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AP Calculus BC

Created by Paul Prencis

  
1

Limits and Derivatives



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2

Related Rates and Motion

With an introduction to integration and differential equations



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3

Applications of the Derivative

2.6 - Related Rates
3.1 - Extrema on an Interval
3.2 - Rolle's Theorem and the Mean Value Theorem
3.3 - Increasing and Decreasing Functions and the First Derivative Test
3.4 - Concavity and the Second Derivative Test
3.5 - Limits at Infinity
3.6 - A Summary of Curve Sketching
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4

Integration

4.1 Indefinite Integrals
4.5 Integration by Substitution
4.2 Area and Summation
4.3 Riemann Sums and Definite Integrals
4.4 The Fundamental Theorem of Calculus
4.5 Numerical Integration (Approximation Techniques)
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This topic 5

Transcendental Functions, Slope Fields and Differential Equations

5.1 Differentiating the Natural Logarithm
5.2 Integration with Logarithms
5.4 Exponential Functions
5.5 Bases other than e
5.6 Differential Equations: Growth and Decay
5.6 Differential Equations: Slope Fields
5.7 Differential Equations:Separation of Variables
5.7 Differential Equations: Euler's Method
5.8 Differentiating the Inverse Trigonometric Functions
5.9 Integration with Inverse Trigonometric Functions
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6

Applications of the Definite Integral

  • Area between 2 curves
  • Volume of Solid of Revolutions (Disk/Washer Method)
  • Volume of Solid of Revolutions (Shell Method)
  • Volume of a Solid with a Known Cross Section
  • Arc Length
  • Surface area of a Solid of Revolution
  • Work

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7

Techniques of Integration

7.1 Choosing a technique
7.2 Integration by Parts
7.3 Powers of Sine and Cosine
7.4 Trigonometric Substitutions
7.5 Partial Fractions
7.7 L'Hopital's Rule
7.8 Improper Integrals
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8

Series and Sequences

8.1 Sequences
8.2 Series and Convergence
8.3 The Integral Test
8.4 Comparison of Series
8.5 Alternating Series
8.6 The Ratio and Root Tests
8.7 Taylor Polynomials
8.8 Power Series
8.9 Representation of Functions by Power Series
8.10 Taylor and Maclaurin Series


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9
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10
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