COURSE NUMBER AND TITLE: MATH 2011 Calculus and Analytic Geometry I

CREDIT HOURS: 4

CATALOG DESCRIPTION: An introduction to calculus including limits and continuity, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential, and logarithmic functions, applications of derivatives, and basic integration.

PREREQUISITE(S): MATH 1113 (grade of C or better) or placement.

SUGGESTED TEXT(S):
Calculus, by Salas, Hille, Etgen
Calculus, by Rogawski

COURSE OUTLINE:

1. Continuous Functions and Limits
   • Functions
   • Limits of Functions
   • Calculating Limits Using the Limit Laws
   • Continuity
2. Derivatives and Techniques
   • Tangent Problems
   • Formulas for Obtaining Derivatives
   • The Chain Rule
   • Differentiating Trigonometric Functions, Inverse Trigonometric Functions, Logarithmic Functions, Exponential Functions, and Hyperbolic Functions
   • Implicit Differentiation
3. Applications of Derivatives
   • The Derivative as a rate of Change; Velocity Problems
   • Increasing and Decreasing Functions
   • Local and Absolute Extreme Values
   • Concavity; Points of Inflection
   • Curve Sketching
   • Linear Approximation, Differentials
   • Intermediate Value Theorem
   • Newton-Raphson Approximations
4. Integration
   • Riemann Sums
   • Antiderivatives
   • The u-Substitution Method
   • Definite Integrals
   • The Fundamental Theorem of Integral Calculus
5. Transcendental Functions
   • Logarithmic Functions
   • Exponential Functions
   • Inverse Trigonometric Functions
   • Hyperbolic Sine and Cosine Functions
6. L’Hôpital’s Rule