Math 1710   Spring 2017

Topics and Skills

By the end of the class students should be able to do, find, and/or explain the following.

  1. Know the basic definitions and concepts behind the following:
    1. L'Hôpitals Rule
    2. Techniques of Integration
    3. Improper Integrals
    4. Work
    5. Volumes by Integration
    6. Arc Length and Areas of Revolution
    7. Convergence of Series
    8. Power and Taylor Series
  2. L'Hôpitals Rule
    1. Indeterminate forms
    2. Proper use and notation
    3. Form to rewrite for L'Hôpitals Rule
  3. Techniques of Integration
    1. Parts
    2. Partial Fractions
    3. Trigonometric Integrals
    4. Trigonometric Substitutions
    5. Improper Integrals
    6. Numerical Approximations
  4. Applications of Integration
    1. Work
    2. Volumes
    3. Volumes of Revolution
    4. Arc Length and Areas of Revolution
    5. Differential Equations
  5. Series
    1. Definition of Series
    2. Definition of Convergence of Series
    3. Integral Test for Convergence of Series
    4. Comparison Test for Convergence of Series
    5. Ratio and Root Tests for Convergence of Series
  6. Power Series
    1. Definition of Power Series
    2. Radius and Interval of Convergence
    3. Differential and Integration of Power Series
    4. Taylor and Maclaurin Series
    5. Finding Taylor Series Using Derivatives
    6. Finding Taylor Series Using Other Taylor Series
  7. Calculators
    1. Know how to work without a calculator
    2. Using a calculator for numerical calculations
  8. Clearly write out assignments