Calculus I

Catalogue Description: This is the first course in calculus and analytic geometry. It explores various characteristics and equations of conics and covers techniques of differentiation for algebraic and trigonometric functions. It also includes an introduction to the Fundamental Theorem of Calculus. Technology and writing as appropriate to the discipline will be emphasized throughout the course. The included curriculum is broken into 4 units

Students the Course is Expected to Serve: This course is intended for students who plan to major in business, mathematics, engineering, and science.

Course Objectives:

1. Discuss the equations and characteristics of various conics.
2. Understand the concepts of a limit, continuity, and differentiability.
3. Apply the sum, product, quotient, and chain rules of differentiation.
4. Differentiate algebraic and trigonometric functions.
5. Apply the concepts of differential calculus to contextual (real-world) situations.
6. Understand the definition and basic properties of the Riemann sum.
7. Understand the concept of an antiderivative and its role in the Fundamental Theorem of Calculus.

Student Learning Outcomes: Upon satisfactory completion of the course, students will be able to:
A. Estimate limits and derivatives graphically and by using tables of values.
B. Calculate limits of functions algebraically.
C. Calculate derivatives of functions using the definition of a derivative.
D. Identify points where a function fails to be continuous or differentiable.
E. Calculate derivatives of functions using the sum, product, quotient and chain rules.
F. Determine derivatives of functions using implicit differentiation.
G. Determine the equation of a tangent line to the graph of a function.
H. Approximate changes in a function using differentials.
I. Apply the Intermediate, Mean, and Extreme Value Theorems to a function defined on a closed and bounded interval.
J. Apply derivatives to problems involving optimization and related rates.
K. Analyze the behavior of functions and their graphs using first and second derivatives (e.g., determine local and absolute extrema, concavity, and inflection points).
L. Determine antiderivatives of functions.
M. Apply the concepts of first and second derivatives and antiderivatives to motion problems
N. Calculate a Riemann sum of a function on a closed interval.
O. Evaluate definite integrals by using the Fundamental Theorem of Calculus.

Topical Outline: The course will cover the following topics:

1. Review and Preview
2. Functions, Graphs, Limits, and Continuity
3. The Derivative
4. Derivatives and Graphs
5. The Integral
6. Applications of Definite Integrals

A more detailed breakdown of topics and curriculum outline can be found here.