Catalog

Single Variable Calculus

Mathematics MIT CC BY-NC-SA 4.0 35 lectures

This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

Syllabus

  1. 1 Lecture 1: Rate of Change
  2. 2 Lecture 2: Limits
  3. 3 Lecture 3: Derivatives
  4. 4 Lecture 4: Chain Rule
  5. 5 Lecture 5: Implicit Differentiation
  6. 6 Lecture 6: Exponential and Log
  7. 7 Lecture 7: Exam 1 Review
  8. 8 Lecture 9: Linear and Quadratic Approximations
  9. 9 Lecture 10: Curve Sketching
  10. 10 Lecture 11: Max-min
  11. 11 Lecture 12: Related Rates
  12. 12 Lecture 13: Newton's Method
  13. 13 Lecture 14: Mean Value Theorem
  14. 14 Lecture 15: Antiderivatives
  15. 15 Lecture 16: Differential Equations
  16. 16 Lecture 18: Definite Integrals
  17. 17 Lecture 19: First Fundamental Theorem
  18. 18 Lecture 20: Second Fundamental Theorem
  19. 19 Lecture 21: Applications to Logarithms
  20. 20 Lecture 22: Volumes
  21. 21 Lecture 23: Work, Probability
  22. 22 Lecture 24: Numerical Integration
  23. 23 Lecture 25: Exam 3 Review
  24. 24 Lecture 27: Trig Integrals
  25. 25 Lecture 28: Inverse Substitution
  26. 26 Lecture 29: Partial Fractions
  27. 27 Lecture 30: Integration by Parts
  28. 28 Lecture 31: Parametric Equations
  29. 29 Lecture 32: Polar Coordinates
  30. 30 Lecture 33: Exam 4 Review
  31. 31 Lecture 35: Indeterminate Forms
  32. 32 Lecture 36: Improper Integrals
  33. 33 Lecture 37: Infinite Series
  34. 34 Lecture 38: Taylor's Series
  35. 35 Lecture 39: Final Review

Course materials