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# MAT291F-2011-Schedule%26SuggestedProblems.pdf

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School
University of Toronto St. George
Department
Mathematics
Course
MAT223H1
Professor
Robert Brym
Semester
Winter

Description
Department of Mathematics, University of Toronto MAT291H1F - Calculus III Schedule and Suggested Problems - Fall 2011 Your instructor may be slightly ahead or behind this schedule. Your ability to correctly and completely solve the problems listed below is a very good indicator of your progress with the material. You are expected to solve at the very minimum all of the problems on this list. Week 1 beginning September 8. Lecture: Introduction. Week 2 beginning September 12. Tutorials begin. Lectures: Chapter 12: Functions of Several Variables, x12.1 Planes and Surfaces, x12.2 Graphs and Level Curves, x12.3 Limits and Continuity. Section 12.1: 3, 5, 11, 13, 15, 21, 23, 29, 35, 37, 41, 45, 49, 53, 57, 63, 67, 75, 79, 85. Section 12.2: 3, 13, 17, 27, 34, 37, 39, 43, 47, 67. Section 12.3: 7, 9, 11, 15, 19, 23, 25, 27, 29, 31, 33, 37, 41, 45, 47, 49, 53, 61, 63, 65, 69. Week 3 beginning September 19. Lectures: x12.3 Limits and Continuity (continued), x12.4 Partial Derivatives, x12.5 The Chain Rule. Section 12.4: 1, 7, 9, 15, 19, 21, 27, 33, 39, 41, 43, 45, 57, 59, 61, 63, 67, 69, 71, 75. Section 12.5: 3, 7, 13, 15, 17, 27, 29, 37, 44, 47, 49, 51, 53, 57. Week 4 beginning September 26. Problem Set 1 due. Lectures: x12.6 Directional Derivatives and the Gradient, x12.7 Tangent Planes and Linear Approximation, x12.8 Maximum/Minimum Problems. Section 12.6: 3, 4, 5, 11, 13, 15, 19, 21, 25, 31, 35, 37, 43, 51, 53, 57, 71, 72. Section 12.7: 3, 5, 11, 17, 23, 29, 33, 43, 51, 57, 58, 59. Section 12.8: 3, 4, 8, 11, 13, 17, 21, 27, 31, 33, 39, 41, 43, 45, 47, 49, 51, 53, 55, 67. Week 5 beginning October 3. Lectures: x12.9 Lagrange Multipliers, Supplementary Problems* Section 12.9: 1, 5, 7, 13, 15, 19, 21, 25, 34, 39, 41, 53, 55. Week 6 beginning October 10. Quiz 1 covers: x12.1-12.9. Lectures: Review of Chapter 12, Chapter 13: Multiple Integration, x13.1 Double Integrals over Rectangular Regions. Chapter 12 Review (page 872): 1, 3, 7, 9, 13, 19, 21, 25, 27, 29, 30, 35, 37, 42, 47, 49, 51, 55, 59, 61, 63, 65, 69, 71, 75, 79, 83, 87. Section 13.1: 1, 5, 9, 15, 21, 25, 29, 30, 33, 39, 43, 51. 1 of 3 Week 7 beginning October 17. Lectures: x13.2 Double Integrals over General Regions, x13.3 Double Integrals in Polar Coordinates, x13.4 Triple Integrals. Section 13.2: 5, 7, 11, 17, 21, 23, 27, 31
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