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 or equivalent 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. Applications of the definite integral; calculus of transcendental functions and techniques of integration, finite series, plane curves, polar coordinates, and conic sections. (CAN MATH 20) (With Math 30, CAN MATH SEQ B) (With Math 30 & 31, 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. demonstrate knowledge of inverse functions by graphing functions
and their inverses, and solving exponential, logarithmic, and
trigonometric equations;
2. calculate derivatives and anti-derivatives of trigonometric,
logarithmic, exponential and algebraic functions and their inverses;
3. apply the techniques of integration to reduce an integral to one
listed in integral tables and then use the tables to find
anti-derivatives;
4. use integration, differentiation, and inverse functions to solve
problems in the physical and biological sciences as well as in
business and economics;
5. solve integration and differentiation problems using parametric
equations and/or polar coordinates;
6. evaluate limits of indetermine forms using l''Hospital''s rule;
7. demonstrate knowledge and theory of infinite series by applying
appropriate theorems to determine convergence and divergence; and
8. 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. Calculus of Transcendental Functions
A. Exponential Functions and Their Derivatives
B. Logarithmic Functions
C. Derivatives of Logarithmic Functions
D. Exponential Growth and Decay
E. Inverse Trigonometric Functions
F. Hyperbolic Functions
G. Indeterminate Forms and l''Hospital''s Rule
II. Techniques of Integration
A. Integration by Parts
B. Trigonometric Integrals
C. Trigonometric Substitutions
D. Integration of Rational Functions by Partial Fractions
E. Rationalizing Substitutions
F. Strategy for Integrations
G. Using Tables of Integrals and Computer Algebra Systems
H. Numerical Integration
I. Improper Integrals
III. Applications of Integration
A. Differential Equations
B. Arc Length
C. Area of a Surface of Revolution
D. Moments and Centers of Mass
E. Hydrostatic Pressure and Force
F. Applications to Economics and Biology
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: (Credit courses require two hours of independent work outside of class per unit of credit for each lecture hour. List types of assignments, including library assignments.)

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

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

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

SECTION D

SECTION E

SECTION F

SECTION G