| Mathematics 32AH |
| Calculus of Several Variables |
Instructor Info
Instructor: Anush Tserunyan
Office: MS 6139
Email: anush@math.ucla.edu
Lectures: MWF 9:00-9:50am, MS 5117
Office hours: M 3-4pm, W 4-6pm
TA Info
Teaching Assistant: Michael Hall
Office: MS 3955
Email: michaelhall@math.ucla.edu
Discussion Section: Tuesday 9:00-9:50 am, MS 5117
Office hours: T 10-11am (after class), R 4-5pm
Content
The main goal of this course is to get students comfortable with basic analytic geometry and linear algebra of R^n, as well as limits, continuity and differentiability of multivariable functions. As an application, we will solve the "Two Body Problem" and derive Kepler's first law stating that each planet moves in an elliptical orbit with the sun at one focus. Also, we will state and discuss the Implicit Function Theorem, and solve some optimization problems: finding max/min of multivariable functions w/wo constraints (Lagrange multipliers).
Since this is an honors course, there will be proofs in lectures, as well as in every homework and exam (at least one problem in each). Consequently, unlike calculus courses the students might have encountered in the past, this course won't have the format of "instructor gives recipes for solving problems and students follow them". The good news is that the lectures are intended to teach you how to construct mathematical arguments.
It is strongly advised that the students read the textbook after each lecture in order to thouroughly understand the material.
Textbook: R. Williamson, H. Trotter, Multivariable Mathematics, 4th Ed.
Additional material: Prof. Yiannis Moschovakis's notes on The Two Body Problem, a handout of statements of Inverse and Implicit Function Theorems
Course outline: Click here.
Logistics
There will be weekly quizzes and homework, two midterms and a final exam.
Grading scheme: Maximum of:
Final 40%, Midterms 40% (20%+20%), Homework 10%, Quizzes 10%
Final 55%, Maximum of two midterms 25%, Homework 10%, Quizzes 10%
Letter grades: The final letter grade will be assigned based solely on the percentage obtained by the above grading scheme. There will be some sort of curving in the very end applied only to the final percentages (no exam will be curved individually). You must take the final exam in order to pass the course regardless of your total percentage.
Grading disputes: All the grades (homework, quizzes, midterms and final) will be recorded on MyUCLA in a timely fashion. Please verify regularly that grades for all submitted assignments are present and correct. Any grading complaints must be sumbitted within two weeks of the due date or exam/quiz date of the grade in question.
Homework
Homework will usually be collected on Friday at the beginning of lecture and returned in discussion section (Tuesday). The lowest homework score will be dropped (won't count towards the total homework percentage). Late homework will not be accepted.
Homework assignments: Click here.
Homework ethic: You may use resources like textbooks and calculators while doing homework. You can also get help at the Student Math Center, as well as discuss solutions with friends, but do not blindly copy from each other! If the grader (TA) notices such a thing, the consequences will be dramatic. The same applies to copying solutions from the internet or other sources.
Quizzes and Exams
On the quizzes and exams, no resources other than pencil and paper will be allowed.
Quizzes: There will be a quiz each week during the first or last 10 minutes of the discussion section. The lowest quiz score will be dropped (won't count towards the total quiz percentage).
Midterm 1: October 19 (Wednesday), 9:00-9:50 am
Location: MS 5117 (the usual classroom)
Material: Sections 1.1-1.6, 4.1 and 8.2-8.3 of the book.
Midterm 2: November 16 (Wednesday), 9:00-9:50 am
Location: MS 5117 (the usual classroom)
Material: Sections 4.2-4.3, 5.1-5.3 of the book.
Practice Problems for Midterm 2
Final exam: December 6 (Tuesday), 3:00-6:00 pm
Location: MS 5117 (the usual classroom)
Material: Everything covered during the course except for Kepler's Law.
Practice Problems for the Final Exam (Last update: Dec 4, 3:18pm)