Math 1230

Math 1230 Topics and Skills, Fall 2026

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. Sequence and Convergence of Sequences
   8. Infinite Series and Convergence of Series
   9. Power and Taylor Series
2. L'Hôpitals Rule
   1. Indeterminate forms
   2. Proper use and notation
   3. Forms 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. Separable Differential Equations
5. Sequences and Series
   1. Definition of an Infinite Sequence
   2. Definition of Convergence of Sequences
   3. Definition of Infinite Series
   4. Definition of Convergence of Series
   5. Integral Test for Convergence of Series
   6. Comparison Test for Convergence of Series
   7. 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 and computers
   1. Know how to work without a calculator/computer
   2. Using a calculator/computer for numerical calculations
8. Clearly write out assignments