u=0 for x SOLVE (u=v,x) - solve u=v for x SOLVE (u<v,x) - solve u<v for x SOLVE (u=v,x,a,b) - solve u=v for x in [a,b], if in approximate mode SOLVE ([u1=v1,u2=v2,...], [x1,x2,...]) - solve system linear in x1, x2, ... Back to main menu, function menu or Derive Basics Exponential functions (Section 6.1): SQRT (z) - square root of z (or press Alt-Q) EXP (z) - #e raised to the power z Logarithmic functions (Section 6.2): LN (z) - natural log of z LOG (z) - natural log of z LOG (z,w) - log of z to the base w Trigonometric functions (Section 6.3): SIN (z*deg) - sine of z degrees SIN (z) - sine of z radians COS (z) - cosine of z radians TAN (z) - tangent of z radians COT (z) - cotangent of z radians SEC (z) - secant of z radians CSC (z) - cosecant of z radians Inverse trigonometric functions (radians) (Section 6.4): ATAN (z) - angle whose tangent is z ATAN (y,x) - angle of the point (x,y) ACOT (z) - angle whose cotangent is z ACOT (x,y) - angle of the point (x,y) ASIN (z) - angle whose sine is z ACOS (z) - angle whose cosine is z ASEC (z) - angle whose secant is z ACSC (z) - angle whose cosecant is z Back to main menu, function menu or Derive Basics Hyperbolic functions (Section 6.5): SINH (z) - hyperbolic sine of z COSH (z) - hyperbolic cosine of z TANH (z) - hyperbolic tangent of z COTH (z) - hyperbolic cotangent of z SECH (z) - hyperbolic secant of z CSCH (z) - hyperbolic cosecant of z Inverse hyperbolic functions (Section 6.6): ASINH (z) - inverse hyperbolic sine of z ACOSH (z) - inverse hyperbolic cosine of z ATANH (z) - inverse hyperbolic tangent of z ACOTH (z) - inverse hyperbolic cotangent of z ASECH (z) - inverse hyperbolic secant of z ACSCH (z) - inverse hyperbolic cosecant of z Piecewise continuous functions (Section 6.7): ABS (x) - absolute value of x SIGN (x) - sign of x MAX (x, y, ...) - maximum of arguments MIN (x, y, ...) - minimum of arguments STEP (x) - returns 1 if x>0, 0 if x<0 CHI (a, x, b) - returns 1 if a<x<b, 0 if x<a or x>b FLOOR (m, n) - greatest integer <= m/n FLOOR (m) - integer part of m MOD (m, n) - m modulo n (nonnegative remainder of m/n) MOD (m) - fractional part of m MODS (m, n) - symmetric m modulo n Back to main menu, function menu or Derive Basics Complex variable functions (Section 6.8): ABS (z) - magnitude of z SIGN (z) - radial projection of z on unit circle RE (z) - real part of z IM (z) - imaginary part of z CONJ (z) - complex conjugate of z PHASE (z) - phase angle of z Probability functions (Section 6.9): z! - z factorial GAMMA (z) - gamma function of z PERM (z,w) - permutations of z things taken w at a time COMB (z,w) - combinations of z things taken w at a time RANDOM (n) - if n>1, a random INTEGER in the interval [0,n) RANDOM (n) - if n=1, a random NUMBER in the interval [0,1) RANDOM (n) - if n<1, initialize random number seed to n RANDOM (n) - if n=0, initialize seed based on current time Statistical functions (Section 6.10): AVERAGE (z1, ..., zn) - arithmetic mean (average) RMS (z1, ..., zn) - root mean square VAR (z1, ..., zn) - variance STDEV (z1, ..., zn) - standard deviation FIT (v, A) - least squares fit of label vector v to data matrix A Back to main menu, function menu or Derive Basics Error functions (Section 6.11): ERF (z) - error function ERF (z,w) - generalized error function ERFC (z) - complementary error function NORMAL (z,m,s) - normal distribution with mean m and standard deviation s NORMAL (z) - cumulative distribution of z ZETA (s) - the Riemann zeta function of s Financial functions (Section 6.12): PVAL (i, nper, pmt, fval, time) - present value of contract FVAL (i, nper, pmt, pval, time) - future value of contract PMT (i, nper, pval, fval, time) - periodic payment NPER (i, pmt, pval, fval, time) - number of payment periods RATE (nper, pmt, pval, fval, time, min, max) - periodic interest rate Number theory functions (Section 6.13) GCD (m, n, ...) - greatest common divisior of m, n, ... LCM (m, n, ...) - least common multiple of m, n, ... PRIME (n) - true if n is probably prime, false if not PRIME (n,k) - do k iterations of probabilistic primality test before assuming n is prime (default k=5) NEXT_PRIME (n) - next prime larger than n NEXT_PRIME (n,k) - do k iterations of probabilistic primality test before assuming a number is prime (default k=5) Expression decomposition functions (Section 6.14) NUMERATOR (u) - syntactic numerator of u DENOMINATOR (u) - syntactic denominator of u QUOTIENT (u,v) - polynomial quotient of u divided by v REMAINDER (u,v) - polynomial remainder of u divided by v POLY_GCD (u,v) - polynomial gcd of u and v TERMS (u) - vector of syntactic terms of u FACTORS (u) - vector of syntactic factors of u VARIABLES (u) - a vector of the free variables in u LHS (r) - the left (hand) side of relation r RHS (r) - the right (hand) side of relation r Back to main menu, function menu or Derive Basics

Calculus functions

7.1 LIM (u,x,a) - limit of u(x) as x approaches a 7.1 LIM (u,x,a,1) - limit of u(x) as x approaches a from above 7.1 LIM (u,x,a,-1) - limit of u(x) as x approaches a from below 7.2 DIF (u,x) - derivative of u(x) wrt x 7.2 DIF (u,x,n) - nth order derivative of u(x) wrt x 7.3 TAYLOR (u,x,a,n) - nth order Taylor approximation of u(x) about x=a 7.4 INT (u,x) - antiderivative of u(x) wrt x 7.4 DIF (u,x,-n) - nth-order antiderivative of u(x) wrt x 7.4 INT (u,x,a,b) - definite integral of u(x) from x=a to b 7.5 SUM (u,k) - antidifference of u(k) wrt k 7.5 SUM (u,k,m,n) - definite sum of u(k) from k=m to n 7.5 SUM (u,k,v) - sum of u(k) for k an element of vector v 7.5 SUM (v) - sum of the elements of vector v 7.6 PRODUCT (u,k) - antiquotient of u(k) wrt k 7.6 PRODUCT (u,k,m,n) - definite product of u(k) from k=m to n 7.6 PRODUCT (u,k,v) - product of u(k) for k an element of vector v 7.6 PRODUCT (v) - product of the elements of vector v Back to main menu, function menu or Derive Basics

