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Chapter 1 Review of PreCalc
1.1 Lines
1.2 Relations and Functions
1.3 Exponential Growth and Decay
1.5 Exponential and Logarithmic Functions
1.6 Trig Functions
Chapter 2 Limits
2.1 Rates of Change and Limits
2.2 Limits Involving Infinity
2.3 Continuity
2.4 Average Rate of Change
Chapter 3 Derivatives
3.1 The Definition of a Derivative
3.2 Differentiability
3.3 Rules for Differentiation
3.4 Velocity and Other Rate of Change
3.5 Derivative of Trig Functions
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Derivatives of Inverse Trig Functions
3.9 Derivatives of Exponential and Logarithmic Functions
Chapter 4 Application of Derivatives
4.1 Extreme Values of Functions
4.2 The Mean Value Theorem
4.3 Relating derivatives to the original function
4.4 Optimization
4.5 Linearization
4.6 Related Rates
Chapter 5 The Definite Integral
5.1 Estimating with Finite Sums
5.2 The Definite Integral
5.3 Properties of Integrals
5.4 The Fundamental Theorem of Calculus
5.5 Trapezoidal Approximation
Chapter 6 Differential Equations and Mathematical Modeling
6.1 Differential Equations and Slope Fields
6.2 Indefinite Ingtegrals
6.3 Anti-Differentiation by Parts
6.4 Exponential Growth and Decay
6.5 Integration by Partial Fractions
Review Problems
Chapter 7 Applications of Integrals
7.1 Integrals as Net Change
7.2 Areas Between Curves
7.3 Integrals as Volumes
7.4 Arc Length
Chapter 8 Sequences, Series, L'Hopitals Rule, and Improper Integrals
8.1 Sequences
8.2 L'Hopital's Rule
8.3 Relative Rates of Growth
8.4 Improper Integrals
Chapter 9 Series
9.1 Power Series
9.2 Taylor Series
9.4 Radius of Convergence
9.5 Testing Intervals of Convergence
Chapter 10 Polar and Parametric Functions
10.1 Parametric Differentiation
10.2 Vectors in a Plane
10.3 Polar Curves
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6.2 Indefinite Ingtegrals
6.2 Indefinite Integrals
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