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Calculus

P. Prerequisite: Functions

• P.1. Functions
• P.2. Inverse Functions
• P.3. Composition of Functions
• P.4. Odd and Even Functions
• P.5. Graphs of Functions

1. The Derivative

• 1.1. Limits and Continuity
• 1.2. Definition of the Derivative
• 1.3. Derivatives of Polynomials
• 1.4. The Tangent Line
• 1.5. Velocity and Acceleration
• 1.6. Derivatives of Trigonometric Functions
• 1.7. The Product Rule
• 1.8. The Quotient Rule
• 1.9. The Chain Rule

2. Maxima and Minima

• 1.1 The Intermediate Value Theorem
• 1.2. Critical Points
• 1.3. Local Maxima and Minima
• 1.4. Global Maxima and Minima

3. The Integral

• 3.1. Definition: Riemann Integration
• 3.2. The Fundamental Theorem of Calculus
• 3.3. Integrals of Polynomials
• 3.4. Trigonometric Integrals

4. Methods of Integration

• 4.1. Substitution
• 4.2. Integration by Parts
• 4.3. Integration by Partial Fractions

5. Exponential and Logarithmic Functions

• 5.1. The Natural Logarithm
• 5.2. Other Logarithms
• 5.3. Exponential Functions
• 5.4. Derivatives Involving Exponential and Logarithmic Functions
• 5.5. Integrals Involving Exponential and Logarithmic Functions
• 5.6. Applications of Exponential and Logarithmic Functions

6. Differential Equations

• 6.1. Exponential and Logarithmic Functions
• 6.2. Trigonometric Functions
• 6.3. Other Examples
• 6.4. Applications

7. Taylor Series

• 7.1. Definition
• 7.2. Computing Taylor Series
• 7.3. Numerical Estimation