7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)

Completion of Math. 30 with a grade of "C" or better

7b. Co-requisite(s):  (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)

7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course.  Also known as “Course Advisory”.)

9b. Catalog Description:

Continuation of Math. 30. Content includes techniques of integration, improper integrals, applications of integration, infinite series, parametric equations and polar coordinates. (CAN MATH 20) (With Math. 30, CAN MATH SEQ B) (With Math. 30 & 32, CAN MATH SEQ C)

10. Student Performance Outcomes: (Outcomes for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Outcomes must be related to items listed in Section 11.)

1. calculate anti-derivatives of algebraic, trigonometric, inverse and transcendental functions using appropriate integration techniques;
2. apply the techniques of integration to reduce an integral to one listed in integral tables and then use the tables to find anti-derivatives;
3. use integration, differentiation, and inverse functions to solve applied problems;
4. solve integration and differentiation problems using parametric equations and/or polar coordinates;
5. demonstrate knowledge and theory of infinite series by applying appropriate theorems to determine convergence and divergence;
6. use infinite series to solve appropriate problems in mathematics and the sciences.

11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

I. Integrals
A. Review of the Definite Integral and the Fundamental Theorem of Calculus
B. Net Change Theorem
C. Substitutions in the Definite Integral
D. Numerical Integration
II. Techniques of Integration
A. Basic Substitutions
B. Integration by Parts
C. Trigonometric Integrals
D. Trigonometric Substitutions
E. Integration of Rational Functions by Partial Fractions
F. Rationalizing Substitutions
G. Strategy for Integrations
H. Using Tables of Integrals and Computer Algebra Systems
I. Numerical Integration
J. Improper Integrals
III. Applications of Integration
A. Area between curves
B. Volumes
C. Differential Equations
D. Arc Length
E. Area of a Surface of Revolution
F. Moments and Centers of Mass
G. Work
H. Average Value of a Function
I. Hydrostatic Pressure and Force
IV. Parametric Equations and Polar Coordinates
A. Curves Defined by Parametric Equations
B. Tangents and Area
C. Arc Length and Surface Area
D. Polar Coordinates
E. Areas and Lengths in Polar Coordinates
F. Conic Sections
G. Conic Sections in Polar Coordinates
V. Infinite Sequences and Series
A. Sequences
B. Series
C. Integral Test and Estimation of Sums
D. Comparison Tests
E. Alternating Series
F. Absolute Convergence and the Ratio and Root Tests
G. Strategy for Testing Series
H. Power Series
I. Representation of Functions as Power Series
J. Taylor and Maclaurin Series
K. Binomial Series
L. Application of Taylor Polynomials

12. Typical Assignments: (List types of assignments, including library assignments.)

a. Reading Assignments: (Submit at least 2 examples)

Read selected topics throughout the course from the textbook. For example, how to calculate the volume of a solid of revolution.

Read supplementary handouts on topics such as Newton, Liebniz, and the development of Calculus.

b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

1. Students will write a report on Newton's discovery of the binomial series.
2. Complete homework problems from the textbook on topics throughout the course.

c. Other (Terms projects, research papers, portfolios, etc.)

SECTION D

SECTION E

SECTION F

SECTION G