Generating vectors and matrices (Section 8.2) [x1, x2, ..., xn] - n-element vector [[a, b], [c, d]] - 2x2 matrix VECTOR (u,k,n) - vector of u(k) as k goes from 1 thru n in steps of 1 VECTOR (u,k,m,n) - vector of u(k) as k goes from m thru n in steps of 1 VECTOR (u,k,m,n,s) - vector of u(k) as k goes from m thru n in steps of s VECTOR (u,k,v) - vector of u(k) applied to elements of vector v IDENTITY_MATRIX (n) - nxn identity matrix DIMENSION (v) - number of elements of vector v ABS (v) - magnitude (length) of vector v Vector manipulation functions (Section 8.3) v SUB n - nth element of vector v ELEMENT(v,n) - nth element of vector v A SUB j SUB k - element in jth row and kth column of matrix A ELEMENT(A,j,k) - element in jth row and kth column of matrix A APPEND (v,w) - vector of elements of v followed by elements of w DELETE_ELEMENT (v,n) - delete element n from vector v INSERT_ELEMENT (u,v,n) - insert u before the nth element of v REPLACE_ELEMENT (u,v,n) - replace the nth element of v with u REVERSE_VECTOR (v) - reverse elements of vector v SELECT (u,k,m,n,s) - vector of k as k goes from m thru n in steps of s for which u(k)is true SELECT (u,k,v) - vector of those elements of v for which u(k) is true Vector operations (Section 8.4) v . w dot product of vectors v and w (period NOT required if v and w declared Nonscalar) CROSS (v,w) - cross product of vectors v and w Matrix operations 8.4 A.B - dot product of matrices 8.5 A` - transpose of A (On PC-9801 use Yen char) 8.5 DET (A) - determinant of A 8.5 TRACE (A) - trace of A (sum of diagonal elements) 8.5 A^-1 - inverse of A 8.6 ROW_REDUCE (A) - row echelon form of A 8.6 ROW_REDUCE (A, B) - row echelon form of A augmented by B 8.7 CHARPOLY (A, mu) - characteristic polynomial of A, using mu 8.7 EIGENVALUES (A, mu) - eigenvalues of A Back to main menu, function menu or Derive Basics Differential vector calculus (Section 8.9): GRAD (expn) - gradient of expn depending on x, y, and z GRAD (expn,v) - gradient of expn depending on variables in vector v GRAD (expn,A) - gradient of expn in coordinate system A DIV (v,A) - divergence of vector v LAPLACIAN (expn,A) - divergence of the gradient of expn CURL (v,A) - curl of vector v Integral vector calculus (Section 8.10): POTENTIAL (v) - scalar potential of vector v POTENTIAL (v,w) - potential of vector v with starting coordinates w POTENTIAL (v,w,A) - potential of vector v in coordinate system A VECTOR_POTENTIAL(v,w,A) - vector potential of vector v

Programming functions and operators

3.10 APPROX (u) - approximate u using the current digits of precision 3.10 APPROX (u,n) - approximate u using n digits of precision 4.4 EXPAND (u,amount,x,y,...) - expand u(x,y) by amount wrt variables x,y,... 4.6 FACTOR (u,amount,x,y,...) - factor u(x,y) by amount wrt variables x,y,... 4.10 x : domain - declare x an element of domain (Integer, Real, Complex or Nonscalar) 4.10 x : domain interval - declare x an element of domain (Integer or Real) and interval e.g. [-2,10) 4.11 x := u - assign variable x the value u 4.11 x := - make x an arbitrary variable 4.12 f(x,y,...) := u - define function f of variables x,y,... the definition u 4.12 f(x,y,...) := - make f an arbitrary function 10.1 ITERATES (u,x,x0) - returns the vector [x0,u(x0),u(u(x0)),...] until an element is repeated 10.1 ITERATES (u,x,x0,n) - returns the first n+1 elements of the vector [x0,u(x0),u(u(x0)),...] 10.2 ITERATE (u,x,x0) - returns the first repeated element of the sequence x0, u(x0), u(u(x0)), ... 10.2 ITERATE (u,x,x0,n) - returns the n+1th element of the sequence x0, u(x0), u(u(x0)), ... 10.2 ITERATE (u,[x1,x2,...],[x01,x02,...]) - first repeated element of [x01,x02,...],u(x01,x02,...),... 10.3 IF (r) - if relation r is true, return 1; if false return 0 10.3 IF (r,t,f) - if relation r is true, return expression t; if false, return expression f 10.3 IF (r,t,f,u) - if relation r is true, return expression t; if false, return expression f; if truth unknown, return u Back to main menu, function menu or Derive Basics

