Anne Arundel Community College

MAT 230: Elementary Calculus


CATALOG DESCRIPTION:
Basic concepts of calculus with applications to business and social sciences. Topics include limits, continuity, differentiation and integration of polynomial, rational, exponential and logarithmic functions; maxima and minima; curve sketching; and applications of integration.

Prerequisite: MAT 121, MAT 131, MAT 151 or equivalent.

Note: Credit is not given for both MAT 230 and MAT 122 or MAT 230 and MAT 191.

LEARNING OBJECTIVES:
Upon completion of this course, the student will be able to:
  1. Find limits of functions algebraically, numerically, and/or graphically and interpret these limits.
  2. Perform differentiation of functions algebraically, numerically and graphically.
  3. Analyze graphs and behaviors of functions with regard to rate of change and concavity.
  4. Solve problems from business and the social sciences that involve rates of change.
  5. Find indefinite integrals.
  6. Evaluate definite integrals.

COURSE OUTLINE:
Functions, Graphs, and Models:
  • Graphs and Equations
  • Functions and Models
  • Finding Domain and Range
  • Slope and Linear Functions
  • Nonlinear Functions and Models

Differentiation:
  • Limits: Numerically and Graphically
  • Algebraic Limits and Continuity
  • Average Rates of Change
  • Differentiation Using Limits of Difference Quotients
  • Differentiation Techniques: The Power and Sum-Difference Rules
  • Differentiation Techniques: The Product and Quotient Rules
  • The Chain Rule
  • Higher-Order Derivatives

Applications of Differentiation:
  • Using 1st Derivatives to Find Maximum and Minimum Values Sketch Graphs
  • Using 2nd Derivatives to Find Maximum and Minimum Values Sketch Graphs
  • Graph Sketching: Asymptotes and Rational Functions
  • Using Derivatives to Find Absolute Maximum and Minimum Values
  • Maximum-Minimum Problems: Business and Economic Applications
  • Marginals and Differentials
  • Implicit Differentiation and Related Rates

Exponential and Logarithmic Functions:
  • Exponential Functions and Their Derivatives
  • Logarithmic Functions and Their Derivatives
  • Applications: The Uninhibited Growth Model, (dP)/(dt)=kP
  • Applications: Decay
  • The Derivative of ax and loga x
  • An Economics Application: Elasticity of Demand

Integration:
  • Area and Riemann Sums
  • Area, Antiderivatives and Integrals
  • The Fundamental Theorem of Calculus
  • Properties of Definite Integrals
  • Integration Techniques: Substitution
  • Consumer's and Producer's Surplus
  • Differential Equations

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