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.

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