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AP Calculus AB Topics

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3. Derivative Applications

3.1

Slope and equation of tangent line

3.2

Critical number and maximum and minimum values

3.3

Curve sketching

3.4

Mean value theorem

3.5

Rectilinear motion: Derivative

3.6

Related rates

3.7

Optimization

4. Integrals

4.1

Antiderivatives

4.2

Riemann sum

4.3

Definite integral

4.4

Fundamental theorem of calculus

5. Integration techniques

5.1

U-Substitution

5.2

Integration using trigonometric identities

5.3

Trigonometric substitution

6. Integral Applications

6.1

Average value of a function

6.2

Areas between curves

6.3

Volumes of solids with known cross-sections

6.4

Volumes of solids of revolution - Disc method

6.5

Volumes of solids of revolution - Shell method

7. Differential Equations

7.1

Introduction to differential equations

7.2

Separable equations

7.3

Modelling differential equations

7.4

Slope fields

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