Resources for Calculus 1

Welcome to the multimedia version of Calculus 1 (MTH 229). Collected below are a number of resources designed assist you during your first semester Calculus course. 

Java Applets

The applets below will allow us to visually explore and experiment will the concepts that we will discuss in this class.  Note: You must have the freely available Java 1.4.1 runtime environment (JRE) or higher installed for the applets to work.

  1. Epsilon-Delta Limit Definition
  2. Secant and Tangent Lines
  3. Tangent Lines and the first Derivative
  4. The Chain Rule
  5. The First and Second Derivatives
  6. Riemann Sums and the Definite Integral
  7. Series Grapher - Linear and Quadratic approximation, Taylor Series
  8. Parametric Curves
  9. Antiderivatives and Direction Fields

Course Outline and Resources

Review and Intro to Calculus

  1. Calculus: basic ideas and problems
  2. Functions and Inverses, Exponential and Logarithmic
  3. Trig review - Applet

Limits and Derivatives

  1. quessingLimitsPitfall.m - illustrates the danger in quessing limits by plugging in numbers near the limiting value and also uses the Matlab symbolic toolbox to evaluate the limit symbolically.
  2. squeeze theorem (sqeeze.m) - demonstrates application of squeeze theorem to problem #34, section 2.3
  3. Limits, delta-epsilon definition - Applet
  4. Continuity
  5. Limits at Infinity
  6. Tangents, Velocities, and Other Rates of Change - Applet
  7. Derivatives
  8. The Derivative as a Function - Applet

Differentiation Rules

  1. Derivatives of Polynomials and Exponential Functions
  2. The Product and Quotient Rules
  3. Rates of Change in the Natural and Social Sciences
  4. Derivatives of Trigonometric Functions
  5. The Chain Rule - Applet
  6. Implicit Differentiation
  7. Higher Derivatives - Applet
  8. Hyperbolic Functions
  9. Related Rates
  10. Linear/Quadratic Approximations and Differentials - Applet

Application of Differentiation

  1. Maximum and Minimum Values
  2. The Mean Value Theorem
  3. Indeterminate Forms and L'Hospital's Rule
  4. Optimization Problems
  5. Iteration and Cobweb Plots - Applet
  6. Fixed Point Iteration (Applet), Secant Method (Applet), Newton's Method (Applet)
  7. Antiderivatives and Direction Fields - Applet

Integrals

  1. Areas and Distances
  2. The Definite Integral - Applet
  3. The Fundamental Theorem of Calculus
  4. Indefinite Integrals and the Total Change Theorem
  5. The Substitution Rule

Worksheets/Labs

Updated each semester the class is offered.