Course Notes

Calculus Course Notes

Richard Hammack

The following chapters are aligned with the lectures. (For example, Lecture 3 is on Chapter 3, etc.)

You will find the solutions to a chapter's odd numbered problems at the end of that chapter.

Part 1: Function Review

	4. Inverse Functions
	5. Exponential and Logarithm Functions
	6. Inverse Trig Functions

Part 2: Limits

	7. Limits: The Way to Tangent Lines
	8. Limits and Limit Laws
	9. Computing Limits Algebraically
	10. Limits of Trig Functions
	11. Continuity and Limits of Compositions
	12. Infinite Limits
	13. Limits at Infinity
	14. Formal Definitions of Limits

Part 3: Differentiation

	15. Slopes of Tangent Lines
	16. The Derivative of a Function
	17. Derivative Rules
	18. Notation, Examples, Differentiability
	19. The Derivative of the Natural Exponential Function
	20. Product and Quotient Rules
	21. Derivatives of Trig Functions
	22. Higher Derivatives
	23. The Chain Rule
	24. Derivatives of Exponential and Logarithm Functions
	25. Derivatives of Inverse Trig Functions
	26. Meanings of the Derivative
	27. Implicit Differentiation
	28. Logarithmic Differentiation
	29. Related Rates

Part 4: Applications of Differentiation

	30. Increase-Decrease
	31. Local Extrema and the First Derivative Test
	32. Concavity and the Second Derivative Test
	33. Global Extrema
	34. Optimization Problems
	35. The Mean Value Theorem
	36. Linear Approximation and Newton's Method
	37. L'Hopital's Rule

Part 5: Integration

	38. Antiderivatives
	39. Differentials and Differential Equations
	40. Area
	41. Definite Integrals
	42. The Fundamental Theorem of Calculus
	43. More on the Fundamental Theorem
	44. Integration by Substitution
	45. Working with Calculus

© 2021 by Richard Hammack
This work is licensed under the Creative Commons Attribution-Non Commercial-No Derivative Works 3.0 License

I am actively adding content. Stay tuned!

I am always happy to correct typos and/or mistakes. Please notify me if you find any!

--Thanks, RH