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CHAPTER 1 Limits and Their Properties
1.1 Preview of Calculus
1.2 Finding Limits
1.3 Evaluating Limits Analytically
1.4 Continuity and One Sided Limits
1.5 Infinite Limits
CHAPTER 2 Differentiation
2.1 Defining a Derivative
2.2 Basic Differentiation Rules
2.3 Product & Quotient Rules
2.4 The Chain Rule
2.5 Implicit Differentiation
2.6 Related Rates
CHAPTER 3 Applications of Differentiation
3.1 Extrema on an Interval
3.2 Rolle's Theorem and Mean Value Theorem
3.3 First Derivative Test
3.4 Second Derivative Test
3.5 Limits on Infinity
3.6 Curve Sketching
3.7 Optimization Problems
CHAPTER 4 Integration
3.9 Differentials
4.1 Antiderivatives and Indefinite Integration
4.2 Area
4.3 Riemann Sums and Definite Integrals
4.4 The Fundamental Theorem of Calculus
4.5 Integration by Substitution
CHAPTER 5 Logarithmic, Exponential, and Other Transcendental Functions
5.1 The Natural Log: Differentiation
5.2 The Natural Log: Integration
5.4 Exponential Functions
6.1 Slope Fields
Slope Fields
6.2 Growth and Decay
Solving Differential Equations
Growth & Decay (w. Differential Equations)
5.7 Inverse Trig Functions: Differentiation
5.8 Inverse Trig Functions: Integration
5.9 Hyperbolic Functions
CHAPTER 7 Applications of Integration
7.1 Area Between Two Curves
7.2 Volume: The Disk Method
Washer Method
Cross Sections
7.3 Volume: The Shell Method
Shell Method
Disk vs Shell
7.4 Arc Length and Surfaces of Revolution
7.5 Work
7.6 Moments, Centers of Mass, and Centroids
Moment of Inertia and Algebra
Moments of Inertia and Calculus
7.7 Fluid Pressure and Fluid Force
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