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

Completion of Math D with grade 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”.)

Completion of Math 12 strongly recommended, especially for students who have not recently taken Math. D

9b. Catalog Description:

Introduction to differential and integral calculus, with particular emphasis on applications in the fields of business, economics, and social sciences. Includes: concepts of a function, limits, derivatives, integrals of polynomial, exponential and logarithmic functions, optimization problems, and calculus of functions of more than one variable. Not open to those with credit for Math. 30. (CAN MATH 34)

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. Construct functions of various types (linear, quadratic, rational, exponential, logarithmic, and logistic) from real world information.
2. Evaluate limits at a point, at infinity, and compute derivatives using the limit definition.
3. Calculate derivatives of polynomial, rational, radical, exponential, and logarithmic functions using basic derivative rules including product, quotient, and chain rules.
4. Solve business application problems involving demand, cost, revenue, profit, and marginality.
5. Investigate real world functions using derivatives to find such information as optimal points, rates of change, and shape of graph.
6. Solve exponential equations, logarithmic equations and application problems related to exponential growth and decay, as well as logistic and learning curves.
7. Apply integration techniques to determine the area under a curve, determine consumer and producer's surplus, and solve basic differential equations.
8. Investigate antiderivatives to infer formulas for integration, including the substitution technique.
9. Calculate partial derivatives of two variables and use to solve optimization problems in three dimensions.
10. Analyze the meaning of the derivative and the integral in the context of real world situations.

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. Functions and Limits
A. Functions
1. Linear Functions
2. Quadratic Functions
3. Business Applications - demand, cost, revenue, profit, etc.
4. Finding Formulas for Functions
B. Limits
1. Limits at infinity
2. Limits at a point

II. Differentiation
A. Slopes of Tangents
B. Limit definition of the Derivative
C. Rules for Computing Derivatives
D. Marginal Cost, Revenue and Profit

III. Applications of Differentiation
A. Rates of Change
B. Curve Sketching
C. Optimization
D. Rational Functions
E. Percentage Rate of Change

IV. Exponential and Logarithmic Functions
A. Compound Interest
B. Exponential Functions
C. Logarithmic Functions
D. Derivatives of Exponential and Logarithmic Functions
E. Models of Growth

V. Integration
A. Antidifferentiation
B. The Definite Integral
C. Area
D. Integration using Substitution

VI. Applications of Integration
A. Consumer and Producer's Surplus
B. Differential Equations

VII. Differentiation of Functions of More than One Variable
A. Functions of More Than One Variable
B. Partial Derivatives
C. Optimization
D. Constrained Optimization
E. Lagrange Multipliers

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

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

1. Students will read selected topics throughout the course from the textbook. For example, students will read how to construct a revenue function from real world data.
2. A typical homework assignment includes many application problems that the students will read. Example as follows. A rumor about a county official's willingness to accept bribes is circulating. So far, 25,000 of the 300,000 citizens of the county have heard the rumor. Suppose the rumor spreads logistically through the county, and during the next 8 days, 10,000 more citizens will hear the rumor. How many of the county's citizens will have heard the rumor 15 days from now.

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

1. Students will complete homework problems from the textbook on topics throughout the course. Such problems may involve computation, sketching graphs and diagrams, solving equations, applying mathematical concepts, or explaining mathematical ideas.
2. Students will solve application problems in class. For example, students will use the derivative to compute the marginal cost for a real world situation, and write an explanation on what information the marginal cost conveys to the business owner.

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

SECTION D

SECTION E

SECTION F

SECTION G