Single Variable Calculus I

1.1 Four Ways to Represent a Function +

1.2 Mathematical Models: A Catalog of Essential Functions +

1.3 New Functions from Old Functions +

1.4 The Tangent and Velocity Problems +

1.5 The Limit of a Function +

1.6 Calculating Limits Using the Limit Laws +

1.7 The Precise Definition of a Limit +

1.8 Continuity +

2.1 Derivatives and Rates of Change +

2.2 The Derivative as a Function +

2.3 Differentiation Formulas +

2.4 Derivatives of Trigonometric Functions +

2.5 The Chain Rule +

2.6 Implicit Differentiation +

2.7 Rates of Change in the Natural and Social Sciences +

2.8 Related Rates +

2.9 Linear Approximations and Differentials +

3.1 Maximum and Minimum Values +

3.2 The Mean Value Theorem +

3.3 What Derivatives Tell Us about the Shape of a Graph +

3.4 Limits at Infinity; Horizontal Asymptotes +

3.5 Summary of Curve Sketching +

3.7 Optimization Problems +

3.8 Newton's Method +

3.9 Antiderivatives +

4.1 The Area and Distance Problems +

4.2 The Definite Integral +

4.3 The Fundamental Theorem of Calculus +

4.4 Indefinite Integrals and the Net Change Theorem +

4.5 The Substitution Rule +

5.1 Areas between Curves +

5.2 Volumes +

5.3 Volumes by Cylindrical Shells +

5.4 Work +

5.5 Average Value of a Function +