MATH 201 Syllabus, Fall 2018

American University of Beirut - Faculty of Arts and Sciences Department of Mathematics Math 201: Calculus III Fall 2018 Professor: Dr Arman Taghavi-Chabert Office: Bliss 320 Office Phone: 4226 E-mail: at68@aub.edu.lb Office hours: 14:00-15:30 MF and by appointment Class meetings: 11:00-11:50 MWF, Nicely Hall 415, Aug 30 – Dec 20, 2018 Recitations: Section 9: 15:00 F, Nicely Hall 108 Section 10: 16:00 F, Nicely Hall 412 Section 11: 17:00 F, Nicely Hall 412 Text Thomas’ Calculus, 13th edition by Thomas, Weir, and Hass Catalogue course description Sequences and series, multivariable functions, partial derivatives, cylindrical and spherical coordinates, multiple integrals, and integration in vector fields. Course learning outcomes At the end of the course, students will be able to: • Define the sum of a series as a limit of a sequence • Use tests to decide about the convergence of a series • Use series to approximate functions • Define differentiability for functions of several variables • Find the derivative of a function in a given direction • Maximize or minimize a function subject to a given constraint • Define the integral of a function of several variables • Use Fubini’s theorem to evaluate double and triple integrals • Apply double integrals (in cartesian & polar coordinates) to find areas & centers of “mass” • Apply triple integrals (in cartesian, cylindrical and spherical coordinates) to find volumes & centers of mass • Study substitutions in double & triple integrals. • Line Integrals • Green’s Theorem (if time permits) ‘AUB strives to make learning experiences as accessible as possible. If you anticipate or experience academic barriers due to a Disability (including mental health, chronic or temporary medical conditions), and in order to help establish reasonable accommodations and facilitate a smooth accommodations process, you are encouraged to contact the Accessible Education Office in West Hall 314’. Title Section Assigned homework problems Sequences 10.1 1, 5, 7, 10, 13, 16, 20, 21, 24, 28, 31, 32, 41-55, 65, 67, 78-82, 87, 88. Infinite series 10.2 11,15,16,19, 23, 25, 28, 34, 36-40, 43, 44, 47- 68. Integral test 10.3 6, 9, 10, 11, 16, 21, 22, 25- 28, 32-38, 43, 55, 56 Comparison tests 10.4 6-14,18, 25-32,34,42, 43,47, 56, 58, 60,63,65,67 Absolute convergence; Ratio and Root tests 10.5 8, 11, 18,14, 20, 22, 23, 25, 27-40. Alternating series 10.6 8-10,14, 18, 21,22, 23, 26, 29,30,34, 36, 40, 43, 49-51. Power series 10.7 4,8,10,14,18,20,22,25,29,31,33,34,36,39,41,42,53- 60. Taylor series 10.8 3, 5, 11, 21, 23, 26, 29. Error estimates 10.9 1, 5, 8-10,11-13,15, 18, 19, 20, 22, 23, 25, 28,35-50. Binomial series 10.10 2, 3, 5, 12, 15-24, 53-55. Exam 1 (25% of course grade) Saturday, September 29, 1:00 → 2:00 pm Polar coordinates 11.3 1,3, 6,7, 9,11, 13, 15, 17, 19,21,23,25, 27, 28, 33-38, 63, 68 Graphing in polar coordinates 11.4 1, 3 ,5, 6, 21-24. Cylinders and quadric surfaces12.6 1-12 Functions of several variables14.1 2, 6, 7, 8, 13-15, 22- 30. Limits and continuity 14.2 3, 6, 17, 18, 27, 35, 36, 39, 41,44,46, 47,49 50,54- 58. Partial derivatives 14.3 1, 7, 12, 17, 19, 21, 22, 25, 26, 30, 43, 49, 51,55. The chain rule 14.4 1, 3, 4, 7, 8, 9, 25, 26, 27, 30, 31,32, 33, 35, 37. Directional derivative 14.5 5, 7, 12, 16, 17, 20, 23, 26, 29, 31, 32,33. Tangent planes 14.6 1, 3, 8, 9,12, 13, 17, 19-22. Extreme values 14.7 1, 3, 7, 9, 12, 30, 31, 41, 49. Exam 2 (25% of course grade) Saturday, November 3, 1:00 → 2:00 pm Lagrange multipliers 14.8 1, 9, 11, 12, 17, 21, 23, 25,27. Double integrals I 15.1 6, 7, 10, 11, 12, 15,16, 21, 22. Double integrals II 15.2 9- 25, 33,35,37,39,41,43,45,47,49,51,83. Area by double integration 15.3 1,3, 5, 7,9, 11,13,15,17, 19, 21. Double integrals in polar 15.4 3,5,7,13,15,17,19,28,31,32,41. Triple integrals 15.5 3, 5, 8, 9, 10, 13, 15, 17, 22, 25, 31, 33, 41, 43. Moments and centers of mass 15.6 1,3, 5, 13. Triple integrals in cylindrical and spherical 15.7 3, 5, 7, 9, 11,15, 17,21,23,27,29,31,34,37,43,50,61. Substitutions in multiple integrals 15.8 1, 3, 5, 7,9, 13,18,19, 20,21,23,24. Line integrals 16.1 1-9, 11, 13, 15, 16, 17, 19, 21,23,25,26-28. Final Exam comprehensive (50 % of course grade) TBA