MCCCD Official Course Competencies:

MAT230  2007 Spring – 2011 Summer II

Calculus with Analytic Geometry II

1.

Evaluate indefinite, definite and improper integrals using various algebraic, trigonometric and numerical techniques. (I, II)

2.

Solve applied problems taken from the sciences using integration. (I, II)

3.

Analyze curves in the plane described using parametric and polar equations. (III)

4.

Define, classify, and analyze conic sections. (III)

5.

Determine the convergence or divergence of sequences, series of constants, and power series. (IV, V)

6.

Compute polynomial approximation and power series representation of elementary functions using derivatives and integrals. (V)

7.

Compare alternate solution strategies, including technology. (I, II, III, IV, V)

8.

Communicate process and results in written and verbal formats. (I, II, III, IV, V)

9.

Justify and interpret solutions to application problems. (I, II, III, IV, V)

MCCCD Official Course Outline:

MAT230  2007 Spring – 2011 Summer II

Calculus with Analytic Geometry II

I. Techniques of Integration

A. Integration by parts

B. Trigonometric integrals

C. Trigonometric substitution

D. Integration of rational functions by partial fractions

E. Integration tables

F. Improper Integrals

II. Applications of Integral Calculus

A. Determination of volumes

B. Physical and other sciences

III. Elements of Analytic Geometry

A. Parametric equations

B. Polar equations

C. Conic sections

IV. Sequences and Series

A. Basic Definitions

1. Geometric sequences and series

2. Telescoping series

3. P-series

4. Alternating series

B. Various tests for Conditional or Absolute Convergence

1. Divergence test

2. Integral test

3. Direct and limit comparison tests

4. Alternating series test

5. Ratio test

V. Power Series

A. Interval of convergence

B. Polynomial approximations

C. Power series representations of functions

D. Differentiation and integration of power series