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 appoint-
ment – Voice: (617) 384-5026 – E-mail:
[email protected] •
Preceptor: Dr. Natasha Devroye – Office: MD 342
Office Hours: 10-11: 10-11:30 30 a.m. Monda Monday y and Wednesd ednesday ay—or —or by ap– Office pointment – Voice: (617) 496-8734 – E-mail:
[email protected] •
Teaching Fellows: Behtash Babadi Babadi : Office MD 113, Voice: Voice: 617-496-7410, 617-496-7410, E-mail: E-mail: be– Behtash
[email protected] (office hours: Wednesdays 2:30-4:00) – Hongtao Hongtao Wang Wang:: Office: Office: 12 Oxford Oxford Street Room M137, M137, Voice: oice: 617617-
495-5540,
[email protected] [email protected] ard.edu (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 Saligheh Rad: Office MD MD 113, E-mail: E-mail: hamid@seas
[email protected] .harvard.ed ard.edu u – Hamidreza (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-A Calculus-An n Intro Introduction duction to Applie Applied Math ,
Greenspan and Benney, McGraw Hill Publishers -Fall 2007-2008, – Lecture Notes: Lecture Notes of Applied Math 21a -Fall 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
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Class Time: Tuesdays and Thursdays, 1:00-2:30
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Location: Jefferson 250
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Prob Proble lem m So Solv lvin ingg Sess Sessio ion n Times Times + Office Office Hours Hours for the TFs: On the the Attached Paper
The following topics (and more) will be covered in this course: •
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Vector ector Algebra Algebra,, properti properties es of vector vectors, s, dot and cross product products, s, lines, lines, planes, triple products. Vector ector Calculu Calculus: s: vector vector functio functions, ns, polar polar unit unit vector vectors, s, curve curves, s, tangen tangentt 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 unctions of Several Several Variables ariables and Partail Partail Differen Differentiation: tiation: functions 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
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Midterm II, November 15, 2007
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Final Exam: TBD
No aids of any kind (calculators, notes, etc.) are allowed in any of the above exam exams. s. Th Thee fin final al exam will be a stan standa dard rd 3 ho hour ur exam, exam, an and d ab abse senc ncee will will result in an ABS grade. Important Note: This course is foundational, and knowledge of the course
material will be crucial crucial to understandi understanding ng the future courses courses that the students students may may und underta ertake ke.. It is thus thus extremely extremely importan importantt that the studen students ts become become comf comfort ortab able le with these these topic topicss at the end of the the seme semeste ster. r. In light light of the the above, there is a real possibility that lack of acceptable performance results in an unsatisfactory (UNSAT) grade. 3
