COURSE DESCRIPTION: Applications of calculus in mathematics, science, economics, psychology, the
social sciences, involve several variables. This course extends calculus to
several variables: vectors, partial derivatives, multiple integrals. There is
also a unit on infinite series, sometimes with applications to differential
equations. This course is the right starting point for students who have seen
differentiation and integration before. Students with the equivalent of advanced
placement of AB 4, BC 3 or above should enroll in Mathematics 105.
Prerequisites: Mathematics 104 or equivalent,
such as satisfactory performance on an Advanced Placement Examination. No
enrollment limit (expected: 45). NOTE:
We will be moving at a very fast pace. You should spend at least one
if not two hours a day (every day!) on this course. I strongly encourage you to
work in groups, and you should skim the reading before each class. We will not
cover all the material in the book in class; you are responsible for reading the
other examples at home.
GRADING / HW: Homework
15%,
Midterms 40% (there will be 2 or 3), Final 45%.
Exams are black tie optional. Homework is to be handed in on time, stapled and legible;
there will be HW due each class.
Late, messy or unstapled homework will not be graded. I encourage you to work in
small groups, but everyone must submit their own homework assignment.
All exams are cumulative, the lowest midterm grade will be dropped. There are
also three other options. Doing one of the two options below reduces the exams
from 85% to 80%; doing two reduces the exams to 75%, doing three reduces it to
70%.
Quizzes: You may take the weekly quizzes at home. There is no partial credit, lowest quiz grade is dropped.
Project:: You may explore a topic in multivariable calculus in great detail and write it up.
SYLLABUS GENERAL: The textbook is the fifth edition of Vector Calculus by Jerrold E. Marsden and Anthony Tromba (ISBN: 0-7167-4992-0, ISBN-13: 978-0-716-74992-9); there will be supplemental handouts. Please read the relevant sections before class. This means you should be familiar with the definitions as well as what we are going to study; this does not mean you should be able to give the lecture. You do not need a calculator for this class, though I strongly urge you to become familiar with either Matlab or Mathematica to plot some of the multi-dimensional objects. There are many good references on the web. You can access certain books online: Calculus in Vector Spaces (Lawrence J. Corwin, Robert Henry Szczarba) and Multivariable Calculus (Lawrence J. Corwin, Robert Henry Szczarba) are somewhat theoretical expositions. Another great source is Cain and Herod's book on multivariable calculus (which you can download in its entirety for free). If you have any concerns or suggestions for the course and would prefer to communicate them anonymously, you may email me by using the account mathephs@gmail.com (the password is the first seven Fibonacci numbers, 11235813).
