METU-NCC Math

    Math 120 Calculus for Functions of Several Variables (Summer 2013)

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Students should use ODTU-Class

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:
Jun.24-28		 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.
3 §12.5: Equations of Lines and Planes (cont).
§12.6: Cylinders and Quadric Surfaces
 Gallery of Quadric Surfaces.
4
Chapter 13. Vector Functions
§13.1: Vector Functions and Space Curves.
§13.2: Derivatives and Integrals of Vector Functions
 Motion in 3D.
5
Chapter 14. Partial Derivatives
§14.1: Functions of Several Variables
 Functions of Two Variables (MIT OCW).
§14.2: Limits and Continuity.
Week 2:
Jul.1-5		 6 §14.3: Partial Derivatives.
§14.4: Tangent Planes and Linear Approximations.
7 §14.5: The Chain Rule.
8 §14.6: Directional Derivatives and the Gradient Vector.
9 §14.7: Maximum and Minimum Values.
10 §14.8: Lagrange Multipliers.
Week 3:
Jul.8-12		 11
Chapter 15. Multiple Integrals
§15.1: Double Integrals over Rectangles.
§15.2: Iterated Integrals.
12 §15.3: Double Integrals over General Regions.
§15.5: Applications of Double Integrals.
13 §10.3: Polar Coordinates.
§15.4: Double Integrals in Polar Coordinates.
14 §15.10: Change of Variables in Multiple Integrals.
15 §15.7: Triple Integrals.
Week 4:
Jul.15-19		 16
Chapter 16. Vector Calculus
§16.1: Vector Fields.
17 §16.2: Line Integrals.
18 §16.3: The Fundamental Theorem for Line Integrals.
19 §16.4: Green's Theorem.
20 §16.5: Curl and Divergence.
Week 5:
Jul.22-26		 21
Chapter 11. Infinite Sequences and Series
§11.1: Sequences.
22 §11.2: Series.
23 §11.3: The Integral Test (Up to Estimating the Sum of a Series).
§11.4: The Comparison Tests (Up to Estimating Sums).
24 §11.5: Alternating Series.
§11.6: Absolute Convergence and the Ratio and Root Tests.
25 §11.7: Strategy for Testing Series.
§11.8: Power Series.
Week 6:
Jul.29-
Aug.3		 26 §11.9: Representations of Functions as Power Series.
27 §11.10: Taylor and Maclaurin Series.
28 §11.11: Applications of Taylor Polynomials.
29
FINAL EXAM

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