Algebra Window Command Menu

To issue a menu option command, press Space bar until desired command is highlighted, then press Enter key. Alternatively, type the letter that is capitalized in the desired command. The following gives the section in the DERIVE User Manual that describes each command menu option. 3.1 Author - enter new expression on author line 3.5 Build - combine expressions using operators and functions Calculus 7.2 Differentiate - differentiate an expression 7.4 Integrate - integrate an expression 7.1 Limit - find the limit of an expression 7.6 Product - find the closed-form product of an expression 7.5 Sum - find the closed-form sum of an expression 7.3 Taylor - find Taylor polynomal series approximation 8.2 Vector - generate a vector of values Declare 4.12 Function - define a function and assign it a definition Variable 4.11 Value - declare a variable and assign it a value 4.10 Integer - declare an integer-valued variable 4.10 Real - declare a real-valued variable 4.10 Complex - declare a complex-valued variable 4.10 Nonscalar - declare a variable nonscalar 8.1 Matrix - enter a matrix 8.1 vectoR - enter a vector 4.4 Expand - expand an expression wrt some or all variables 4.6 Factor - factor an expression wrt some or all variables 2.5 Help get on-line help on: 2.4 Editing - line editing commands 6 Functions - pre-defined functions and constants 2.2 Algebra - algebra window commands 5.1 2D-plot - 2D-plot window commands 5.2 3D-plot - 3D-plot window commands 9 Utility - utility file functions 2.14 State - current state of system control variables 2.5 Return - return to DERIVE 3.3 Jump - move highlight to selected expression 4.14 soLve - solve equation, relation, or linear system of equations Manage 3.12 Annotate - annotate an expression 4.5 Branch - select principal, real, or any branch simplification 6.1 Exponential - collect or expand exponentials 6.2 Logarithm - collect or expand logarithms 4.3 Ordering - specify variable ordering 3.7 Renumber - sequentially renumber expressions in algebra window 4.8 Substitute - substitute a value for variables or subexpressions 6.3 Trigonometry - collect or expand trig functions and select angle mode Options Color 2.12 Menu - set menu, message, and status line colors 2.12 Work - set foreground and background colors of expressions 2.12 Display - set graphics or text display mode 2.7 Execute - execute a DOS command 4.1 Input - set variable name, case sensitivity, and arrow key modes 2.3 Mute - turn on or off audible error beeps 3.9 Notation - set notation used to display numbers 3.13 Output - set display format and times operator 3.8 Precision - set precision used for arithmetic operations 3.11 Radix - set input and output radix bases 5.2 Plot - switch to a 2D-plot or 3D-plot window 2.6 Quit - quit DERIVE; return to DOS 3.7 Remove - delete a block of one or more expressions 3.2 Simplify - simplify an expression or subexpression Back to main menu, function menu or Derive Basics Transfer Load 2.9 Derive - load expressions from MTH file 2.14 State - load control settings from INI file 2.9 daTa - load numeric data arrays from DAT file 2.9 Utility - load, but do not display, definitions from MTH file Save 2.8 Derive - save expressions in MTH file 2.8 Basic - save expressions in BAS file 2.8 C - save expressions in a C file 2.8 Fortran - save expressions in FOR file 2.8 Pascal - save expressions in PAS file 2.8 Options - select save range, file linelength, and annotation saving 2.14 State - save current control settings in INI file 2.9 Merge - merge expressions from MTH file 2.9 Clear - clear all expressions from algebra window 2.9 Demo - run demonstration (DMO) file Print Expressions 2.10 Printer - print expressions in algebra window 2.10 File - send text image of expressions to an ASCII file 2.10 Options - select print range, annotation, and character set Screen 2.11 Printer - print screen image (= Shift-F10 or Shift-F9) 2.11 File - save screen image in TIF file (= Ctrl-F10 or Ctrl-F9) 2.11 Options - select print region, positioning, TIF file name 2.10 Layout - set page size and margins 2.10 Options - select printer type, font size, orientation, paper size 3.7 Unremove - recover last removed expressions 3.6 moVe - move a block of one or more expressions Window 2.13 Close - close a window 2.13 Designate - redesignate active window 2.13 Flip - flip overlaid windows (= F2 key) 2.13 Goto - go to given window 2.13 Next - go to next window (= F1 key) 2.13 Open - open new window 2.13 Previous - go to previous window (= Shift-F1) Split 2.13 Horizontal - split active window horizontally 2.13 Vertical - split active window vertically 3.10 approX - approximate an expression or subexpression Back to main menu, function menu or Derive Basics Algebra window function key commands: F1 - go to next window F2 - flip overlaid windows F5 - switch to previous display mode Shift-F10 - print entire screen (not available on PC-9801) Shift-F9 - print current window (not available on PC-9801) Ctrl-F10 - send entire screen to TIF file Ctrl-F9 - send current window to TIF file

2D-plot Window Command Menu

To issue a menu option command, press Space bar until desired command is highlighted, then press Enter key. Alternatively, type the letter that is capitalized in desired command. The following gives the section in the DERIVE User Manual that describes each 2D-plot window's command menu option. 5.1.4 Algebra - switch to an algebra window 5.1.3 Center - center window on the cross Delete delete from plot list: 5.1.4 All - all expressions 5.1.4 Butlast - all but the last expression 5.1.4 First - first expression 5.1.4 Last - last expression 2.5 Help - (same as algebra window's Help command) 5.1.1 Move - move cross to the specified coordinates Options 5.1.5 Accuracy - set plot accuracy Color 5.1.2 Auto - turn off auto color change 5.1.2 Plot - set plot and axes colors 2.12 Menu - set menu, message, and status line colors 2.12 Work - set plot area background color 2.12 Display - set graphics or text display mode 2.7 Execute - execute a DOS command 2.3 Mute - turn on or off audible error beeps 3.9 Notation - set notation used to display numbers 3.8 Precision - set precision used for arithmetic operations 3.11 Radix - set input and output radix bases 5.1.6 State - select coordinates, follow mode, trace mode, and point size 5.1.1 Plot - plot highlighted expression 2.6 Quit - quit DERIVE; return to DOS 5.1.3 Range - set plot range (field of view) 5.1.3 Scale - set plot scale Transfer Load 2.14 State - load control settings from INI file Save 2.14 State - save current control settings in INI file Print Screen 2.11 Printer - print screen image (= Shift-F10 or Shift-F9) 2.11 File - save screen image in TIF file (= Ctrl-F10 or Ctrl-F9) 2.11 Options - select print region, positioning, and TIF file name 2.10 Layout - set page size and margins 2.10 Options - select printer, font size, orientation, paper size 2.13 Window - (same as Window command of algebra window) 5.1.2 aXes - set aspect ratio, and axes titles and labels 5.1.3 Zoom - zoom (adjust) plot scale in or out Back to main menu, function menu or Derive Basics

2D-plot window function key commands:

F1 - go to next window F2 - flip overlaid windows F3 - toggle trace mode F5 - switch to previous display mode F7 - zoom y-axis in F8 - zoom y-axis out Shift-F7 - zoom x-axis in Shift-F8 - zoom x-axis out F9 - zoom both axes in F10 - zoom both axes out Shift-F10 - print entire screen (not available on PC-9801) Shift-F9 - print current window (not available on PC-9801) Ctrl-F10 - send entire screen to TIF file Ctrl-F9 - send current window to TIF file Back to main menu, function menu or Derive Basics

