Notes and Resources for Math 101
Textbook
Larson and Edwards, Calculus, 11th edition
- Review examples
- Section 5.7 Inverse Trigonometric Functions: Differentiation
Examples: Application problems
Handout: Inverse trig functions
Proof of Inverse Trig Derivatives
- Section 5.8 Inverse Trigonometric Functions: Integration
- Section 5.9 Hyperbolic Functions
External link: Calculus with Hyperbolic Functions
External link: Basics of Hyperbolic Functions
- Section 7.1 Area of a Region Between two Curves
Handout: Area between curves
Handout: Fundamental Theorem of Calculus
Video: Areas by integration
- Section 7.2 Volume: The Disk Method
Example: Another example to supplement the notes
Example: Problem #14 section 7.2
Solids with known cross sections
External link: Volumes of solids of revolution
- Section 7.3 Volume: The Shell Method
- Section 7.4 Arc Length and Surfaces of Revolution
Example: Surface area of a sphere
External link: Arc Length
External link: Area of Surface of Revolution
- Section 7.5 Work
- Section 7.6 Moments, Centers of Mass, and Centroids
Examples: Center of mass examples
- Section 8.1 Basic Integration Rules
Handout: Basic Integration Formulas
- Section 8.2 Integration by Parts
Handout: Integration by Parts
- Section 8.3 Trigonometric Integrals
Handout: Trigonometric formulas
- Section 8.4 Trigonometric Substitution
Handout: Trigonometric Substitution (by George Ballinger)
- Section 8.5 Partial Fractions
Example: Quadratic denominator
Example: What method to use?
Handout: Partial Fractions
- Section 8.6 Numerical Integration (Covered in Math 100)
Handout: The Trapezoidal Rule
Handout: Simpson's Rule
- Section 8.7 Integration by Tables
Appendix B: Integration Tables
- Section 5.6 Indeterminate Forms and L'Hôpital's Rule
Handout: Indeterminate forms of limits
Handout: Review of Limits (by George Ballinger)
Video: Failure of L'Hôpital's Rule
- Section 8.8 Improper Integrals
External link: Improper Integrals
- Section 9.1 Sequences
- Section 9.2 Series and Convergence
- Section 9.3 The Integral Test and p-Series.
Handout: Harmonic series
- Section 9.4 Comparisons of Series
- Section 9.5 Alternating Series
- Section 9.6 The Ratio and Root Tests
Handout: Summary of tests for series
- Section 9.7 Taylor Polynomials and Approximations
- Section 9.8 Power Series
External link: Power Series
- Section 9.9 Representation of Functions by Power Series
Example: An integral with series
- Section 9.10 Taylor and Maclaurin Series
Handout: Maclaurin series of sin(x)
Handout: Basic Maclaurin series
- Section 10.1 Conics and Calculus
- Section 10.2 Plane Curves and Parametric Equations
Desmos graph of a parametric curve
External link: Cycloid
External link: Parametric Equations
- Section 10.3 Parametric Equations and Calculus
- Section 10.4 Polar Coordinates and Polar Graphs
Handout: Polar graphs examples
- Section 10.5 Area and Arc Length in Polar Coordinates
External link: Area in Polar Coordinates