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 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 differential and integral calculus. Content includes limits, continuity, differentiation and integration of algebraic, trigonometric, exponential, logarithmic and other transcendental functions; as well as application problems. (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 using limit laws and L'Hospital's Rule;
2. determine whether or not a function is continuous at a point and on an interval;
3. calculate the derivative of algebraic, trigonometric, exponential, logarithmic, and other transcendental functions using derivates rules;
4. use the derivative in various applications, such as calculating velocity, acceleration, the slope of a tangent line, optimization, curve sketching, and related rates;
5. evaluate anti-derivatives and definite integrals using the Fundamental Theorem of Calculus;
6. demonstrate improved algebra and trigonometry skills by applying these skills to solve 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
B. Graphing Functions, Including Shifting and Scaling
C. Inverse Functions
D. Exponential and Logarithmic Functions

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. Derivatives
A. Definition of the Derivative of a Function
B. Differentiation Formulas
C. Derivatives of Functions
1. Polynomials
2. Exponential Functions
3. Trigonometric Functions
4. Inverse Trigonometric Functions
5. Logarithmic Functions
E. Chain Rule
F. Implicit Differentiation
G. Higher Order Derivatives
H. Related Rates
I. Differentials: Linear and Quadratic Approximations

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 Infinity; Horizontal Asymptotes
F. Curve Sketching
G. Applied Maximum and Minimum Problems
H. Indeterminate forms and L'Hospital's Rule
I. Newton's Method
J. Antiderivatives

V. Integration
A. Summation Notation
B. Area under a Curve
C. The Definite Integral
D. Fundamental Theorem of Calculus

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 the first and second derivative of a function influence the graph of the function.

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. Write a report on the historical and mathematical origins of l'Hospital's rule.

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