3D-plot Window Command Menu

To issue a menu option command, press Space bar until desired command is highlighted, then press Enter key. Alternatively, type the letter that is capitalized in desired command. The following gives the section in the DERIVE User Manual that describes each 3D-plot window's command menu option. 5.2.4 Algebra - switch to algebra window 5.2.2 Center - set coordinates of box center 5.2.3 Eye - set coordinates of viewer's eye 5.2.3 Focal - set coordinates of focal point 5.2.1 Grids - set number of grid panels 5.2.1 Hide - control display of hidden lines 5.2.2 Length - set lengths of sides of transparent box Options Color 5.2.1 Plot - set top, bottom, and axes colors 2.12 Menu - set menu, message, and status line colors 2.12 Work - set background color of plot area 2.12 Display - set graphics or text display mode 2.7 Execute - execute a DOS command 2.3 Mute - turn on or off audible error beeps 3.9 Notation - set notation used to display numbers 3.8 Precision - set precision used for arithmetic operations 3.11 Radix - set input and output radix bases 5.2.1 Plot - plot highlighted expression 2.6 Quit - quit DERIVE; return to DOS Transfer Acrospin 5.2.4 Run - run AcroSpin with an existing ACD data file 5.2.4 Save - save 3D plot points in an ACD data file Load 2.14 State - load control settings from INI file Save 2.14 State - save current control settings in INI file Print Screen 2.11 Printer - print screen image (= Shift-F10 or Shift-F9) 2.11 File - save screen image in TIF file (= Ctrl-F10 or Ctrl-F9) 2.11 Options - select print region, positioning, and TIF file name 2.10 Layout - set page size and margins 2.10 Options - select printer, font size, orientation, paper size 2.13 Window - (same as Window command of algebra window) 5.2.1 aXes - control axes display 5.2.2 Zoom - zoom box side lengths in or out Back to main menu, function menu or Derive Basics 3D-plot window function key commands: F1 - go to next window F2 - flip overlaid windows F5 - switch to previous display mode F7 - zoom y-axis in F8 - zoom y-axis out Shift-F7 - zoom x-axis in Shift-F8 - zoom x-axis out F9 - zoom both axes in F10 - zoom both axes out Shift-F10 - print entire screen (not available on PC-9801) Shift-F9 - print current window (not available on PC-9801) Ctrl-F10 - send entire screen to TIF file Ctrl-F9 - send current window to TIF file Back to main menu, function menu or Derive Basics

Utility File Functions (Chapter 9)

