Loyola University Chicago

Mathematics and Statistics

MATH 162: Calculus II

Credit Hours

4

Prerequisites

MATH 161

Description

A continuation of MATH 161. Calculus of logarithmic, exponential, inverse trigonometric, and hyperbolic functions. Techniques of integration. Applications of integration to 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.

Textbook

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

Common Syllabus for MATH 162

Review. Prerequisite Material from MATH 161 [1 Week]
    Rapid review of differentiation rules. 
    More detailed review of integration (Ch. 5): areas and distances; the definite integral; the fundamental theorem of calculus. 

Chapter 6. Applications of Integration  [1.5 weeks; 2 weeks if Section 6.4 is covered] 
 
  6.1  Area Between Curves
    6.2  Volumes
    6.3  Volumes by Cylindrical Shells
    6.4  Optional: Work ( This Sections could be covered with Chapter 8)
    6.5  Average Value of a Function

Chapter 7: Techniques of Integration [3 weeks]
    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 11: Infinite Sequences and Series [4 weeks]
   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 [1-1.5 weeks]
   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