## Math 120 Calculus for Functions of Several Variables (Spring 2022)

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There will be 28 lectures given by the instructors, each lasting 2 class hours. The actual timing of the lectures may differ slightly from section to section because of the holidays, but the total number will be the same. Besides these lectures, there will be recitations, 2 hours per week, during which the assistants will solve extra problems and give quizzes.

The table below is a rough guideline for the content of course lectures. Professors may reorder content as necessary/desired. The section and page numbers below are from the textbook, Calculus, by James Stewart, 7th international metric ed., 2012.

 Week 1: Mar.7-11 1 Chapter 12. Vectors and the Geometry of Space§12.1: Three-Dimensional Coordinate Systems. §12.2: Vectors. §12.3: The Dot Product. 2 §12.4: The Cross Product. §12.5: Equations of Lines and Planes. Week 2: Mar.14-18 3 §12.5: Equations of Lines and Planes (cont). 4 §12.5: Equations of Lines and Planes (cont). §12.6: Cylinders and Quadric Surfaces Gallery of Quadric Surfaces. Week 3: Mar.21-25 5 §12.6: Cylinders and Quadric Surfaces (cont). Chapter 13. Vector Functions§13.1: Vector Functions and Space Curves. 6 §13.2: Derivatives and Integrals of Vector Functions Motion in 3D. Week 4: Mar.28-Apr.1 7 Chapter 14. Partial Derivatives§14.1: Functions of Several Variables Functions of Two Variables (MIT OCW). §14.2: Limits and Continuity. 8 §14.3: Partial Derivatives. §14.4: Tangent Planes and Linear Approximations. Week 5: Apr.4-8 9 §14.5: The Chain Rule. 10 §14.6: Directional Derivatives and the Gradient Vector. Week 6: Apr.11-15 11 §14.7: Maximum and Minimum Values. 12 §14.8: Lagrange Multipliers. Week 7: Apr.18-22 13 Chapter 15. Multiple Integrals§15.1: Double Integrals over Rectangles. §15.2: Iterated Integrals. 14 §15.3: Double Integrals over General Regions. §15.5: Applications of Double Integrals. Week 8: Apr.25-29 15 §10.3: Polar Coordinates. §15.4: Double Integrals in Polar Coordinates. 16 §15.10: Change of Variables in Multiple Integrals. HOLIDAY: Mon-Wed, 2-4 April Week 9: May 9-13 17 §15.7: Triple Integrals (Simple regions. Omit moments & center of mass.). 18 Chapter 16. Vector Calculus§16.1: Vector Fields. §16.2: Line Integrals. Week 10: May 16-20 19 §16.3: The Fundamental Theorem for Line Integrals. 20 §16.4: Green's Theorem. Holiday: Thursday, 19 May Week 11: May 23-27 21 Chapter 11. Infinite Sequences and Series§11.1: Sequences. 22 §11.1: Sequences (cont) (Including Monotonic Sequence Thm). §11.2: Series. Week 12: May 30-June 3 23 §11.2: Series (cont). §11.3: The Integral Test (Not including 'Estimating the Sum of a Series'). 24 §11.4: The Comparison Tests (Including 'Estimating Sums'). Week 13: June 6-10 25 §11.5: Alternating Series (Including 'Estimating Sums'). §11.6.1: Absolute Convergence. 26 §11.6.2: The Ratio and Root Tests. §11.7: Strategy for Testing Series (Reading/Recitation Assignment). Week 14: June 13-17 27 §11.8: Power Series. §11.9: Representations of Functions as Power Series. 28 §11.9: Representations of Functions as Power Series (cont). §11.10: Taylor and Maclaurin Series. FINAL EXAMS: 20 June -- 2 July

* Reading assignments may be tested in the exams and quizzes.