9.1 SOLVE.MTH - Solving Nonlinear Systems: Simplify using approX command. Use complex x0 for complex solutions. NEWTONS(u,x,x0,n) := n iterations of Newton's method for vector u(x)=0 FIXED_POINT(g,x,x0,n) := n iterations of vector x=g(x), starting at x=x0 TAYLOR_SOLVE(u,x,y,x0,y0,n) := nth order series solution y(x) of u(x,y)=0 TAYLOR_INVERSE(u,x,y,x0,n) := nth order series expansion of inverse of y=u(x) 9.2 VECTOR.MTH - Additional Vector and Matrix Functions. If v and w are vectors, and A and B are matrices: i_ := [1, 0, 0]: unit vector for x-axis j_ := [0, 1, 0]: unit vector for y-axis k_ := [0, 0, 1]: unit vector for z-axis OUTER (v,w) := outer product of v and w KRONECKER (i,j) := Kronecker delta function ADJOIN_ELEMENT (e,v) := adjoin e to front of v APPEND_COLUMNS (A,B) := append columns of A and B MINOR (A,i,j) := delete row i and column j from A SWAP_ELEMENTS (v,i,j) := interchange elements i and j of v SCALE_ELEMENT (v,i,s) := multiply element i of v by s SUBTRACT_ELEMENTS (v,i,j,s) := subtract element j*s from element i of v FORCE0 (A,i,j,p) := force element i,j of A to 0 using pivot row p PIVOT (A,i,j) := force column j below row i to 0 by pivoting MATPROD (A,B,i,j) := element i,j of the dot product of A and B COFACTOR (A,i,j) := numerator of element i,j of A inverse ADJOINT (A) := adjoint of square matrix A RANK (A) := rank of matrix A EXACT_EIGENVECTOR (A,mu) := eigenvector of A < 4x4 for eigenvalue mu APPROX_EIGENVECTOR (A,mu) := approximate eigenvector of A: Use approX command JACOBIAN (u,v) := Jacobian for vector x=u(c), curvilinear coord c and Cart. x COVARIANT_METRIC_TENSOR (A) := covariant metric tensor of Jacobian matrix A GEOMETRY_MATRIX (c,G) := geometry matrix of curv coord c and metric tensor G cylindrical := geometry matrix for cylindrical coordinates r,theta, z spherical := geometry matrix for spherical coordinates r, theta, phi Back to main menu, function menu or Derive Basics 9.3 NUMERIC.MTH - Numeric Differentiation and Integration: Use approX command. DIF_NUM (y,x,x0,h) := 1st derivative of y wrt x at x0 using step size h DIF2_NUM (y,x,x0,h) := 2nd derivative of y wrt x SMOOTH_VECTOR (v) := smoothed copy of vector v SMOOTH_COLUMN (A,j) := matrix A with column j smoothed DIF_DATA (A) := 1st derivative of 2-column numeric data matrix A DIF2_DATA (A) := 2nd derivative of A INT_DATA (A) := antiderivative of A 9.4 DIF_APPS.MTH - Applications of Differentiation CURVATURE (y,x) := curvature of y(x) CENTER_OF_CURVATURE (y,x) := center of curvature of y(x) TANGENT (y,x,x0) := line tangent to y(x) at x=x0 PERPENDICULAR (y,x,x0) := line perpendicular to y(x) at x=x0 OSCULATING_CIRCLE (y,x,theta) := circle osculating y(x), in terms of theta PARA_DIF (v,t,n) := nth derivative of v wrt t, where v=[x(t),y(t)] PARA_CURVATURE (v,t) := curvature of v PARA_CENTER_OF_CURVATURE (v,t) := center of curvature of v PARA_TANGENT (v,t,t0,x) := line tangent to v at t=t0, in terms of x PARA_PERPENDICULAR (v,t,t0,x) := line perpendicular to v at t=t0 PARA_OSCULATING_CIRCLE (v,t,t0,phi) := circle osculating v, in terms of phi POLAR_DIF (r,theta,n) := nth derivative of r(theta), in terms of theta POLAR_CURVATURE (r,theta) := curvature of r POLAR_CENTER_OF_CURVATURE (r,theta) := center of curvature of r POLAR_TANGENT(r,theta,theta0,x):=line tangent to r at theta=theta0 in terms of x POLAR_PERPENDICULAR(r,theta,theta0,x):=line perpendicular to r at theta=theta0 POLAR_OSCULATING_CIRCLE(r,theta,theta0,phi):=osculating circle in terms of phi IMP_DIF (u,x,y,n) := implicit derivative DIF(y,x,n) for u(x,y)=0 IMP_CURVATURE (u,x,y) := curvature of implicit curve u=0 IMP_CENTER_OF_CURVATURE (u,x,y) := center of curvature of u=0 IMP_TANGENT (u,x,y,x0,y0) := line tangent to u=0 at x=x0 and y=y0 IMP_PERPENDICULAR (u,x,y,x0,y0) := line perpendicular to u=0 at x0 and y0 IMP_OSCULATING_CIRCLE (u,x,y,x0,y0,phi) := osculating circle in terms of phi TANGENT_PLANE (u,v,v0) := plane tangent to u(x,y,z)=0 at [x,y,z]=v=v0 NORMAL_LINE (u,v,v0,t) := line normal to u=0 at v=v0, using parameter t 9.5 INT_APPS.MTH - Applications of Integration FOURIER (y,t,t1,t2,n) := nth-harmonic Fourier series of y(t) from t=t1 to t2 LAPLACE (y,t,s) := Laplace transform of y(t) for transform domain variable s. s must be declared sufficiently large for the integral to converge. To find the inverse Laplace transform, use the Expand command to find the partial fraction expansion, then lookup the inverse in a table. ARC_LENGTH (y,x,x1,x2) := arc length of y(x) from x=x1 to x2 ARC_LENGTH (y,x,x1,x2,mu) := integral of mu(x) along arc y(x) from x=x1 to x2 POLAR_ARC_LENGTH (r,th,th1,th2) := arc length of polar r(th) from th1 to th2 POLAR_ARC_LENGTH (r,th,th1,th2,mu) := integral of mu(th) along arc r PARA_ARC_LENGTH (v,t,t1,t2) := arc length of vector v(t) from t=t1 to t2 PARA_ARC_LENGTH (v,t,t1,t2,mu) := integral of mu(t) along v AREA (x,x1,x2,y,y1,y2) := area of region x=x1 to x2 and y=y1(x) to y2(x) AREA (x,x1,x2,y,y1,y2,mu) := integral of mu(x,y) over region AREA_CENTROID (x,x1,x2,y,y1,y2) := areal centroid of region AREA_CENTROID (x,x1,x2,y,y1,y2,mu) := centroid of density mu(x,y) over region AREA_INERTIA (x,x1,x2,y,y1,y2) := areal inertia tensor of region AREA_INERTIA (x,x1,x2,y,y1,y2,mu) := inertia tensor of density mu(x,y) POLAR_AREA (r,r1,r2,th,th1,th2) := area of th=th1 to th2 and r=r1(th) to r2(th) POLAR_AREA (r,r1,r2,th,th1,th2,mu) := integral of mu(th) over region SURFACE_AREA (z,x,x1,x2,y,y1,y2) := area of surface z(x,y) SURFACE_AREA (z,x,x1,x2,y,y1,y2,mu) := integral of mu(x,y) over surface z VOLUME(x,x1,x2,y,y1,y2,z,z1,z2):=volume y=y1(x) to y2(x), z=z1(x,y) to z2(x,y) VOLUME (x,x1,x2,y,y1,y2,z,z1,z2,mu) := integral of mu(x,y,z) over region VOLUME_CENTROID (x,x1,x2,y,y1,y2,z,z1,z2) := volumetric centroid of region VOLUME_CENTROID (x,x1,x2,y,y1,y2,z,z1,z2,mu) := centroid of density mu(x,y,z) VOLUME_INERTIA (x,x1,x2,y,y1,y2,z,z1,z2) := volumetric inertia tensor VOLUME_INERTIA (x,x1,x2,y,y1,y2,z,z1,z2,mu) := inertia tensor of mu(x,y,z) SPHERICAL_VOLUME(r,r1,r2,th,th1,th2,phi,phi1,phi2):=volume in spherical coord. r=r1 to r2, th=th1(r) to th2(r), phi=phi1(r,th) to phi2(r,th) SPHERICAL_VOLUME (r,r1,r2,th,th1,th2,phi,phi1,phi2,mu) := integral of mu CYLINDRICAL_VOLUME(r,r1,r2,th,th1,th2,z,z1,z2) := volume in ylindrical coord. z=z1 to z2, th=th1(z) to th2(z), r=r1(th,z) to