Anne Arundel Community College

MAT 191: Calculus & Analytic Geometry 1


CATALOG DESCRIPTION:
A first course in calculus. Topics include limits and continuity; the derivative and its applications; derivatives of powers, products, quotients, implicit functions and trigonometric functions; chain rule; Mean Value Theorem; differentials; the integral; Fundamental Theorem of Integral Calculus; derivatives and integrals of exponential, logarithmic and inverse trigonometric functions; L'Hospital's Rule.

Prerequisite: MAT 142 or MAT 151 or equivalent, or completion of three years of high school mathematics including trigonometry and achieving an appropriate score prescribed by the Mathematics department on the mathematics part of the ACT or SAT or scoring at an appropriate level on the Mathematics Placement Test.

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

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

COURSE OUTLINE:
Limits of Functions:
  • Tangent and Velocity Problems
  • The Limit of a Function
  • The Definition of Limit
  • Continuity

Derivatives:
  • Derivatives and Rates of Change
  • The Derivative as a Function
  • Differentiation
  • Derivatives of Trigonometric Functions
  • The Chain Rule
  • Implicit Differentiation
  • Rates of Change in the Natural and Social Sciences
  • Linear Approximations and Differentials

Applications of the Derivative:
  • Related Rates
  • Maximum and Minimum
  • The Mean Value Theorem
  • How Derivatives Affect the Shape of a Graph
  • Limits at Infinity; Horizontal Asymptotes
  • Curve Sketching with Calculus and Calculators
  • Optimization Problems
  • Newton's Method

Integrals:
  • Antiderivatives
  • Areas and Distances
  • The Definite Integral
  • The Fundamental Theorem of Calculus
  • Indefinite Integrals and the Net Change Theorem
  • The Substitution Rule

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions:
  • Inverse Functions
  • Exponential and Logarithmic Functions
  • Exponential Growth and Decay
  • Inverse Trigonometric Functions
  • Hyperbolic Functions
  • Indeterminate Forms and L'Hospital's Rule

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