Calculus

Notes

  1. Are you ready for Calculus?
  2. An Intuitive Way to Think About Limits
  3. The Epsilon-Delta Definition of a Limit
  4. The Limit Laws
  5. Continuous Functions
  6. The Intermediate Value Theorem
  7. Limits at Infinity
  8. Antiderivatives
  9. Acceleration, Velocity & Speed
  10. Summation and Sigma Notation
  11. Two Important Properties of Sums
  12. The Principle of Mathematical Induction
  13. Motivating the Riemann Sum

Proofs

  1. The Sum Law for Limits
  2. The Derivative of a Constant is Zero
  3. The Binomial Theorem
  4. The Power Rule for Derivatives (for integer powers)
  5. The Power Rule for Derivatives (for rational powers)
  6. The Constant Multiple Rule for Derivatives
  7. The Derivative of a Sum or Difference
  8. The Product Rule
  9. The Quotient Rule
  10. The Chain Rule
  11. The Derivatives of Trigonometric Functions
  12. The Derivatives of Inverse Functions
  13. The Derivatives of Exponential and Logarithmic Functions

For Fun

  1. What does QED mean?

Practice

  1. Exercises - Limits
  2. Exercises - Continuity
  3. Exercises - Intermediate Value Theorem
  4. Exercises - The Definition of the Derivative
  5. Exercises - Simple Differentiation Rules
  6. Exercises - The Product Rule
  7. Exercises - The Quotient Rule
  8. Exercises - The Chain Rule
  9. Exercises - Higher Order Derivatives
  10. Exercises - Logarithmic Differentiation
  11. Exercises - Finding Derivatives (Mixed Techniques)
  12. Exercises - Differentiability and Continuity
  13. Exercises - Implicit Differentiation
  14. Exercises - Related Rates
  15. Exercises - The Mean Value Theorem
  16. Exercises - Extrema of Functions
  17. Exercises - Infinite Limits and Limits at Infinity
  18. Exercises - Graphing Functions
  19. Exercises - Optimization
  20. Exercises - Antiderivatives
  21. Exercises - Acceleration, Velocity, and Speed
  22. Exercises - Induction and Sums
  23. Exercises - Induction in Other Contexts
  24. Exercises - Riemann Sums
  25. Exercises - Integration (with u-substitution)
  26. Exercises - Fundamental Theorem of Calculus
  27. Exercises - Differential Equations
  28. Exercises - Mean Value Theorem for Integrals
  29. Exercises - Area Between Curves
  30. Exercises - Volumes of Revolution