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AP Calculus On Line Tutorials

These on-line tutorials are organized according to the sequence of our course syllabus and textbook, and they are available in your Calculus group at WWW.SOPHIA.ORG.

1. Limits and Their Properties

1.0 Class Notes, Projects, Activities, and Assignments

1.1 A Preview of Calculus

1.2 An Introduction to Limits.

1.3 Evaluating Limits Analytically

1.4 Continuity and One-Sided Limits

1.5 Infinite Limits

2. Differentiation

2.0 Class Notes, Projects, Activities, and Assignments

2.1 The Derivative of a Function

2.2 Basic Differentiation Rules and Rates of Change

2.3 Product and Quotient Rules and Higher Order Derivatives

2.4 The Chain Rule

2.5 Implicit Differentiation

2.6 Related Rates

3. Applications of Differentiation

3.0 Class Notes, Projects, Activities, and Assignments

3.1 Extrema of a Function

3.2 Rolle's Theorem and Mean Value Theorem

3.3 Increasing and Decreasing Functions. First Derivative Test

3.4 Concavity and the Second Derivative Test

3.5 Limits at Infinity

3.6 Curve Sketching

3.7 Optimization Problems

3.8 Newtons Method

3.9 Differentials

4. Integration

4.0 Class Notes, Projects, Activities, and Assignments

4.1 Antiderivatives and Indefinite Integrals

4.2 Area of a Plane Region and Sigma Notation

4.3.1 Riemann Sums

4.3.2 Definite Integrals

4.4.1 The Fundamental Theorem of Calculus

4.4.2 The Mean Value Theorem for Integrals

4.5.1 Integration by Substitution

4.5.2 U-substitution, Trigonometric Substitution

4.6 Numerical Integration. Trapezoidal Rule

5. Logarithmic, Exponential, and other Transcendental Functions

5.0 Class Notes, Projects, Activities, and Assignments

5.1.1 - The Natural Logarithmic Function. Differentiation

5.1.2 - Logarithmic Differentiation

5.2 - The Natural Logarithmic Function. Integration

5.3 - Inverse Functions

5.4.1 - Natural Exponential Function. Differentiation

5.4.2 - Natural Exponential Function. Integration

5.5.1 - Logarithms and Exponentials. Other Bases that e. Differentiation

5.5.2 - Logarithms and Exponentials. Other bases that e. Integration

5.6 - Inverse Trigonometric Functions. Differentiation

5.7 - Inverse Trigonometric Functions. Integration

6. Differential Equations

6.0 Class Notes, Projects, Activities, and Assignments

6.1.1 - Slope Fields

6.1.1 - Euler's Method

6.2 - Differential Equations, Growth and Decay

6.3 - Separation of Variables Method

7. Applications of Integration

7.0 Class Notes, Projects, Activities, and Assignments

7.1 - Area of a Region Between Two Curves

7.2.1 - Volume: The Disk Method

7.2.2 - Solids of Revolution. The Washer Method

7.2.3 - Solids with Known Cross Section

7.3 - The Shell Method

8. Integration Techniques. L'Hopital Rule

8.0 Class Notes, Projects, Activities, and Assignments

8.7 Indeterminate Forms and L'Hopital Rule

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