Math 52 Course Schedule
Spring 2024
Below is the tentative schedule, which may be adjusted as necessary.
Week 1: (April 1-5)
- § 5.1 Double integrals over rectangular regions and volume under a graph; Fubini Theorem on a rectangle (Thm 5.2) and Iterated integrals;
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§ 5.2: Double integrals over (bounded) general regions; Fubini Theorem (Thm 5.4); applications: area, average of a function.
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§ 5.2: Double integrals over general regions; Changing the order of integration
Week 2: (April 8-12)
- § 5.2 Applications: area and average of a function;
mass and center of mass in dimensions 1 and 2 (§ 5.6, Eg 5.55 - 5.59).
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§ 5.3. Polar coordinates; Applications: area between two curves in polar coordinates, volume of solids in polar coordinates.
- § 5.2: Improper integrals and Fubini Theorems (Thms 5.6 and 5.7). Applications to probability (§ 5.1, Eg 5.22).
Week 3: (April 15-19)
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§ 5.4: Triple integrals
- § 5.5: Cylindrical coordinates and Spherical coordinates
- § 5.6: Center of mass and moment of inertia in 3D (p. 601); Pappus Theorem and Parallel Axis Theorem
Week 4: (April 22-26)
- § 5.5-5.6: Applications
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§ 5.7: Linear functions and integration; please review the following topics from the Math 51 textbook, freely available
online:
Linear functions (Math 51: Chapter 13)
Area formula (Math 51: Remark 18.2.6 applied to arbitrary region.)
Paths in R3 and partial derivatives (Math 51: Chapter 9)
Derivative and linear approximation (Math 51: Thm 13.5.8)
- § 5.7: Change of variables in multiple integrals (Thm 5.14 and Thm 5.15) and 1-1 transformations (p. 611)
Midterm 1: Thursday, April 25, 8-10pm, room Hewlett 201.
Material covered: § 5.1-5.6.
Review session: Wednesday, April 24, 5:30-7:30pm, room 380X.
Week 5: (April 29-May 3)
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§ 6.1 Vector fields; Gradient vector fields and conservative vector fields
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§ 6.1: Conservative vector fields and finding a potential function (§ 6.3, Eg. 6.31);
§ 6.2: Scalar line integrals
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§ 6.2: Vector line integrals and work along a path (Examples 6.18, 6.20); Properties of line integrals
Week 6: (May 6-10)
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§ 6.3: Fundamental Theorem for line integrals (Thm 6.7)
- § 6.3: Conservative vector fields; path independence (Thm 6.8); finding a potential function via line integrals (Eg 6.33).
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§ 6.4: Green's Theorem (circulation form, Thm 6.12 and extended form, p. 726); Orientation of boundary; Calculating areas of regions using certain line integrals along their boundary. (Consequence of Green's Theorem)
Week 7: (May 13-17)
- § 6.3: Connected and simply connected regions; Conservative vector fields and the cross partial property on simply connected regions; § 6.4: Green's Theorem (continued)
- § 6.2: Flux across a curve in R2 (Thm 6.6 and Eg 6.24); § 6.4: Flux form of Green's Theorem
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§ 6.5: Divergence and Curl in R3;
Midterm 2: Thursday, May 16, 8-10pm, room Hewlett 201.
Material covered: § 5.7 and § 6.1-6.4 (Green's Thm, circulation form and Green’s Thm on General Regions).
Note: Flux across a curve and Flux form of Green's Thm is NOT included in the material on midterm.
Review session: Wednesday, May 15, 5:30-7:30pm, room 380X.
Week 8: (May 20-24)
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§ 6.6: Parametric surfaces (Eg 6.58 - 6.61); orientation of a surface in R3
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§ 6.6: Surface integrals: Scalar Surface integrals (Eg 6.65 - 6.68)
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§ 6.6: Vector Surface Integrals (Defn 6.20); flux across a surface.
Week 9: (May 29-31) No class May 27 (Memorial Day)
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§ 6.7: Stokes Theorem (Thm 6.19); Curl F = 0 implies integral over closed surface is zero.
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§ 6.8: Divergence theorem (Thm 6.20).
Week 10: (June 3-5)
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Stokes theorem vs Green's theorem and Divergence theorem
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Review.