Standard syllabus
Calculus III · Undergraduate · Math
Topics
Vectors and vector functions
- Vectors in two and three dimensions; dot product, projections, and work
- Cross product, lines and planes in space, and vector-valued functions
Partial derivatives and optimization
- Functions of several variables; limits and continuity in R^n
- Partial derivatives, gradients, and directional derivatives
- Tangent planes, linearization, and the multivariable chain rule
- Lagrange multipliers and constrained optimization
Multiple integrals
- Double integrals over rectangles and general regions in the plane
- Double integrals in polar coordinates; changing the order of integration
- Triple integrals in rectangular, cylindrical, and spherical coordinates
- Change of variables in multiple integrals and the Jacobian determinant
Vector calculus
- Vector fields, line integrals, and circulation
- Fundamental theorem for line integrals; conservative fields and potential functions
- Green's theorem in the plane; curl and divergence (introduction)
- Surface integrals; flux and the divergence theorem (introduction)
- Stokes' theorem (introduction) and connections among the major theorems
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