r2(th,z) CYLINDRICAL_VOLUME (r,r1,r2,th,th1,th2,z,z1,z2,mu) := integral of mu VOLUME_OF_REVOLUTION (y,x,x1,x2) := volume of y(x) revolved about x-axis AREA_OF_REVOLUTION (y,x,x1,x2) := area of y(x) revolved about x-axis VOLUMEY_OF_REVOLUTION (y,x,x1,x2) := volume of y(x) revolved about y-axis AREAY_OF_REVOLUTION (y,x,x1,x2) := area of y(x) revolved about y-axis Back to main menu, function menu or Derive Basics 9.6 ODE1.MTH - First Order Ordinary Differential Equations (Elementary Methods) Specific solution for the initial condition y=y0 at x=x0: DSOLVE1 (p,q,x,y,x0,y0) := solves p(x,y)+q(x,y)y'=0 SEPARABLE (p,q,x,y,x0,y0) := solves y'=p(x)q(y) LINEAR1 (p,q,x,y,x0,y0) := solves y'+p(x)y=q(x) HOMOGENEOUS (r,x,y,x0,y0) := solves y'=r(x,y) if r is homogeneous EXACT (p,q,x,y,x0,y0) := solves p(x,y)+q(x,y)y'=0 if it is exact INTEGRATING_FACTOR (p,q,x,y,x0,y0) := solves p(x,y)+q(x,y)y'=0 if integrating factor exists General solution in terms of the constant c: DSOLVE1_GEN (p,q,x,y,c) := solves p(x,y)+q(x,y)y'=0 SEPARABLE_GEN (p,q,x,y,c) := solves y'=p(x)q(y) LINEAR1_GEN (p,q,x,y,c) := solves y'+p(x)y=q(x) HOMOGENEOUS_GEN (r,x,y,c) := solves y'=r(x,y) if r is homogeneous EXACT_GEN (p,q,x,y,c) := solves p(x,y)+q(x,y)y'=0 if it is exact INTEGRATING_FACTOR_GEN (p,q,x,y,c) := solves p(x,y)+q(x,y)y'=0 if integrating factor exists 9.6 ODE1.MTH - First Order Ordinary Differential Equations (Advanced Methods) MONOMIAL_TEST (p,q,x,y) := integrating factor of p(x,y)+q(x,y)y'=0 if of the form x^m*y^n Specific solution for the initial condition y=y0 at x=x0: BERNOULLI (p,q,k,x,y,x0,y0) := solves y'+p(x)y=q(x)y^k GEN_HOM (r,x,y,x0,y0) := solves y'=r(x,y) if r is generalized homogeneous FUN_LIN_CCF (r,p,q,k,x,y,x0,y0) := solves y'=r(p*x+q*y+k) if p,q,k constant LIN_FRAC (r,a,b,c,p,q,k,x,y,x0,y0) := solves y'=r((ax+by+c)/(px+qy+k)) ALMOST_LIN (r,b,p,q,x,y,x0,y0) := solves r(x,y)y'+p(x)b(y)=q(x) if almost linear General solution in terms of the constant c: BERNOULLI_GEN (p,q,k,x,y,c) := solves y'+p(x)y=q(x)y^k GEN_HOM_GEN (r,x,y,c) := solves y'=r(x,y) if r is generalized omogeneous FUN_LIN_CCF_GEN (r,p,q,k,x,y,c) := solves y'=r(p*x+q*y+k) if p,q,k constant LIN_FRAC_GEN (r,a,b,c,p,q,k,x,y,c) := solves y'=r((ax+by+c)/(px+qy+k)) ALMOST_LIN_GEN (r,b,p,q,x,y,c) := solves r(x,y)y'+p(x)b(y)=q(x) if almost linear CLAIRAUT (p,q,x,y,v,c) := solves p(x*v-y)=q(v) where v represents y' Back to main menu, function menu or Derive Basics 9.7 ODE2.MTH - Second Order Ordinary Differential Equations DSOLVE2 (p,q,r,x,c1,c2) := solves y"+p(x)y'+q(x)y=r(x) DSOLVE2_BV (p,q,r,x,x0,y0,x2,y2) := solves y"+p(x)y'+q(x)y=r(x) DSOLVE2_IV (p,q,r,x,x0,y0,v0) := solves y"+p(x)y'+q(x)y=r(x) AUTONOMOUS_CONSERVATIVE(q,x,y,x0,y0,v0):=solves y"=q(y), y=y0 and y'=v0 at x=x0 LIOUVILLE (p,q,x,y,c1,c2) := solves y"+p(x)y'+q(y)(y')^2=0 AUTONOMOUS (r,v) := dv/dy, given y"=r(y,v), reducing to sequence of 2 1st ord EXACT2 (p,q,x,y,v,c) reduces order of p(x,y,v)y"+q(x,y,v)=0 with v=y' if exact 9.8 ODE_APPR.MTH - Approximate Series Solutions of ODEs Given the equation y'=r(x,y) with y=y0 at x=x0: TAYLOR_ODE1(r,x,y,x0,y0,n) := nth order Taylor series solution PICARD(r,p,x,y,x0,y0) := improved series approximation, given the series p(x) Given m equations yi'=ri(x,y1,...,ym) with yi=yi0 at x=x0: TAYLOR_ODES (r,x,y,x0,y0,n) := vector of nth order Taylor series solutions PICARD(r,p,x,y,x0,y0) := improved series approximation, given the series p(x) Given the equation y''=r(x,y,y') with y=y0 and y'=v=v0 at x=x0: TAYLOR_ODE2(r,x,y,v,x0,y0,v0,n) := nth order Taylor series solution 9.8 ODE_APPR.MTH - Approximate Numerical Solutions of ODEs Given the equation y'=r(x,y) with y=y0 at x=x0: EULER(r,x,y,x0,y0,h,n) := [[x0,y0],...,[xn,yn]] with step size h Given m equations yi'=ri(x,y1,...,ym) with yi=yi0 at x=x0: RK (r,v,v0,h,n) := [[x0, y0(x0), ... ym(x0)], ... [xn, y0(xn), ... ym(xn)]] classic Runge-Kutta with step h. EXTRACT_2_COLUMNS (A,j,k) := columns j and k from A for plots of RK results DIRECTION_FIELD(r,x,x0,xm,m,y,y0,yn,n): grid (x0,y0) to (xm,yn) 9.9 RECUREQN.MTH - Recurrence Equations LIN1_DIFFERENCE (p,q,x,x0,y0) := solves y(x+1)=p(x)y(x)+q(x), y(x0)=y0 RECURRENCE1 (r,x,y,x0,y0,n) := n steps of y(x+1)=r(x,y(x)), y(x0)=y0 GEOMETRIC1 (k,p,q,x,x0,y0) := solves y(k*x)=p(x)y(x)+q(x), y(x0)=y0 CLAIRAUT_DIF (p,q,d,x,y,c) := solves p(y-xd)=q(d), d represents y(x+1)-y(x) LIN2_CCF (p,q,r,x,c1,c2) := solves y(x+2)+p*y(x+1)+q*y(x)=r(x) LIN2_CCF_BV (p,q,r,x,x0,y0,x2,y2) := solves y(x+2)+p*y(x+1)+q*y(x)=r(x) 9.10 APPROX.MTH - Pade Rational Approximation PADE(y,x,x0,n,d):=approx y(x) near x=x0, n=numr deg, d=denr deg, n=d or d-1 Back to main menu, function menu or Derive Basics 9.11 EXP_INT.MTH - Exponential, Log, Sine, and Cosine Integrals: use approX EI(x,m):=m terms of series for exponential integral INT(#e^-t/t,t,-x,inf), x>0 LI(x,m):=m terms of series for logarithmic integral INT(1/LN t,t,0,x), x>1 EN (n,z) := nth exponential integral INT(exp(-zt)/t^n,t,1,inf), RE(z)>0, n>=0 EN_ASYMP (n,z,m) := m+1 terms of asymptotic series for EN(n,z), |z| large E1(z,m) := m terms of series for exponential integral E1(z)=EN(1,z) SI(z) := sine integral INT(SIN(t)/t,t,0,z) CI(z) := cosine integral INT(COS(t)/t,t,0,z), |phase z| < pi 9.12 PROBABIL.MTH - Additional Probability Functions: use approX POCHHAMMER (a,x) := Pochhammer symbol (a)x = GAMMA(a+x)/GAMMA(a) PSI (z) := DIF(GAMMA(z),z)/GAMMA(z), |phase z| < pi/2 POLYGAMMA (n,z,m) := m+1 terms of series for DIF(PSI(z),z,n), z/=0,-1,-2,... INCOMPLETE_GAMMA (z,w) := P(z,w)=INT(#e^-t*t^(z-1),t,0,w)/GAMMA(z), RE(z)>0 INCOMPLETE_GAMMA_SERIES (z,w,m) := m+1 terms of series for above BETA (z,w) := beta function B(z,w)=GAMMA(z)*GAMMA(w)/GAMMA(z+w) INCOMPLETE_BETA (x,z,w) := Bx(z,w) = INT(t^(z-1)*(1-t)^(w-1),t,0,x) POISSON_DENSITY (k,t) := Poisson probability density #e^-t*t^k/k! POISSON_DISTRIBUTION (k,t) := SUM (#e^-t*t^j/j!,j,0,k) BINOMIAL_DENSITY (k,n,p) := COMB(n,k)*p^k*(1-p)^(n-k) BINOMIAL_DISTRIBUTION (k,n,p) := SUM (COMB(n,j)*p^j*(1-p)^(n-j), j, 0, MIN(k,n)) HYPERGEOMETRIC_DENSITY (k,n,m,j) := COMB(m,k)*COMB(j-m,n-k)/COMB(j,n) HYPERGEOMETRIC_DISTRIBUTION (k,n,m,j) := cumulative hypergeometric distribution STUDENT (t,v) := student's cumulative probability distribution A(t|v) F_DISTRIBUTION (f,v1,v2) := the F cumulative distribution P(f|v1,v2) CHI_SQUARE (u,v) := Chi-square