Karl Heinz Dovermann,   Professor

Research Papers

Calculus without Limits (Lecture Notes for Applied Calculus)

Vectors and Plane Geometry (Lecture Notes for the first week in Math 241 or 251A)

Calculus Lecture Notes for Math 161

Common Math 241 Final Exams and Practice Materials

Office Phone Email
Keller Hall 405
(808) 956-4654 heiner@math.hawaii.edu
 
Fall 2019
Course title Course number Room Hours
Introduction to Linear Algebra Math 311 Kel 313 MWF 11:30 -- 12:20
Introduction to Topology Math 421 Kel 301 MWF 9:30 -- 10:20
Transformation Groups Math 649 PSB 317 TR 9:00 -- 10:20
Office hours
M--F 10:30 -- 11:20
and by appointment



Announcement for Math 307 (Summer 2019):

  • Syllabus for Math 307
  • Look up your grades for Summer 2019: (Use your student ID#)
  • First Math 307 midterm (Summer 2019)
  • Second Math 307 midterm (Summer 2019)
  • First Math 307 midterm (Fall 2018)
  • Second Math 307 midterm (Fall 2018)
  • Math 307 Final (Fall 2018)
  • First Math 307 midterm (Summer 2018)
  • Second Math 307 midterm (Summer 2018)
  • Math 307 final (Summer 2018)
  • A first Math 307 midterm (Spring 2015)
  • A second Math 307 midterm (Spring 2015)
  • Math 307 final (Spring 2015)
  • A first Math 307 midterm (Fall 2012)
  • A second Math 307 midterm (Fall 2012)
  • Math 307 Final (Fall 2012)
  • A first Math 307 midterm (Fall 2011)
  • A final for Math 307
  • A final for Math 307 with solutions
  • Announcement for Math 311 (Fall 2019):

  • Syllabus for Math 311
  • Look up your grades for Fall 2019: (Use your student ID#)
  • HW1, due Wednesday, August 28th: p. 18f, CE 2, 4 and WE 3.
  • HW2, due Friday, August 30th: p. 37f, CE 2, 4 and WE 2.
  • HW3, due Wednesday, September 4th: p. 37f, CE 3, 5 and WE 4.
  • HW4, due Friday, September 6th.
  • HW5, due Monday, September 9th.
  • HW6, due Wednesday, September 11th.
  • HW7, due Friday, September 13th: p. 49, CE 2, 3 and WE 2.
  • HW8, due Monday, September 16th: p. 49, CE 5 and WE 5, 7.
  • HW9, due Wednesday, September 18th: p. 64, CE 1 (a, b, c, f), 2 (a, b), WE 1, 2.
  • HW10, due Friday, September 20th: p. 64, CE 5, 6, WE 3, 5.
  • HW11, due Wednesday, September 25th: p. 64, CE 1(d, e), 2c. Let P_3 be the vector space of polynomials of degree at most 3. Let D:P_3 -> P_3 be differentiation. As basis of P_3 (domain and codomain) use {x-1, x^2-2x, x^3+5, 1+x+x^2+x^3}. Find the matrix of D with respect to these basis.
  • HW12, due Friday (make it Monday), September 27th: p. 77, CE 1, 3, WE 1, 2.
  • HW13, due Monday, October 7th: p. 77, CE 5 a, c, WE 8, 9, 11.
  • HW14, due Friday, October 10th: p. 93, CE 1, 3, 6.
  • HW15, due Monday, October 14th: p. 93, CE 4, WE 3, 4.
  • HW16, due Wednesday, October 16th: Compute Vandermond's determinant (any size).
  • HW17, due Friday, October 18th: Find eigen values and eigen vectors for the matrices (1,-1,1;0,2,5;0,0,3), (2,-8,0;0,2,0;-10,-16,3), (2,7,42;0,-3,-30;0,1,8). Entries in a row are separated by commata, rows by semicola.
  • HW18, due Friday, October 25th: Compute the inner product for any pair (f,g) of functions in the set {1, sin(nx), cos(nx)}. The inner product is the intergral of the product of the functions for x in [-pi,pi].
  • HW19, due Monday, October 28th: p. 108, WE 3,4.
  • HW20, due Friday, November 1st: Consider the vector space of polynomials with the inner product (f,g) = \int_0^1 x f(x) g(x) dx. Orthonormalize the set {1, x, x^2}.
  • First Math 311 midterm (Summer 2019)
  • First Math 311 midterm (Summer 2019)
  • Second Math 311 midterm (Summer 2019)
  • Exam I (Fall 2016) with solutions.
  • Exam II (Fall 2016) with solutions.
  • Final (Fall 2016) with solutions.
  • First Math 311 exam with solution (Summer 2016).
  • Second Math 311 exam with solution (Summer 2016).
  • First Math 311 exam with solution (Spring 2016).
  • Second Math 311 exam with solution (Sping 2016).
  • Final for Math 311 (Spring 2016)
  • First exam for Math 311 (Spring 2012)
  • First exam for Math 311 with solutions (Spring 2012)
  • A second exam for Math 311 with solutions (Spring 2012)
  • Another second exam for Math 311
  • A final for Math 311 (Spring 2007)
  • Another final for Math 311 (Spring 2012)
  • Announcement for Math 421 (Fall 2019):