AP Calculus

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1.Pre Requisites for Calculus

1.1  Lines

1.2  Functions and Graphs

1.3  Exponential Functions

1.4  Parametric Equations

1.5  Functions and Logarithms

1.6  Trigonometric Functions

2. Limits and Continuity

2.1  Rates of Changes and Limits, Step Function

2.2  Limits Involving Infinity

2.3  Continuity

2.4  Rates of change and Tangent Lines

3.    Derivatives

3.1  Derivatives of a Function

3.2  Differentiability

3.3  Rules for Differentiation

3.4  Velocity and Other Rates of Change

3.5  Derivatives of trigonometric Functions

3.6  Chain rule

3.7  Implicit Differentiation

3.8  Derivatives of Inverse Trigonometric Functions

3.9  Derivatives of Exponential and Logarithmic Functions

4.    Applications of Derivatives

4.1  Extreme Values of functions

4.2  Mean Value Theorem

4.3  Connecting f´and f´´ with the graph of f

4.4  Modeling Optimization

4.5  Linearization andNewton’s Method

4.6  Related Rates

5.    The Definite Integral

5.1  Estimating with Finite Sums

5.2  Definite Integrals

5.3  Definite Integrals and Anti Derivatives

5.4  Fundamental Theorem of Calculus

5.5  Trapezoidal Rule

6.     Differential Equations and Mathematical Modeling

6.1  Slope Fields and Euler’s Method

6.2  Anti Differentiation by Substitution

6.3  Anti Differentiation by Parts

6.4  Exponential Growth and Decay

6.5  Logistic Growth

7.   Applications of Definite Integrals

7.1  Integral as Net Change

7.2  Areas in the Plane

7.3  Volumes

7.4  Lengths and Curves

7.5  Applications from Science and Statistics

8.   Sequences and Improper Integrals

8.1  Sequences

8.2  L Ho’pital Rule

8.3  Relative Rates of growth

8.4  Improper Integrals

9.  Infinite Series

9.1  Power Series

9.2  Taylor Series

9.3 Taylor’s Theorem

9.4  Radius of Convergence

9.5  Testing Convergence at Endpoints

10. Parametric, Vector and Polar Functions

10.1    Parametric functions

10.2   Vectors in the Plane

10.3    Polar functions