Harvard Applied Mathematics 21a Syllabus

Applied Mathematics 21a Fall 2007-2008 School of Engineering and Applied Sciences Harvard University

General Information: • Instructor: Vahid Tarokh – Office: MD 347 – Office Hours: Tuesdays and Thursdays 3:00-5:00 p.m. or by appointment – Voice: (617) 384-5026 – E-mail: [email protected] • Preceptor: Dr. Natasha Devroye – Office: MD 342 – Office Hours: 10-11:30 a.m. Monday and Wednesday—or by appointment – Voice: (617) 496-8734 – E-mail: [email protected] • Teaching Fellows: – Behtash Babadi : Office MD 113, Voice: 617-496-7410, E-mail: [email protected] (office hours: Wednesdays 2:30-4:00) – Hongtao Wang: Office: 12 Oxford Street Room M137, Voice: 617495-5540, [email protected] (office hours: Monday 5-6:30 in Cruft 318) – Chuck McBrearty: Office MD 215, E-mail: [email protected] (office hours: Thursdays 5:30-7) – Hamidreza Saligheh Rad: Office MD 113, E-mail: [email protected] (office hours: Wednesdays 5:30-7) • Reading Materials 1

– Text Book: Calculus, One and Several Variables by Salas, Hille and Etgen, Tenth edition, John Wiley and Sons Inc. – Additional Reference: Calculus-An Introduction to Applied Math, Greenspan and Benney, McGraw Hill Publishers – Lecture Notes: Lecture Notes of Applied Math 21a-Fall 2007-2008, Tarokh and Devroye, available at the course web-site. • Pre-requisites: A solid knowledge of calculus including the ability to compute limits and having a good understanding of continuity, integration, and differentiation of functions of one variable • Class Time: Tuesdays and Thursdays, 1:00-2:30 • Location: Jefferson 250 • Problem Solving Session Times + Office Hours for the TFs: On the Attached Paper The following topics (and more) will be covered in this course: • Vector Algebra, properties of vectors, dot and cross products, lines, planes, triple products. • Vector Calculus: vector functions, polar unit vectors, curves, tangent and normal vectors, curvature. • Sequences and Series: convergence and divergence of sequences, improper integrals, infinite series, convergence and divergence of series, geometric series, non-negative series, harmonic series, integral test, ratio and root tests, alternating series, power series, Taylor series, applications. • Functions of Several Variables and Partail Differentiation: functions of multiple variables, quadratic surfaces, continuity of functions of multiple variables, partial derivatives, increments and differentials, chain rule, gradient, curl, extreme values, surface normal, tangent plane,Taylor expansion of functions of several variables, Lagrange multipliers. • Double and Triple Integrals: double integrals, double integration in polar coordinates, triple integrals, triple integrals in cylindrical and spherical 2

coordinates, application to computation of areas, volumes and centroids, Jacobians. • Line and Surface Integrals: Line integrals, Green’s Theorem, Divergence Theorem, Stokes Theorem, surface integrals, applications. Grading Scheme and Exams The grading scheme is as follows: 1. Homeworks and assignments will be given/posted on the webpage of the course. (10%) 2. Midterm I: (15 %) 3. Mideterm II: (30 %) 4. Final exam (45 %) All the exams are all inclusive. The exam dates are: • Midterm I, October 16, 2007 • Midterm II, November 15, 2007 • Final Exam: TBD No aids of any kind (calculators, notes, etc.) are allowed in any of the above exams. The final exam will be a standard 3 hour exam, and absence will result in an ABS grade. Important Note: This course is foundational, and knowledge of the course material will be crucial to understanding the future courses that the students may undertake. It is thus extremely important that the students become comfortable with these topics at the end of the semester. In light of the above, there is a real possibility that lack of acceptable performance results in an unsatisfactory (UNSAT) grade. 3