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

Completion of Math. 8 and either Math. 12 or Math. 29 or equivalent high school classes with grades of "C" or better, or placement by matriculation assessment process

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:

Introduction to analytic geometry, limits, continuity, differentiation and integration of algebraic, trigonometric, and transcendental functions, as well as many application problems; a limited number of problems will be solved utilizing appropriate computer software. No programming knowledge is required. The 5-unit option includes instruction on the use of math power tool(s). Specific graphics calculator required for course will be indicated in class schedule and purchased by student. (CAN MATH 18) (With Math 31, CAN MATH SEQ B) (With Math 31 & 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. evaluate the limit of a function;
2. determine whether or not a function is continuous at a point or on
an inteval;
3. calculate the derivative of algebraic and trigonometric functions,
using derivates rules;
4. use the derivative in various applications, such as calculating
velocity, acceleration, the slope of a tangent line, marginal
cost, marginal revenue;
5. use derivatives and limits to sketch curves;
6. evaluate anti-derivatives and definite integrals using the
Fundamental Theorem of Calculus and "u substitutions" as
appropriate;
7. use integration to determine the area between curves, volumes of
solids of revolution, work, and average value of a function; and
8. algebra and trigonometry skills will be measurable better and will
be demonstrated through the application of these skills to solve
complex calculus problems.

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. Review
A. Algebra of Functions, Including Composition and Inverse
Functions
B. Graphing Functions, Including Shifting and Scaling
II. Limits and Rates of Change
A. Discussion of the Tangent and Velocity Problems
B. Limit of a Function
C. Calculating Limits using Properties of Limits
D. Formal Definition of a Limit and delta-Epsilon Proofs
E. Continuity
F. Applications
1. tangents
2. velocities
3. other
III. Deriviatives
A. Definition of the Derivative of a Function
B. Differentiation Formulas
C. Rates of Change in the Natural and Social Sciences
(Optional)
D. Derivatives of the Trigonometric Functions
E. Chain Rule
F. Implicit Differentiation
G. Higher Order Derivatives
H. Related Rates
I. Differentials: Linear and Quadratic Approximations
J. Newton''s Method
IV. Curve Sketching and Additional Applications
A. Maximum and Minimum Values of a Function
B. Mean Value Theorem
C. Monotonic Functions and the First Derivative Test
D. Concavity and Points of Inflection
E. Limits at Infinite; Horizontal Asymptotes
F. Curve Sketching
G. Applied Maximum and Minimum Problems
H. Application to Economics (Optional)
I. Antiderivatives
V. Integration
A. Summation Notation
B. Area under a Curve
C. The Definite Integral
D. Fundamental Theorem of Calculus
E. Subsitution Rule
VI. Applications of Integration
A. Area between Curves
B. Volume
1. volumes by disks and washers
2. volumes by the slicing method
3. volumes by cylindrical shells
C. Work
D. Average Value of a Function

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