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Highlights of Calculus

Mathematics MIT CC BY-NC-SA 4.0 17 lectures

Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The series is divided into three sections: Introduction - Why Professor Strang created these videos - How to use the materials Highlights of Calculus - Five videos reviewing the key topics and ideas of calculus - Applications to real-life situations and problems - Additional summary slides and practice problems Derivatives - Twelve videos focused on differential calculus - More applications to real-life situations and problems - Additional summary slides and practice problems About the Instructor Professor Gilbert Strang is a renowned mathematics professor who has taught at MIT since 1962. {{% resource_link "3d84bdff-6952-4314-bf16-0d071c2759b3" "Read more about Prof. Strang" %}}. Acknowledgements Special thanks to Professor J.C. Nave for his help and advice on the development and recording of this program. The video editing was funded by the Lord Foundation of Massachusetts.

Syllabus

  1. 1 Derivative of sin x and cos x
  2. 2 Product Rule and Quotient Rule
  3. 3 Chains f(g(x)) and the Chain Rule
  4. 4 Limits and Continuous Functions
  5. 5 Inverse Functions f ^-1 (y) and the Logarithm x = ln y
  6. 6 Derivatives of ln y and sin ^-1 (y)
  7. 7 Growth Rate and Log Graphs
  8. 8 Linear Approximation/Newton's Method
  9. 9 Power Series/Euler's Great Formula
  10. 10 Differential Equations of Motion
  11. 11 Differential Equations of Growth
  12. 12 Six Functions, Six Rules, and Six Theorems
  13. 13 Big Picture of Calculus
  14. 14 Big Picture: Derivatives
  15. 15 Max and Min and Second Derivative
  16. 16 The Exponential Function
  17. 17 Big Picture: Integrals

Course materials