SYLLABUS FOR MATHEMATICS 5B CALCULUS SPRING 2011
Professor
John Douglas Moore Office:
SH 6714 Office hours: TuWTh
2-3
Telephone: 893-3688 email:
moore@math.ucsb.edu (I may
not be able to answer all emails.)
Lectures: Chemistry 1179 MWF 1
Text: Miroslav Lovric, Vector calculus, Wiley, 2007, New York.
Course
web page: http://www.math.ucsb.edu/~moore/s5bs2011.html
Midterm
I, Friday, April 22 15%
Midterm
II, Friday, May 13 15%
Homework 10%
Quizzes 15%
Final ,
Wednesday, June 8, 4-7pm, 45%
(The
percentages are tentative--- the professor reserves the right to change them.)
TARDIS Codes. On all quizzes and exams, you will need to print
your name, sign your name and print your TARDIS code. You will receive your TARDIS code from your TA at your first
discussion meeting. TARDIS stands
for TA, Regular Discussion, Individual Student.
QUIZZES AND EXAMS WITHOUT TARDIS CODES WILL NOT BE
GRADED.
Exams will cover material presented
in lecture, as well as material from the text and homework problems. The quizzes in discussion sections will
also help prepare for midterms and finals.
Quizzes in discussion sections: Quizzes will be given in almost
every discussion section.
Pop quizzes: 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 1pm (although the first week is special), and is available online at
the website: http://webwork.math.ucsb.edu/
Calculators and computers: You are free 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
work you did. There are no makeup exams.
Optional early final on Wednesday, June 1: 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
May 20 if you plan to take this exam.
You must give a reason that I find compelling.
Teaching Assistants:
Andrew
Jaramillo (1) Office SH 6431P TBA
email: drewj@math.ucsb.edu
1. Thursday 8 HSSB 1206
2. Thursday 17 HSSB 1211
3. Thursday 18 HSSB 1211
4. Thursday 16 HSSB 1211
Neil
Hanson (2) Office SH 6431J TBA
e-mail: dancinhanson@math.ucsb.edu
1. Tuesday 17 HSSB 1206
2. Tuesday 18 NH 1109
3. Tuesday 19 NH 1111
4. Tuesday 16 HSSB 1207
Brandon
Kerr (3) Office SH
6431C TBA e-mail: bkerr@math.ucsb.edu
1.
Thursday 19 NH 1109
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 from his universal law of gravitation. A modern treatment of his derivation uses many of the techniques studied in this course (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 required 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 from a set of axioms. 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 led to the problems calculus helps 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. If you have trouble with these concepts, I encourage you to ask for help in the Math Lab.
During the nineteenth century it was realized that the somewhat informal way in which calculus was used was subject 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 notation that is introduced at various points in the text by Lovric. 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 might fail. More advanced courses (such as Math 117 and 118ABC) examine how far the techniques of calculus can be extended, and what one must do to get around potential difficulties.
Your goals in this course are developing intuition, an understanding of basic definitions and an ability to solve problems. The text, the lectures, the quizzes and the homework should all complement each other in helping to learn the material and prepare for the exams.
TENTATIVE COURSE
OUTLINE
Monday, March 28: Dot and cross products (Chapter 1)
Wednesday, March 30: Real and vector valued functions of several variables (2.1)
Friday, April 1: Level sets (2.2,2.3)
Monday, April 4: Derivatives of functions of several variables (2.4)
Wednesday, April 6: Parametrization of curves (2.5)
Friday, April 8: Chain rule (2.6)
Monday, April 11: Gradient, spherical coordinates (2.7,2.8)
Wednesday, April 13: Length of curves (3.3)
Friday, April 15: Higher order derivatives (4.1,4.2)
Monday, April 18: Maxima and minima (4.3)
Wednesday, April 20: Lagrange multipliers (4.4, 4.5)
Friday, April 22: MIDTERM I
Monday, April 25: Divergence and curl (4.6)
Wednesday, April 27: Parametrization of paths and line integrals (5.1, 5.2)
Friday, April 29: Integrating vector fields along paths (5.3)
Monday, May 2: Conservative fields (5.4)
Wednesday, May 4: Double integrals I (6.1)
Friday, May 6: Double integrals II (6.2,6.3)
Monday, May 9: Change of variables in multiple integrals (6.4)
Wednesday, May 11: Triple integrals (6.5)
Friday, May 13: MIDTERM II
Monday, May 16: Parametrized surfaces (7.1, 7.2)
Wednesday, May 18: Surface integrals of real-valued functions (7.3)
Friday, May 20: Surface integrals of vector fields (7.4)
Monday, May 23: GreenÕs Theorem (8.1)
Wednesday, May 25: Divergence Theorem I (8.2)
Friday, May 27: Divergence Theorem II (8.2)
Monday, May 30: MEMORIAL DAY
Wednesday, June 1: StokesÕs Theorem (8.3)
Friday, June 3: REVIEW