SYLLABUS FOR MATHEMATICS 5B   CALCULUS   SPRING 2011

 

 

Professor John Douglas Moore   Office: South Hall 6714   Office hours: M3, TuTh 1

Telephone:  893-3688   email:  moore@math.ucsb.edu

Lectures:   TD-W 1701 MWF 12

Text:  Briggs and Cochran, Calculus, Early Transcendentals, Addison-Wesley-Pearson, Boston 2010.

 

PLEASE NOTE:  Briggs and Cochran is different from the text usually used for Math 5B.  The publisher is making this text available to students for free.  If you are registered in the class, you can pick up your copy of the text on Friday, September 23 after class in SH 6617 from 1 to 2:30 pm.

 

Course web page: http://www.math.ucsb.edu/~moore/s5bf2011.html

 

Additional course information: https://gauchospace.ucsb.edu/courses/

 

Midterm I, Friday, October 21   15%

Midterm II, Friday, November 9   15%

Homework   10%

Quizzes   15%

Final, Tuesday, December 6, 12noon to 3pm   45%

(The percentages are tentative---the professor reserves the right to change them.)

 

EXAM PROCEDURE:  You will need to sign your name, print your name and enter your perm number, TA and discussion time on the quizzes in the lecture, on the midterms and the final.  You need to bring some identification to each midterm and to the final. 

 

Exams will cover material presented in lecture, as well as material from the text and homework problems.

 

Quizzes will be given in almost every discussion section.

 

Pop quizzes in lectures: It is very important not to skip class and to arrive on time for class.  Pop quizzes may occur during any lecture, and are most likely on mornings when attendance is a bit low.  It is impossible to make up a pop quiz.

 

Homework: will generally be due on Fridays at 12 noon and is available online through MyMathLab, a homework system developed by the publisher of the text.  Details on how to use the homework software will be presented in the first meeting of the class.

 

Calculators and computers:  You are encouraged to use these when solving homework problems, but calculators and computers are not allowed on exams or quizzes.

 

Help!   Mathlab in South Hall 1607 is staffed M-F noon-5pm by TA's who will be happy to help you.  Help is also available through CLAS, the Campus Learning Assistance Service; see http://www.clas.ucsb.edu

 

Sickness or missing an exam:  If you miss a midterm or quiz due to illness you should bring your TA a note from a medical worker or another person in a position of responsibility.  At the discretion of the TA, you will be given an average based upon the other work you did.  There are no makeup exams.

 

Optional early final on Friday, December 2:  There is a cost of 10%, which will be subtracted from your score for taking this early exam.  The exam will be different than the regular one and may be a little harder.  You must inform me in writing by November 18 if you plan to take this earlier exam, and you must give a reason that I find compelling.

 

Teaching Assistants:

 

Martin (1)   Office hours Th 5-6 SH6432F  email: cmart07@math.ucsb.edu

1.  Wednesday 6   Girvetz 1119

2.  Monday 6   Phelps 1445

3.  Wednesday 5   Phelps 1448

4.  Wednesday 7   Phelps 1448

 

Smith (2)   Office hours W 9-10 SH 6431D  e-mail: dls@math.ucsb.edu

1.  Monday 5   Phelps 1444

2.  Monday 8am   Phelps 1444

 

OVERVIEW OF COURSE

 

Math 5B is the fifth in a six-quarter sequence of UCSB courses on calculus:

 

Course Number           Contents                                                         Yearly enrollment

3A                               Differential calculus                                                    1246

3B                               Integral calculus                                                          1517

3C                               Differential equations and linear algebra I                   1436

5A                               Differential equations and linear algebra II                 900

5B                               Several variable calculus                                              611

5C                               Fourier series and PDE                                               386

 

A substantial number of students enter the sequence at 3B or 3C.  Many majors require only Math 3ABC, but all six quarters are required for physics, engineering and many mathematics majors.  This is one reason for the smaller enrollments in more advanced courses.  Most of the students taking Math 5B are also taking a series of physics courses.

