Calculus Notes

1.1 Functions and Their Representations

1.2 A Catalog of Essential Functions

1.3 The Limit of a Function

1.4 Calculating Limits

1.5 Continuity

1.6 Limits Involving Infinity

 

2.1 Derivatives and Rates of Change (9/18)

2.2 The Derivative as a Function (9/21-9/23)

2.3 Basic Differentiation Formulas (9/23-9/24)

2.4 The Product and Quotient Rules (9/25-9/30)

2.5 The Chain Rule (10/1)

2.6 Implicit Differentiation (10/2-10/5)

2.7 Related Rates (10/9)

 

3.1 Exponential Functions (10/12-10/14)

3.2 Inverse Functions and Logarithms (10/19-10/21)

3.3 Derivatives of Logarithmic and Exponential Functions (10/21-10/22)

3.5 Inverse Trigonometric Functions (10/23-10/26)

3.6 Hyperbolic Functions (10/28-10/29)

3.7 Indeterminate Forms and L'Hospital's Rule (10/29)

 

4.1 Maximum and Minimum Values (11/6)

4.2 The Mean Value Theorem (11/9)

4.3 Derivatives and the Shapes of Graphs (11/11-11/12)

4.5 Optimization Problems (11/12-11/13)

4.6 Newton's Method (11/16)

4.7 Antiderivatives (11/18)

 

5.1 Areas and Distances (11/23)

5.2 The Definite Integral (11/30)

5.3 Evaluating Definite Integrals (12/2)

5.4 The Fundamental Theorem of Calculus (12/3)

5.5 The Substitution Rule (12/4)