MATH 83

Calculus

5.0 hours per week: (4.0 hours lecture, 1.0 hours laboratory).
Associate Degree Applicable.
Prerequisite: MATH 65B (Analytic Geometry and Calculus) or equivalent with a grade of C or better.
Presents a study of differentiation and integration of multiple variable functions, parametric curves in two and three dimensions, optimization, line integrals, and the calculus of vector fields. Specific topics include vector functions, partial derivatives, surfaces, parametric equations, multiple integrals (with rectangular, polar, cylindrical, and spherical coordinates), and vector calculus (including line integrals, flux integrals, Greens Theorem, the Divergence Theorem, and Stokes Theorem). Every topic will be taught geometrically, numerically, and algebraically.
Transfer: CSU; UC

Student Learning Outcomes

By the end of this course, the student will be able to:

1. Make computations and interpretations involving the derivatives of multivariable functions:

· partial derivatives

· gradients

· directional derivatives

· tangent planes

· extrema

· optimization

· graphical interpretation of partial derivatives

2. Make computations and interpretations involving the integrals of multivarible functions:

· rectangular triple integrals

· cylindrical triple integrals

· spherical triple integrals

· graphical interpretation of multiple integrals

3. Make computations and interpretations involving the calculus of vector functions:

· derivatives

· integrals

· an application

· graphical interpretation of vector functions

4. Make computations and interpretations involving the calculus of vector fields:

· divergence

· curl

· line integrals and work

· the fundamental theorem of line integrals

· Green's theorem

· surface integrals and flux

· the divergence theorem

· Stoke's theorem

· graphical interpretation of vector fields