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Hamilton AP Calculus
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Semester 1 Review
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Chapter 1 - Prequisites
Chapter 1.1 Lines
Chapter 1.2 Functions and Graphs
Chapter 1.3 Exponential Functions
Chapter 1.4 Parametric Equations
Chapter 1.5 Functions and Logarithms
Chapter 1.6 Trigonometric Functions
Chapter 2 - Limits and Continuity
Chapter 2.1 Rates of Change and Limits
Chapter 2.2 Limits Involving Infinity
Chapter 2.3 Continuity
Chapter 2.4 Rates of Change and Tangent Lines
Chapter 3 - Derivatives
Chapter 3.1 Derivative of a Function
Chapter 3.2 Differentiability
Chapter 3.3 Rules for Differentiation
Chapter 3.4 Velocity and Other Rates of Change
Chapter 3.5 Derivatives of Trigonometric Functions
Chapter 3.6 Chain Rule
Chapter 3.7 Implicit Differentiation
Chapter 3.8 Derivatives of Inverse Trigonometric Functions
Chapter 3.9 Derivatives of Exponential and Logarithmic Functions
Chapter 4 - Applications of Derivatives
Chapter 4.1 Extreme Values of Functions
Chapter 4.2 Mean Value Theorem
Chapter 4.3 Connecting ƒ’ and ƒ’’ with the Graph of ƒ
Chapter 4.4 Modeling and Optimization
Chapter 4.5 Linearization and Newton's Method
Chapter 4.6 Related Rates
Chapter 5 - The Definite Integral
Chapter 5.1 Estimating with Finite Sums
Chapter 5.2 Definite Integrals
Chapter 5.3 Definite Integrals and Antiderivatives
Chapter 5.4 Fundamental Theorem of Calculus
Chapter 5.5 Trapezoidal Rule
Chapter 6 - Differential Equations and Mathematical Modeling
Chapter 6.1 Slope Fields and Euler's Method
Chapter 6.2 Antidifferentiation by Substitution
Chapter 6.3 Antidifferentiation by Parts
Chapter 6.4 Exponential Growth and Decay
Chapter 6.5 Logistic Growth
Chapter 7 - Applications of Definite Integrals
Chapter 7.1 Integral as Net Change
Chapter 7.2 Areas in the Plane
Chapter 7.3 Volumes
Chapter 7.4 Lengths of Curves
Chapter 7.5 Applications from Science and Statistics
Chapter 8 - Sequences, L'Hopital's Rule, and Improper Integrals
Chapter 8.1 Sequences
Chapter 8.2 L'Hôpital's Rule
Chapter 8.3 Relative Rates of Growth
Chapter 8.4 Improper Integrals
Chapter 9 - Infinite Series
Chapter 9.1 Power Series
Chapter 9.2 Taylor Series
Chapter 9.3 Taylor's Theorem
Chapter 9.4 Radius of Convergence
Chapter 9.5 Testing Convergence at Endpoints
Chapters 10 - Parametric, Vector and Polar Functions
Chapter 10.1 Parametric Functions
Chapter 10.2 Vectors in the Plane
Chapter 10.3 Polar Functions
Hamilton AP Calculus
Chapter 8 - Sequences, L'Hopital's Rule, and Improper Integrals
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