distribution P(u|v), u = Chi^2 Back to main menu, function menu or Derive Basics 9.13 FRESNEL.MTH - Fresnel Integrals: use approX FRESNEL_SIN (z) := Fresnel sine integral S(z)=INT(SIN(pi*t^2/2),t,0,z) FRESNEL_SIN_SERIES (z,m) := m+1 terms of series for sine integral FRESNEL_COS (z) := Fresnel cosine integral C(z)=INT(COS(pi*t^2/2),t,0,z) FRESNEL_COS_SERIES (z,m) := m+1 terms of series for cosine integral FRESNEL_SIN_ASYMP (z) := two-term asymptotic series for sine integral FRESNEL_COS_ASYMP (z) := two-term asymptotic series for cosine integral 9.14 BESSEL.MTH - Bessel and Airy Functions: use approX BESSEL_J (n,z) := Bessel function of first kind Jn(z), n numeric BESSEL_J_SERIES (n,z,m) := m+1 terms of series for above BESSEL_J_ASYMP (n,z) := 1 term of asymptotic series for above for large |z| BESSEL_Y (n,z) := Bessel function of second kind Yn(z), n fractional BESSEL_Y_SERIES (n,z,m) := m+1 terms of series for above BESSEL_Y_ASYMP (n,z) := 1 term of asymptotic series for above for large |z| BESSEL_I (n,z) := modified Bessel function of first kind In(z), n numeric BESSEL_I_SERIES (n,z,m) := m+1 terms of series for above BESSEL_I_ASYMP (n,z) := 1 term of asymptotic series for above for large |z| BESSEL_K (n,z) := modified Bessel function of second kind Kn(z), n fractional BESSEL_K_ASYMP (n,z) := 1 term of asymptotic series for above for large |z| SPHERICAL_BESSEL_J(n,z) := closed-form spherical Bessel fcn of 1st kind,jn(z) SPHERICAL_BESSEL_Y(n,z) := closed-form spherical Bessel fcn of 2nd kind,yn(z) AI_SERIES (z,m) := m+1 terms of series for Airy function Ai(z) BI_SERIES (z,m) := m+1 terms of series for Airy function Bi(z) 9.15 HYPERGEO.MTH - Hypergeometric Functions: use approX KUMMER (a,b,z) := Kummer's confluent hypergeometric function M(a,b,z) KUMMER_SERIES (a,b,z,m) := m+1 terms of series for M(a,b,z) HYPERGEOMETRIC (a,b,c,z) := Gauss hypergeometric function F(a,b;c;z) HYPERGEOMETRIC (a,b,c,z,m) := m+1 terms of series for F(a,b;c;z) 9.16 ELLIPTIC.MTH - Elliptic Integrals: use approX ELLIPTIC_F (phi,m) := elliptic integral of 1st kind F(phi\m) ELLIPTIC_E (phi,m) := elliptic integral of 2nd kind E(phi\m) ELLIPTIC_PI (phi,m,n) := elliptic integral of 3rd kind II(n;phi\m) Back to main menu, function menu or Derive Basics 9.17 ORTH_POL.MTH - Orthogonal Polynomials CHEBYCHEV_T (n,x) := nth Chebychev polynomial of 1st kind Tn(x) CHEBYCHEV_U (n,x) := nth Chebychev polynomial of 2nd kind Un(x) LEGENDRE_P (n,x) := nth Legendre polynomial Pn(x) ASSOCIATED_LEGENDRE_P (n,m,x) := nth associated Legendre polynomial Pn^m(x) HERMITE_H (n,x) := nth Hermite polynomial Hn(x) HERMITE_HE (n,x) := nth associated Hermite polynomial HEn(x) WEBER_D (n,x) := Weber's nth parabolic cylinder function Dn(x) GENERALIZED_LAGUERRE(n,a,x):=nth generalized Laguerre polynomial n^a(x). Use a=0 for ordinary Laguerre polynomials JACOBI_P (n,a,b,x) := nth Jacobi polynomial Pn^(a,b)(x) GEGENBAUER_C (n,a,x) := nth Gegenbauer ultraspherical polynomial Cn^a(x) 9.18 ZETA.MTH - Generalized Riemann Zeta Functions HURWITZ_ZETA (s,a,m) := m+1 terms of series for SUM((k+a)^-s,k,0,inf) POLYLOG (n,z,m) := m terms of series for Jonquire's polylogarithm Lin(z) LERCH_PHI (z,s,a,m) := m terms of series for Lerch transcendent Phi(z,s,a) DILOG (x) := dilogarithm function INT(LN(t)/(t-1),t,1,x) 9.19 GRAPHICS.MTH - Plotting Space Curves, Parametric Surfaces and Complex Values Isometric projections for 2D Plot: Use Options State Rectangular Connected axes := 3D coordinate axes ISOMETRIC (v) := matrix for space curve v = [x(t),y(t),z(t)]: Plot ROTATE_X (phi) := matrix A so that A . [x,y,z] rotates angle phi about x axis ROTATE_Y (phi) := matrix A so that A . [x,y,z] rotates angle phi about y axis ROTATE_Z (phi) := matrix A so that A . [x,y,z] rotates angle phi about y axis ISOMETRICS (v,s,s0,sm,m,t,t0,tn,n):=matrix for surface [x(s,t),y(s,t),z(s,t)] s=s0...sm, t=t0...tn: approX then Plot COPROJECTION (A) := convert matrix from lines of constant t to constant s CYLINDER (r,theta,z) := eg. of v for ISOMETRICS (v,theta,...,z,...) SPHERE (r,theta,phi) := eg. of v for ISOMETRICS (v,theta,...,phi,...) TORUS (r,theta,phi) := eg. of v for ISOMETRICS (v,theta,...,phi,...) CONE (phi,theta,z) := eg. of v for ISOMETRICS (v,theta,...,z,...) Back to main menu, function menu or Derive Basics 2D Plots of complex-expression w(z) where z = x + #i y = r #e^(#i theta) Use approX and Options State Rectangular Connected RAYS (w,z,z00,zmn,m,n):= matrix of w vectors for z = x0 + #i y0 ... xm + #i y HORIZONTALS (w,z,z00,zmn,m,n) := w-plane map of rectangular z-plane grid ARCS (w,z,r0,rm,m,th0,thm,n) := w-plane map of polar z-plane grid r=r0...rm, theta=th0...thn 9.20 NUMBER.MTH - Number Theory Functions CEILING (m,n) := smallest integer >= m/n (n defaults to 1) ROUND (m,n) := nearest integer to m/n (n defaults to 1) SQUARE_WAVE (n) := 1 if MOD(n,2)<1, else -1 POWER_MOD (n,d,m) := n^d mod m NTH_PRIME (n) := nth prime number BERNOULLI (n) := nth Bernoulli number CATALAN (n) := nth Catalan number EULER (n) := nth Euler number FIBONACCI (n) := nth Fibonacci number MERSENNE (n) := nth Mersenne prime 9.21 MISC.MTH - Miscellaneous Utility Functions RATIO_TEST (t,n) := if > 1, SUM(t,n,a,inf) converges; < 1, sum diverges LIM2 (u,x,y,x0,y0) := limit of u as [x,y] -> [x0,y0] along slope of @1 LEFT_RIEMANN (u,x,a,b,n) := left Riemann sum for INT(u,x,a,b), n rectangles INT_PARTS (u,v,x) := antiderivative of u(x)*v(x) using integration by parts INT_SUBST (y,x,u) := antiderivative of y(x) by substituting x for u(x) DEF_INT_SUBST (y,x,u,a,b) := integral of y(x) from x=a to b by substitution INVERSE (u,x) := inverse of u(x) with respect to x PROVE_SUM (t,k,a,n,s) := [0,0] if SUM(t,k,a,n)=s POLY_COEFF (u,x,n) := coefficient of x^n term in polynomial u(x) POLY_DEGREE (u,x) := degree of polynomial u(x) random_sign := random 1 or -1 RANDOM_POLY (x,d,s) := poly of degree d in x with random coeffs from -s to s RANDOM_VECTOR (n,s) := n element vector with random elements from -s to s RANDOM_MATRIX (m,n,s) := m by n matrix with random elements from -s to s GOODNESS_OF_FIT (u,x,A) := fit of u(x) to data matrix A POLY_INTERPOLATE (A,x) := polynomial interpolation of data matrix A POLY_INTERPOLATE_EXPRESSION (u,x,a) := polynomial interpolation of u given supporting points vector a Back to main menu, function menu or Derive Basics

