Maricopa Community Colleges  MAT231   19966-19975
Official Course Description: MCCCD Approval: 06/27/95
MAT231 19966-19975 LEC 4 Credit(s) 4 Period(s)
Calculus with Analytic Geometry II
Methods of integration, applications of calculus, elements of analytic geometry, improper integrals, sequences and series. May not receive credit for MAT230 and MAT231. Prerequisites: Grade of "C" or better in MAT220, or MAT221, or equivalent.
Go to Competencies    Go to Outline

MCCCD Official Course Competencies:

MAT231   19966-19975 Calculus with Analytic Geometry II
 1. Extend the operations of differentiation and integration to functions and their inverses. (I) 2. Use L'Hospital's rule to evaluate limits having indeterminate form. (II, IV, VII) 3. Use algebraic and numerical techniques for evaluating integrals. (III) 4. Use integration in applied problems taken from the physical and social sciences. (I, V, VI, VII) 5. Determine the convergence or divergence of an improper integral. (IV) 6. Analyze curves in the plane defined using parametric equations. (VI) 7. Analyze curves in the plane defined using polar equations. (VI) 8. Determine the convergence or divergence of sequences and series having numerical terms. (VII) 9. Find a power series representation for a given function and determine its domain. (VII) 10. Extend the operations of differentiation and integration to functions defined by a power series. (VII) 11. Find a polynomial which approximates a given function to a specified degree of accuracy on a specified interval. (VII)
Go to Description    Go to top of Competencies

MCCCD Official Course Outline:

MAT231   19966-19975 Calculus with Analytic Geometry II
I. The Calculus of Invertible Functions
A. Exponential and Logarithmic Functions
1. Application to Exponential Growth/Radioactive Decay
2. Logarithmic Differentiation
B. Inverse Trigonometric Functions
C. Hyperbolic Functions and Their Inverses
II. Limits Involving an Indeterminate Form
A. L'Hospital's Rule and the Forms: 0/0 or oo/oo
B. Indeterminate Products, Differences, and Powers
III. Methods of Integration
A. Integration by Parts
B. Trigonometric Integrals
C. Trigonometric Substitution
D. Integration of Rational Functions by Partial Fractions
E. Rationalizing Substitutions
F. Integration Tables
G. Numerical Techniques
1. Trapezoidal, Midpoint, and Simpson's Rules
2. Infinite Series
IV. Improper Integrals
A. Definitions
B. Evaluation
V. Applications of Integral Calculus
A. Differential Equations
B. Arc Length
C. Physics
D. Economics
VI. Elements of Analytic Geometry
A. Parametric Equations
1. Parametric Equations for a Given Curve
2. The Graph the Curve Defined Using Parametric Equations
3. Applications
B. Conic Sections
1. In Cartesian Coordinates
2. Applications
C. Polar Equations
1. Finding a Polar Equation from a Cartesian Equation
2. Graphing
3. Applications
D. Conic Sections in Polar Coordinates
VII. Sequences and Series
A. Basic Definitions
1. Geometric 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 Ration Test and the Radius of Convergence
3. Interval of Convergence
4. Term-by-Term Differentiation and Integration
5. Taylor and Maclaurin Series
6. The Binomial Series
7. Taylor Polynomials and Function Approximation
Go to Description    Go to top of Competencies    Go to top of Outline