Anne Arundel Community College

MAT 192: Calculus & Analytic Geometry 2


CATALOG DESCRIPTION:
A second course in calculus. Topics include applications of definite integrals; techniques of integration and numerical integration; improper integrals; separable differential equations; infinite sequences and series; polar coordinates; and parametric equations.

Prerequisite: MAT 191 or equivalent.

LEARNING OBJECTIVES:
Upon completion of this course, the student will be able to:
  1. Use definite integral to find the area, volume, work, arc-length, surface area, etc.
  2. Use advanced techniques of integration such as integration by parts and integration by partial fractions.
  3. Solve separable differential equations, including applications.
  4. Approximate definite integrals numerically and analyze the error.
  5. Determine the convergence or divergence of improper integrals, infinite sequences and infinite series.
  6. Find Taylor Polynomials and apply them to finding approximations.
  7. Extend the concepts of calculus to curves in parametric and polar forms.
  8. Demonstrate applications of the derivatives and integrals referred to in (g) above.
  9. Solve problems numerically, graphically and algebraically.

COURSE OUTLINE:
Review of Calculus I and Introduction to Calculus II:
Applications of Definite Integral:
  • Areas Between Curves
  • Volumes
  • Volumes by Cylindrical Shells
  • Work
  • Average Value of a Function

Techniques of Integration:
  • Integration by Parts
  • Trigonometric Integrals
  • Trigonometric Substitutions
  • Integration of Rational Functions by Partial Fractions
  • Integration Using Tables and Computer Algebra Systems
  • Approximate Integration and Error Analysis
  • Improper Integrals

Further Applications of Integration and Differential Equations:
  • Arc Length
  • Surface Area
  • Differential Equations, Separable Equations, and Exponential Growth and Decay

Infinite Series:
  • Sequences
  • Series
  • The Integral Test and Estimates of Sums
  • The Comparison Tests
  • Alternating Series
  • Absolute Convergence and the Ratio and Root Tests
  • Strategy for Testing Series
  • Power Series
  • Representation of Functions as Power Series
  • Taylor and Maclaurin Series
  • Applications of Taylor Polynomials

Parametric Equations and Polar Coordinates:
  • Parametric Equations
  • Calculus and Parametric Curves
  • Polar Coordinates
  • Areas and Lengths in Polar Coordinates

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