Loyola University Chicago

Mathematics and Statistics

MATH 162: Calculus II

Credit Hours

4

Prerequisites

MATH 161 with a grade of C- or higher

Description

A continuation of MATH 161. Calculus of logarithmic, exponential, inverse trigonometric functions. Techniques of integration. Applications of integration to topics such as volume, surface area, arc length, center of mass, and work. Numerical sequences and series. Study of power series and the theory of convergence. Taylor's Theorem with remainder.

James Stewart. Calculus, Early Transcendentals (packaged with WebAssign) 8th ed. Cengage Learning

Review of prerequisite Material from MATH 161

Chapter 6. Applications of Integration
    6.1  Area Between Curves
    6.2  Volumes
    6.3  Volumes by Cylindrical Shells
    6.4  Optional: Work
    6.5  Average Value of a Function

Chapter 7: Techniques of Integration
    7.1  Integration by Parts
    7.2  Trigonometric Integrals
    7.3  Trigonometric Substitution
    7.4  Integration of Rational Functions by Partial Fractions
    7.5  Strategy for Integration
    7.6  Integration Using Tables and Computer Algebra Systems
    7.7  Approximate Integration
    7.8  Improper Integrals

Chapter 8: Further Applications of Integration
   Instructor chooses from among these topics
   8.1  Arc Length
   8.2  Area of a Surface of Revolution
   8.3  Applications to Physics and Engineering
   8.4  Applications to Economics and Biology
   8.5  Probability

Chapter 11: Infinite Sequences and Series
   11.1  Sequences
   11.2  Series
   11.3  The Integral Test and Estimates of Sums
   11.4  The Comparison Tests
   11.5  Alternating Series
   11.6  Absolute Convergence and the Ratio and Root Tests
   11.7  Strategy for Testing Series
   11.8  Power Series
   11.9  Representations of Functions as Power Series
   11.10  Taylor and Maclauren Series
   11.11  Optional: Applications of Taylor Polynomials

Chapter 10: Parametric Equations and Polar Coordinates
   10.1  Curves Defined by Parametric Equations
   10.2  Optional: Calculus with Parametric Curves
   10.3  Polar Coordinates
   10.4  Optional: Areas and Lengths in Polar Coordinates
   10.5  Optional: Conic Sections
   10.6  Optional: Conic Sections in Polar Coordinates