CALIFORNIA STATE UNIVERSITY, SACRAMENTO Department of Mathematics and Statistics SYLLABUS Math 32: Calculus III Prerequisites: Math 31 This is the third semester of the three semester calculus sequence for students majoring in Mathematics, Physical Science, Engineering, and Computer Science. It provides an introduction to the calculus of functions of several variables and to elementary vector analysis. OUTLINE: I. Three-Dimensional Analytic Geometry 3 1/2 Weeks and Vectors a. Three-dimensional coordinate system b. Vectors c. Dot and cross products d. Vector equations of lines and planes e. Vector functions of one variable and space curves f. Arc length and curvature g. Applications to motion in space h. Cylindrical and spherical coordinates II. Differentiation of Functions of Several 4 Weeks Variables a. Functions of several variables b. Limits and continuity c. Partial derivatives d. Differentiability and tangent plane e. Chain rule f. Directional derivative and gradient g. Extreme values h. Other techniques such as Lagrange multipliers III. Multiple Integrals 3 1/2 Weeks a. Double and triple integrals b. Iterated integrals c. Integrals in polar, cylindrical, and spherical coordinates d. Geometrical and physical applications Math 32 Syllabus, Page 2IV. Vector analysis 3 Weeks a. Scalar and vector fields b. Divergence and curl c. Line integrals d. Conservative fields application to work and conservation of energy e. Green's theorem Stokes' theorem and divergence theorem in the plane Reviewed Spring