MATH 283

Calculus


5.0 hours lecture per week.
Associate Degree Applicable.
Prerequisite: MATH 265B (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


Course Outline

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