Mathematics 5.3 – Multivariable Calculus – Syllabus

4 hours; 4 credits

The numbers after the headings refer to the section numbers in Multivariable Calculus (2^nd edition) by James Stewart.

The order in which these topics are to be presented is left to the instructor’s discretion. Optional topics are indicated with a *.

1. Vectors 11.1 – 11.5, *11.6, 11.7 – 11.9

three-dimensional coordinate systems; spheres (11.1),

introduction to vectors (11.2)

dot product; projections (11.3)

cross product (11.4)

*quadric surfaces (11.6)

vector functions; vector calculus (11.7)

arc length (11.8)

*curvature; unit normal vectors (11.8)

motion in space; velocity and acceleration (11.9)

2. Partial Derivatives 12.1 – 12.8

functions of two or more variables (12.1)

limits and continuity (12.2)

partial derivatives (12.3)

tangent planes; differentials (12.4)

chain rule; implicit differentiation (12.5)

directional derivatives; gradients (12.6)

maxima and minima; saddle points (12.7)

Lagrange multipliers (12.8)

3. Multiple Integrals 13.1 – 13.4, *13.5 – 13.6, 13.7 – 13.8

double integrals over rectangles; volumes (13.1)

iterated integrals (13.2)

double integrals over general regions (13.3)

double integrals in polar coordinates (13.4)

*moments of inertia; surface area (13.5, 13.6)

triple integrals (13.7)

triple integrals in cylindrical and spherical coordinates (13.8)

4. Topics in Vector Calculus 14.1 – 14.4, *14.5 – 14.9