 

The development of calculus is largely due to Sir Isaac Newton (1643-1727).  He was largely motivated by problems of celestial mechanics, and in fact one of his major achievements was a derivation of KeplerÕs three laws of planetary motion from his universal law of gravitation.  A modern treatment of his derivation uses many of the techniques studied in this course (such as systems of differential equations, polar coordinates).  In the eighteenth and nineteenth centuries, the techniques of calculus were extended to many branches of physics.  Many of these applications require calculus of several variables, the topic treated in Math 5B.

 

Calculus of several variables was found to be essential to mathematical models for fluid flow, to vibrating membranes, and to electricity and magnetism, as well as in many other parts of physics and engineering.  For example, James Clerk Maxwell (1831-1879) was able to formulate electricity and magnetism in a set of four differential equations that can be written on the back of a postcard.  Using these equations as axioms, one can more or less develop electricity and magnetism by the same principles of deduction one uses in deriving high school Euclidean geometry.  It was the symmetries exhibited by MaxwellÕs equations that led Albert Einstein (1879-1955) to formulate his special theory of relativity.

 

This short description makes it clear that to fully understand calculus one needs to have some familiarity with the physics which calculus is used to solve.  We will try to keep the knowledge of physics required to a minimum, but we will need to use some ideas from high school physics from time to time, such as the notion of work and NewtonÕs second law of motion.

 

During the nineteenth century the somewhat informal way in which calculus had been treated up to then was subjected to criticism.  Calculus is about functions and badly behaved functions do not have integrals, for example.  Intuition can often lead one astray.  So mathematicians such as Augsutin-Louis Cauchy (1789-1867) and Karl Weierstrass (1815-1897) developed the modern rigorous definition of limits, which is the most theoretical material presented in the text.  Gradually, you should try to accommodate yourself to the notation used for the rigorous arguments.  It will serve you well for more advanced courses, and may help suggest where commonly-used algorithms for solving problems using techniques of calculus might fail.  More advanced courses (such as Math 117 and 118ABC) examine how far these techniques of calculus can be extended, and what one must do to get around potential difficulties.

 

Your goals in this course should be to develop intuition, an understanding of basic definitions and an ability to solve problems.  The text, the lectures, the quizzes and the homework are designed to complement each other in helping you learn the material and prepare for the exams.

 

 

TENTATIVE COURSE OUTLINE

 

Friday, September 23: Vectors (11.1,11.2)

 

Monday, September 26: Dot product (11.3)

Wednesday, September 28: Cross product (11.4)

Friday, September 30: Curves in space (11.5, 11.6)

 

Monday, October 3: Motion in space (11.7)

Wednesday, October 5: Length of curves (11.8)

Friday, October 7: Surfaces (12.1,12.2)

 

Monday, October 10: Limits and partial derivatives (12.3,12.4)

Wednesday, October 12: Chain rule (12.5)

Friday, October 14: gradient, linear approximations (12.6)

 

Monday, October 17: Maxima and minima (12.8)

Wednesday, October 19: Lagrange multipliers (12.9)

Friday, October 21: MIDTERM I

 

Monday, October 24: Lagrange multipliers (12.9)

Wednesday, October 26: Double integrals  (13.1, 13.2)

Friday, October 28: Double integrals in polar coordinates (13.3)

 

Monday, October 31: Triple integrals I (13.4)

Wednesday, November 2: Cylindrical and spherical coordinates (13.5)

Friday, November 4: Mass calculations (13.6)

 

Monday, November 7: Change of variables in multiple integrals I (13.7)

Wednesday, November 9: MIDTERM II

Friday, November 11: HOLIDAY

 

Monday, November 14: Vector fields, line integrals (14.1, 14.2)

Wednesday, November 16: Conservative vector fields (14.3)

Friday, November 18: GreenÕs Theorem (14.4)

 

Monday, November 21: Divergence and Curl (14.5)

Wednesday, November 23: Surface integrals (14.6)

Friday, November 25: HOLIDAY

 

Monday, November 28: StokesÕ Theorem (14.7)

Wednesday, November 30: Divergence Theorem (14.8)

Friday, December 2: REVIEW