MCCCD Program Description

Calculus with Analytic Geometry II

Course: MAT230

First Term: 2011 Fall

Lecture 5.0 Credit(s) 5.0 Period(s) 5.0 Load
Subject Type: Academic
Load Formula: S

Description: Techniques of integration for both proper and improper integrals with applications to the physical and social sciences, elements of analytic geometry, and the analysis of sequences and series.

MCCCD Official Course Competencies
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) 10. Perform operations on vectors. (VII) 11. Use vector operations in applied problems. (VII) 12. Use technology when appropriate (IV, V)
MCCCD Official Course Competencies must be coordinated with the content outline so that each major point in the outline serves one or more competencies. MCCCD faculty retains authority in determining the pedagogical approach, methodology, content sequencing, and assessment metrics for student work. Please see individual course syllabi for additional information, including specific course requirements.

MCCCD Official Course Outline
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 2. P-series 3. Alternating series 4. Convergence and absolute convergence B. Tests for convergence 1. A test for divergence 2. p-test 3. Comparison test 4. Limit comparison test 5. Alternating series test 6. Ratio test 7. Root test 8. Integral test C. Power series 1. Definition 2. The ratio test and the radius of convergence 3. Interval of convergence 4. Term-by-term differentiation and integration 5. Taylor and Maclaurin series 6. Taylor polynomials and function approximation VII. Vector spaces A. Basic operations 1. Dot product 2. Cross product 3. Scaler triple product B. Applications 1. Vector projections 2. Geometric applications

MCCCD Governing Board Approval Date: 6/27/2006

All information published is subject to change without notice. Every effort has been made to ensure the accuracy of information presented, but based on the dynamic nature of the curricular process, course and program information is subject to change in order to reflect the most current information available.