Math 253A-1, Accelerated Calculus III

Final exam is due on Tuesday, May 9 at noon in the envelope stuck to my door at Keller Hall 501.

Click here if you need to download the exam

Instructor -- Pavel Guerzhoy

The class meets Tuesdays and Thursdays 9:00 - 10:15

and Thursdays 10:30 - 11:20

at 401, Keller Hall.


Office: 501, Keller Hall (5-th floor)
e-mail: pavel(at)math(dot)hawaii(dot)edu (usually, I respond to e-mail messages within a day)
Office hours: Tuesdays and Thursdays 12:00-1:00 and by appointment.
Reading
In this class we use the book
  • Calculus Eighth Edition by James Stewart.

    The book is really unavoidable, and cannot be replaced with another calculus textbook!
    Course Objective
    To learn concepts, techniques and applications of differential and integral calculus of two and three variables, culminating with Green's Theorem, Stokes' Theorem and the Divergence Theorem.
    Prerequisites
    Math 252A, AP Calculus BC score of 4 or 5 and consent; or a grade of A in Math 242 and consent.
    Grading Policy
    The course contains a combination of concepts, ideas and techniques. To understand the material means to be able to apply it in solving problems. At the end of the day, your grade will reflect your ability to solve specific differential and integral calculus problems. More specifically, the following rules are to be taken.



  • Final exam is due on Tuesday, May 9 at noon in the envelope stuck to my door.

  • Mid-term test, which covers the material of Chapters 12,13, and 14 from the book counts for 30% of the final grade. The date of the midterm will be announced a week in advanced in class.

    The midterm takes place on Thursday, March 2 at 9am in class.

    Review for the Mid-term test
    Sections 12.1 through 12.4 are preparatory for further material.
    While no problem on the midterm is close to the exercises from these Sections,
    the midterm problems assume thorough knowledge and ability to easily apply the notions and technics introduced in these Sections.
    In particular, it is recommended to pay attention at the following exercises: 
    12.3:   31,32, 54-56
12.4:   29-32, 38
    Section 12.5 applies all the knowledge acquired in previous sections for analyzing the equations of lines and planes.
    Questions related to this material will certainly show up on the exam.
    The students must have a level of fluency in solving these problems.
    The plethora of formulas given in this Section are not subject to memorization, but understanding understanding the underlying ideas and ability to apply these ideas in various situations.
    Specifically, the following exercises are recommended to check the level of preparedness. 
    12.5:  19 - 74
    Section 13.1 is preparatory. From Section 13.2, the following exercises are recommended for review: 
    13.2: 23 - 28
    Everything in Section 13.3 depends on the specific formulas for the arc length, curvature, normal and binormal vector.
    Plugging numbers into formulas is not a skill to acquire in this class.
    The specific formulas are not subject to memorize.
    No problems related to this Section are on the test.

    In Section 13.4, the knowledge about the parametric equations and geometry of space curves is applied to problems related to a moving particle.
    That may be a projectile fired from a cannon, a ball thrown manually, or a planet of the Solar system.
    It is recommended to pay special attention at Example 5 on pp 912-913 from the textbook, and exercise 26 to this Section. 
    13.4: 26
    Section 14.1 is preparatory.
    Section 14.2 contains the important notions of limits and continuity for functions in several variables.
    Specifically, you have to be able to either to justify your claim that either a limit equals a certain quantity or does not exist.
    The following exercises are recommended for review 
    14.2: 5-24, 39-42
    The exam will contain no questions close to the exercises from Section 14.3, 14.4, and 14.5.
    It is assumed that the students understand the material from these Sections well enough for the applications in further Sections.
    The notions of gradient and directional derivatives are introduced in Section 14.6, and the following exercises are recommended for the review 
    14.6: 11-17,21-29,41-46
    In Section 14.7, the technics developed in the previous Sections is applied to solving optimization problems.
    It is recommended to pay special attention to the following exercises.
    Some of these exercises may well be approached with Lagrange multipliers method from Section 14.8.
    Either solution, as soon as it is correct, is acceptable. 
    14.7: 41-50




  • Quizzes will be given approximately biweekly, and the average grade for the quizzes counts for 30% of the final grade.

    The following are not part of the grading scheme:



    Contents


    and Homework assignments
    Only odd-numbered exercises from the lists are assigned; these exercises are supplied with answers in the book.     


     

     CHAPTER 12   Vectors and the geometry of space    
     
 12.1:  1-42 
 12.2:  1-43
 12.3:  1-47
 12.4:  1-37
 12.5:  1-39,45-61
 12.6:  1-28



     CHAPTER 13    Vector functions  
    
 13.1:  1-5,17,19,21-26,27-31,43,45
 13.2:  1-27, 35-41
 12.3:  1-6,11-33,39
 13.4:  1-16,19,23-31



     CHAPTER 14     Partial derivatives  
    
 14.1:   9-21,37,45-51
 14.2:   5-21,25,29-41
 14.3:   15-43,47-57
 14.4:   1-6,11-19,21-31
 14.5:   1-11,21-33,49,55-57
 14.6:   1-25,29,41-45,49-59,63
 14.7:   1-19,31-37,41-55
 14.8:   3-13



     CHAPTER 15 Multiple integrals  
    
 15.1:  15-34,37-43,47-50
 15.2:  13-32,35-38,49-56,59-62,65-69
 15.3:  7-27,29-32,41
 15.4:  1-15
 15.6:  1-22,29-38
 15.7:  1-12,17-25
 15.8:  5-10,15,19-30,35-38,41-43
 15.9:  1-19,21a


     CHAPTER 16 Vector calculus  
    
 16.1:  11-18, 21-25,29-32
 16.2:  1-22
 16.3:  1-26,28-35
 16.4:  1-14,17-19
 16.5:  1-22
 16.6:  1-6,13-26,33-50
 16.7:  1-32
 16.8:  1-10,16-20
 16.9:  1-14,17-20

    Homework, Class and Quizzes Structure