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Dartmouth Mathematics Placement System

## Syllabus: Math 13

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'sCalculustextbook 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.

### 1. Iterated Integrals

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

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)

f. Cylindrical Coordinates (Stewart 15.8)

g. Spherical coordinates (Stewart 15.9)

### 6. Line Integrals

a. Line integrals of scalar functions (Stewart 16.2)

b. Vector fields (Stewart 16.1)

c. Line integrals of vector fields (Stewart 16.2)

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

e. Green's Theorem (Stewart 16.4)

f. Curl and Divergence (Stewart 16.5)

### 7. Surface Integrals, Divergence and Stokes' Theorems

a. Parametrizing surfaces, tangent planes (Stewart 16.6)

b. Surface Area (Stewart 16.6, 15.6)

c. Surface Integrals of Scalar Functions (Stewart 16.7)

d. Surface integrals of vector fields (Stewart 16.7)

e. The Divergence Theorem (Stewart 16.9)

f. Stokes' Theorem (Stewart 16.8)