Free Differential Calculus Textbooks

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Worldwide Differential Calculus

Differential Calculus is the study of instantaneous rates of change. These rates of change are known as derivatives. This book is written by David B. Massey, Ph.D., an award-winning teacher and world-renowned research mathematician, who has been teaching college students for over 25 years. He emphasizes intuitive ideas in conjunction with rigorous statements of theorems, and provides a large number of illustrative examples. In the accompanying videos, Dr. Massey lectures on the core material from each section. See more free textbooks.

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Chapter 1 - Rates of Change and the Derivative
Chapter 2 - Basic Rules for Calculating Derivatives
- 1 - The Power Rule for Integer Powers 2 - The Product and Quotient Rules 3 - The Chain Rule 4 - The Exponential Function 5 - The Natural Logarithm 6 - General Exponential and Logarithmic Functions 7 - Trigonometric Functions: Sine and Cosine 8 - The Other Trigonometric Functions 9 - Inverse Trig Functions 10 - Implicitly Deﬁned Functions
Chapter 3 - Applications of Diﬀerentiation
- 1 - Related Rates 2 - Graphing 3 - Optimization 4 - Linear Approximation, Differentials, and Newton’s Method 5 - Indeterminate Forms and L´Hôpital’s Rule
Chapter 4 - Introduction to Differential Equations
- 1 - Anti-derivatives and Basic Differential Equations 2 - Applications of Differential Equations 3 - Separable Differential Equations 4 - More Applications of Differential Equations 5 - Approximating Solutions of y'=m(x,y)Appendix