Math 5B - Vector Calculus I - Fall 2006

Instructor: Alex Dugas my homepage
Office: 6510 South Hall
Office Hours: T 9:30 - 11:00,  W 12:30 - 2:00, or by appointment.
Office Hours for Finals' week: T 10-12, W 11-1, Th 1-4.

Prerequisites: Math 5A (with a grade of C or better).

Text: Wilfred Kaplan.  Advanced Calculus.  Fifth edition, Addison-Wesley.

Lecture: T Th 8:00 - 9:15 am in 1006 North Hall.

Section: You must sign up for and attend a discussion section as well.  The section times and locations for this course are as follows: 

The GSI for this course is Steve Read.  His office hours are:

Announcements:

 

 

Class Schedule (subject to change)

    Date    

    Topics    

    Reading    

    Homework  (in Kaplan)

    Due Date    

Th 9/28

Vectors, Dot Product, Cross Product, Lines

Ch. 1.1-1.4

p. 15-16 : Ex. 2, 5, 6, 7

10/4

Tu 10/3

Planes, Functions of Several Variables,
Graphing Surfaces, Level Curves

Ch. 2.1-2.3

p. 82 : Ex. 2, 3a,b

10/11

Th 10/5

Limits, Continuity

Ch. 2.4

p. 82 : Ex. 4, 5, 6

Tu 10/10

Partial Derivatives, Total Differential

Ch. 2.5-2.6

p. 89-90 : Ex. 3, 4, 6


10/18

Th 10/12

Chain Rule, Jacobian Matrix

Ch. 2.7-2.9

p. 95 : Ex. 1c,d,e, 2b, 3a,b
p.100 : Ex.  1, 4, 10

Tu 10/17

Implicit Functions, Implicit Differentiation

Ch. 2.10 (review Cramer's rule in Ch. 1.5)

p. 104-105: Ex. 1b, 5, 6d
p. 116-117: Ex. 1d, 5, 6, 7
(use (2.59) for #7)

10/25

Th 10/19

First Midterm Exam

Ch. 1.2-1.4, 2.1-2.9

Exam + Solutions
Prob 2: level curves, graph

 

Tu 10/24

Cylindrical & Spherical Coordinates,
Inverse Functions, Tangent Lines

Ch. 2.12, 2.13

p. 121: Ex. 1,2,3
p. 127-129: Ex. 1,2, 8a-d



 11/1

Th 10/26

Tangent Planes, Gradient,
Directional Derivatives,

Ch. 2.13, 2.14

p. 134-135: Ex. 1a,c,e

Tu 10/31

Higher Order Derivatives,
Relative Extrema

Ch. 2.15, 2.19

p. 142-143: Ex. 1c, 2a, 3
p. 158-159: Ex. 4d,g,h, 5a,d



11/8

Th 11/2

Absolute Extrema, Lagrange Multipliers,

Ch. 2.20,

p. 158-159: Ex. 6b,c,e, 8b,c

Tu 11/7

Vector and Scalar Fields, Gradient,
Divergence, Curl

Ch. 3.1-3.5

p. 180: Ex. 1a,b,c, 7


11/15

Th 11/9

Divergence, Curl, Combined Operations

Ch. 3.6

p. 185: Ex. 3, 5, 7, 9

Tu 11/14

Review of Integration, Multiple Integrals

Ch. 4.1,4.3,4.4

p. 234-5: Ex. 1a,b,c, 2a,c, 5

11/22

Th 11/16

Second Midterm Exam

Ch. 2.10-2.20 (except 2.11, 17)
Ch. 3.2-3.6

Exam + Solutions

 

Tu 11/21

Triple Integrals, Change of Variables

Ch. 4.6

p. 241-2: Ex. 4,7

11/29

Th 11/23

Thanksgiving holiday.  No class.

 

 

 

Tu 11/28

Arc Length, Surface Area,
Line Integrals

Ch. 4.7,
Ch. 5.1-5.2

p. 278: Ex. 1,2


12/6

Th 11/30

Line Integrals

Ch. 5.3-5.4

p. 279: Ex. 3,4

Tu 12/5

Green's Theorem

Ch. 5.5

p. 286-7: Ex. 1, 5a-e, h

 

Th 12/7

Independence of Path

Ch. 5.6-5.7

p.300-1: Ex. 1, 2, 3a-d

F 12/15

Final Exam - 8:00 - 11:00 am

Ch. 1.1 - 5.6

 

 

 

 

 

 

 



Homework:  Homework exercises will be assigned in lecture and listed on the course webpage (sometimes in advance).  All homework problems assigned in a given week are due on the following Wednesday in section.  You may work together on homework problems; however, you must write up your answers individually.  You must show all your work in order to recieve full credit.  Late homeworks will not be accepted.  However, your two lowest homework scores will be automatically dropped.

Exams: There will be two in-class midterm exams on Thursday October 19 and on Thursday November 16 from 8:00 to 9:15 am.  Please arrive promptly.  The final exam will be Friday December 15, 8:00 - 11:00 am.  The problems on the exams will closely resemble those on the homeworks.   No make-up exams will be given, except in extaordinary circumstances.  If you have a serious conflict with any of these exams or miss one for any reason, it is your responsibility to notify me immediately so that other arrangements may be made.

Grades:
  Grades will be computed from your scores on homeworks and exams as follows: Homework = 20%, Each Midterm = 20%, Final = 40%.  No letter grades will be assigned until the end of the semester, and the exact grading scale will depend on the difficulty of the exams.  However,  a 90% or above will guarantee you at least an A-, an 80% will be at least a B-, and 70% will be at least a C-.