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The following is a standard syllabus for Math 13. If you wish to review some or all of the material, we provide three methods.

First, the syllabus closely follows portions of
Stewart's*Calculus*textbook chapters 12-16, which
are marked on the syllabus
below.

Second, we provide links to Khan Academy (KA) videos relevant to the material on that part of the syllabus.

Third, as practice problems are always useful, in addition to the problems available in Stewart and at Khan Academy, we provide practice exams.

**a. Introduction to integration, iterated integrals
(Stewart 15.1,
15.2)**

- Khan Academy
- All sections of Double integrals

**b. Fubini's Theorem, Integration over non-rectangular
regions (Stewart
15.2-15.3)**

**c. Integration in polar coordinates (Stewart
15.4)**

**d. Applications of double integrals (Stewart 15.5)**

**e. Triple integrals (Stewart
15.7)**

- Khan Academy
- All sections of Triple Integrals

**f. Cylindrical Coordinates (Stewart 15.8)**

**g. Spherical coordinates (Stewart
15.9)**

- Khan Academy: see Sample Math 8 Syllabus for detailed topics and links to videos.

- Khan Academy: see Sample Math 8 Syllabus for detailed topics and links to videos.

- Khan Academy: see Sample Math 8 Syllabus for detailed topics and links to videos.

**a. Line integrals of scalar functions (Stewart 16.2)**

- Khan Academy
- All sections of Line integrals for scalar functions

**b. Vector fields (Stewart 16.1)**

**c. Line integrals of vector fields (Stewart 16.2)**

- Khan Academy
- All sections of Line integrals in vector fields

**d. The Fundamental Theorem of Calculus for line integrals
(Stewart
16.3)**

**e. Green's Theorem (Stewart 16.4)**

- Khan Academy
- All sections of Green's Theorem

**f. Curl and Divergence (Stewart 16.5)**

- Khan Academy
- All sections of Partial Derivatives, Gradient, Curl and Divergence

**a. Parametrizing surfaces, tangent planes
(Stewart
16.6)**

- Khan Academy
- All sections of Parametrizing a surface

**b. Surface Area (Stewart 16.6,
15.6)**

**c. Surface Integrals of Scalar Functions
(Stewart 16.7)**

- Khan Academy
- All sections of Surface Integrals

**d. Surface integrals of vector fields (Stewart 16.7)**

**e. The Divergence Theorem (Stewart 16.9)**

- Khan Academy
- All sections of the Divergence Theorem

**f. Stokes' Theorem (Stewart 16.8)**

- Khan Academy
- All sections of Stokes' Theorem Intuition and Application
- All sections of Proof of Stokes' Theorem

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