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Algebra window numerical settings Precision mode *PRECISION* Precision digits *PRECISION-DIGITS* Notation style *NOTATION* Notation digits *NOTATION-DIGITS* Input radix base *INPUT-BASE* Output radix base *OUTPUT-BASE* Algebra window simplification settings Branch selection *BRANCH* Logarithms *LOG-EXPD* Exponentials *EXP-EXPD* Trig functions *TRIG-EXPD* Trig powers toward *TRIG-POWER* Angle mode *ANGLE-MODE* Algebra author line settings Input mode *INPUT-MODE* Character case mode *CASE-MODE* Arrow key mode *ARROW-KEY-MODE* 2D-plot window settings Auto-scale *AUTO-SCALE* Follow cross *FOLLOW-MODE* Plotting accuracy *PLOT-ACCURACY* Coordinate type *COORDINATE-SYSTEM* Plot points *PLOT-POINTS* Point size *POINT-SIZE* Rows per tick *ROWS/TICK* Columns per tick *COLS/TICK* Auto change color *AUTO-COLOR* Axes color *AXES-COLOR* Cross color *CROSS-COLOR* 3D-plot window settings Top color *TOP-COLOR* Bottom color *BOTTOM-COLOR* Printer page layout Page length *PAGE-LINES* Page width *PAGE-COLUMNS* Top margin *TOP-MARGIN* Bottom margin *BOTTOM-MARGIN* Left margin *LEFT-MARGIN* Right margin *RIGHT-MARGIN* Printer options Print style *PRINT-STYLE* Printer type *PRINTER-TYPE* Print orientation *PRINT-ORIENTATION* Font size *PRINT-SIZE* Paper size *PAPER-SIZE* Print background color *PRINT-BACKGROUND* Window color settings Frame color *FRAME-COLOR* Option color *OPTION-COLOR* Prompt color *PROMPT-COLOR* Status color *STATUS-COLOR* Menu background color *MENU-BACKGROUND* Border color *BORDER-COLOR* Work color *WORK-COLOR* Work background color *WORK-BACKGROUND* Hardware settings Display mode *VIDEO-MODE* Character set *CHARACTER-SET* Memory size *MEMORY-SIZE*  Back to main menu, function menu or Derive Basics