Math 318, Spring 2012

Math 318, Spring 2012 Instructor: Ivan Horozov, Cupples I,Room 9, [email protected] Lectures: MWF 10-11am, Crow, Room 206 Office hours: MW 1-2:30pm, Cupples I, Room 9 Required Text: Theodore Shifrin, ”Multivariable Mathematics. Linear Algebra, Multivariable Calculus, and Manifolds”, John Wiley & Sons, 2005. Other texts: 1. Michael Spivak, ”Calculus on Manifolds: A Modern Approach to the Classical Theorems of Advanced Calculus”, W.A. Benjamin, 1965. 2. Michael Artin, ”Algebra” Grading: Homework 15%, Exam 1 25%, Exam 2 25%, Final 35%. If your grade in the final is greater than your lowest midterm grade, then the grade in the midterm gets replaced by the grade in the final. For example, if midterm 1 score is 80/100, midterm 2 score is 50/100 and final score is 70/100, your score in the second midterm gets replaced by 70/100. If you choose to be graded ”Pass/Fail”, a ”Pass” grade requires a grade of C- or higher. Homework: Assignments will be given via email. A grader will grade selected problems. Discussing homework with others is ok. It is expected that everyone writes in his/her own words the homework solutions. Homework is due at the beginning of class on the due date. Prerequisites: Math 233 and Math 309 (not concurrent), or equivalent knowledge of matrix algebra and multivariable calculus. Syllabus: Review of Matrices. A bit of topology. Continuity. Convergence. Partial derivarives. Directional derivarives. Gradient. Linear systems. Gaussian elimination. Basis. Change of basis. Dual basis. Differential forms and differential operators. Maximum value theorem. Quadratic forms. Second derivative test. Lagrange multipliers. Projections. Gram-Schmidt process. Least squares. Inner product spaces. Inverse function theorem. Implicit function theorem.

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