Math 340: Calculus, Linear Algebra, Differential Equations
Fall 2011

Textbook

• C. H . Edwards, Jr Advanced Calculus of Several Variables, Dover
• ISBN 10: 0486683362 ISBN 13: 9780486683362
• 480 pages, Edition 1995

Syllabus

This is the first semester of the two-semester honors sequence Math 340-341 which gives a unified and enriched treatment of multivariable calculus, linear algebra, and ordinary differential equations, with supplementary material from differential geometry, Fourier series and calculus of variations.

Description

Specific topics to be covered in this course are: Linear transformations, Determinants, Continuity, Elementary Topology, Multivariable Chain rule, Lagrange multipliers, Critical values, Newton's method, Implicit and Inverse function theorems, Manifolds, Fubini's theorem, Green's Theorem, Gauss's Theorem, Stokes's Theorem, Isoperimetric inequality.

Grading

Conflicts. If you know before an exam that you have a schedule conflict, contact me in advance.

Religious observances. If your religion dictates that you cannot take an exam or hand in assigned work on a particular date, then contact me at the beginning of the semester to discuss alternatives. You are responsible for making these arrangements at the beginning of the semester.

Disabilities. If you have some disability related to testing under the usual timed, in-class conditions, you may contact the office of Disabled Students Services (DSS) in Shoemaker. If they assess you as meriting private conditions and/or extra time, then you may arrange to take your tests at DSS, with extra time as they indicate. You must arrange this well in advance of a test (in particular: no retakes).

Expectations of students

This is a fast-paced course aimed at excellent highly motivated students; in one semester, we will be covering what is usually taught in two semesters. The students are expected to attend class regularly; it will be hard to catch up,. They should come prepared for class ready to absorb new concepts and ideas. They should be able to apply these concepts to problems that usually are significantly different from the worked-out examples. In all written work, students are expected to provide clear-to-follow solutions. Points will not be given for implicit ideas. The assignments will be graded on only what is written explicitly, legibly.

(It is perhaps worthwhile to mention that the hardest math course aimed at freshmen is supposedly Math 55 at Harvard. Our course, while being challenging, is significantly easier.)

Academic Integrity

The student-administered Honor Code and Honor Pledge prohibits students from cheating on exams, plagiarizing papers, submitting the same paper for credit in two courses without authorization, buying papers, submitting fraudulent documents and forging signatures. On every examination, paper or other academic exercise not specifically exempted by the instructor, students must write by hand and sign the following pledge:

(Discussing homework problems with other students is ok, even encouraged, but please do write up your solutions by yourself. In exams and quizzes, of course, you are assumed to be working by yourself.)

Attendance Policy

Regular attendance and participation in this class is the best way to grasp the concepts and principles being discussed. However, in the event that a class must be missed due to an illness, the policy in this class is as follows:

1. For every medically necessary absence from class (lecture, recitation, or lab), a reasonable effort should be made to notify the instructor in advance of the class. When returning to class, students must bring a note identifying the date of and reason for the absence, and acknowledging that the information in the note is accurate.
2. If a student is absent more than three times, the instructor may require documentation signed by a health care professional.
3. If a student is absent on days when tests are scheduled or papers are due [or other such events as specified in the syllabus] he or she is required to notify the instructor in advance, and upon returning to class, bring documentation of the illness, signed by a health care professional.

Miscellaneous

Matters such as class cancellations, room changes, etc. will be communicated to the students by email (and will be reflected on the class webpage). Please notice that class lectures and other materials are copyrighted and that they may not be reproduced for anything other than personal use without written permission of the instructor.

Class Schedule

Class schedule and homeworks will be announced on the class webpage; please check regularly for updated information.

Class homework

Sep 9, 2011
Sep 16, 2011

Excellent advice about Math 340 from Professor Misha Brin who has taught it previously.

Expectations/philosophy. You are expected to come to class, do the homework, and most important of all be actively engaged in trying to understand.

Tips for success:

• Don't fall behind. (Make a regular schedule of work and don't procrastinate.)
• Make friends. Help each other. (On homework, it's usually best to try alone first.)

In class, we will do some complicated things. But I am thinking of class more for giving context, interpretation, extra material, things that will help the reading and homework, and answering questions.