Math 20C: Multivariable Calculus, Fall 09, (Jacob Sterbenz)

Meetings  Text  Overview  Exams  Review  Practice Exams  Syllabus  Schedule  Homeworks  Grading
ANNOUNCEMENTS:


Meetings



Text

The book store bundles the text with a study guide. Follow the link above for more study material.

Overview

This is a first course in multivariable calculus which builds on your basic knowledge of one variable calculus. We will start with a discussion of multidimensional vector spaces, the multivariable analog of the (x,y) plane. We then move on to the study of vector-valued functions and real valued functions of several variables. With this background, we go on to introduce the fundamental concepts of differentiation and integration in a multivariable setting. Our focus throughout will be on concrete calculations as opposed to proofs, and on applications of the material to problems in the social and physical sciences.

Exams

Please bring identification to the exams. There will be no books or personal notes allowed during exams. However, you may bring these sheets: fact-sheet 1, fact-sheet 2, and fact-sheet 3 to the exams. In general there are no make-up exams.

The exams may have questions about anything covered in homework assignments due before the exams, as well as lectures or assigned reading. Further information about the exams will be given in the lectures.



Review for the exams.


Practice Exams and Solutions to some of the exams.

mid1f02mid1s02mid1w02mid1w01,   mid2f02mid2s02mid2w96,   finf02fins02afinw02a,  
mid1f02smid1s02smid1w02smid1w01s,   mid2f02smid2s02smid2w96s,   finf02sfinw02as,  
mid1s08mid2s08,   fins08

Note: Some are for a slightly different text and syllabus.

A Brief Syllabus

Basically, our goal is to cover Chs. 11-15 of the text. In particular we will discuss (at least) the following:

12.1-2 Vectors.
12.3 Dot product.
12.4 Cross product.
12.5 Planes in 3D.

11.1 & 13.1: Parametric equations & Vector-valued functions.
13.2: Calculus of vector-valued functions.
11.2 & 13.3: Arclength and speed.
13.5: Motion in three-space.

14.1: Functions of two or more variables.
14.2: Limits and continuity in several variables.
14.3: Partial derivatives.
14.4: Differentiability, linear approximation and tangent plane.
14.5: The gradient and directional derivatives.
14.6: The chain rule.
14.7: Optimization in several variables.
14.8: Lagrange multipliers.

15.1: Integration in several variables.
15.2: Double integrals.
15.3: Triple integrals.
12.7: Cylindrical and spherical coordinates.
15.4: Integration in polar, cylindrical and spherical coordinates.

Schedule of Lectures (tentative).

It is important that you have a look at the material before it is covered in the lectures.

 Week  Date (Monday)  Monday  Wednesday  Friday
  0  9/21       12.1
  1  9/28   12.2  12.3   12.4
  2  10/5   12.5   11.1, 13.1   13.2
  3  10/12   11.2, 13.3   13.5   Review
  4  10/19  Exam 1   14.1  14.2    (W drop)
  5  10/26   14.3   14.4   14.5
  6  11/2   14.6   14.7   14.7, 14.8
  7  11/9   14.8   Holiday   Exam 2
  8  11/16   15.1   15.1   15.2
  9  11/23   15.3   12.7   Holiday
  10  11/30  15.4     (F drop)  15.4  Review
  11   12/07       Final: 3:00p - 5:59p in TBA

  • For old lecture notes on a similar course, go here.


  • Homework Assignments:

    Homeworks are due to the TA's box on the 6th floor of AP&M at 4p on Wednesdays. Please write your name and section number on each page. Late homeworks will not be accepted.

    All homeworks problems be handed in, but we do not have resources to grade them all. Therefore, a select number of problems from each set will be graded randomly. However, you will also be graded for attempting each problem.

    HW #1: Due 9/30.   
       12.1: 8, 26, 28, 38, 40, 42, 56, 58.
       12.2: 14, 24, 28, 36, 42, 50.

    HW #2: Due 10/7.   
       12.3: 14, 28, 44, 48, 52, 54, 60, 70.
       12.4: 4, 6, 14, 20, 32, 34, 42, 48.
       12.5: 22, 24, 26, 30, 46, 54, 60.

    HW #3: Due 10/14.   
       11.1: 12, 14, 26, 38.
       13.1: 6, 18, 26, 32.
       11.2: 12, 18, 20.
       13.2: 10, 12, 20, 22, 26, 28, 32, 40, 45, 50.
       13.3: 6, 10, 18.

    HW #4: Due 10/21.   
       13.5: 5, 12, 16, 20, 26.

    HW #5: Due 10/28.   
       14.1: 8, 16, 18, 20, 24, 28, 32, 44.
       14.2: 4, 8, 14, 16, 18, 26.
       14.3: 4, 8, 30, 34, 40, 44, 46, 48, 56, 58, 59, 74, 76.

    HW #6: Due 11/04.   
       14.4: 4, 6, 10, 14, 18, 20, 22.
       14.5: 2, 4, 22, 24, 28, 30, 38, 40, 42, 50, 60.
       14.6: 2, 4, 10, 12, 16, 28, 30.

    HW #7: Due 11/12.   
       14.7: 2, 8, 14, 20, 24, 38, 40.
       14.8: 2, 4, 8, 12, 16, 26, 30.

    HW #6: Due 11/25.   
       15.1: 2, 10, 16, 18, 26, 30, 36, 38, 42, 44.
       15.2: 1, 4, 8, 10, 12, 18, 24, 30, 38, 42, 52, 58, 64.
       15.3: 6, 10, 14, 16, 18, 24, 26.



    Grading

    Your grade will be calculated as follows: At the end of the course, there will be a curve. I will also attempt to give you a clear indication as to where you stand gradewise after each midterm.