MATH 21C: Calculus and Analytic Geometry, Spring quarter 2002:

Preliminary Syllabus

We will use the book `Calculus, early transcendentals' by J. Stewart. The following syllabus is only a rough outline (we may occasionally skip or add some material, or we may move slower or faster depending on how the class goes)

Lec. 1: Sec 10.1: Curves defined by parametric equations.

Lec. 2: Sec 10.2: Tangents and areas for parametric curves.

Lec. 3: Sec 12.1,12.2: Three-dimensional coordinate systems; vectors.

Lec. 5: Sec 12.3: The dot product, projections and components.

Lec. 6: Sec 12.4: The cross product.

Lec. 7: Sec 12.5: Equations of lines and planes.

Lec. 8-9: Sec 13.1-4 vector functions, space curves, arc length

Lec. 10: Sec 14.1: Functions of several variables; level curves.

Lec. 11: Sec 14.2: Limit and continuity.

Lec. 12: Sec 14.3: Partial derivatives.

Lec. 13: Sec 14.4: Tangent planes and linear approximations.

Lec. 14: Sec 14.5: Chain rule (without implicit differentiation).

Lec. 15: Sec 14.6: Directional derivatives and the gradient vector.

Lec. 16: Sec 14.7: Local Maximum and minimum values.

Lec. 17: Sec 14.7: Absolute Maximum and minimum values.

Lec. 18: Sec 14.8: Lagrange multipliers.

Lec. 19: Sec 15.1: Double integrals over rectangles.

Lec. 20: Sec 15.2: Iterated integrals.

Lec. 21: Sec 15.3: Double integrals over general regions.

Lec. 22: Sec 15.4: Double integrals in polar coordinates.

Lec. 23: Sec 15.5/6: Applications of double integrals

Lec. 24: Sec 15.7: Triple integrals.

Lec. 25: Sec.12.7: Cylindrical and spherical coordinates

Lec. 26: Sec. 15.8: Triple integrals in cylindrical and spherical coordinates