Essential Calculus
1.1 Real Numbers and Number Lines
1.2 Integer Exponents
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- Bonus 1: Integer Exponents
1.3 Fractional Exponents and Radicals
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- Bonus 1: Fractional Exponents and Radicals
1.4 Polynomials
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- Bonus 1: Polynomials
1.5 Lines and Their Graphs
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- Bonus 1: Lines and Their Graphs
1.6a An Introduction to Functions
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- Bonus 1: An Introduction to Functions
1.6b Operations with Functions
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- Bonus 1: Operations with Functions
1.7 Functions and Their Graphs: A Calculator Section
1.8 Functions and Models
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- Bonus 1: Functions and Models
2.1a Left and Right-Hand Limits
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- Bonus 1: Left and Right-Hand Limits
2.1b Limits
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- Bonus 1: Limits
2.2a Average Rate of Change
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- Bonus 1: Average Rate of Change
2.2b Instantaneous Rate of Change and Interpreting Graphs
2.3a Definition of the Derivative and Power Rule
2.3b Slope and Rate of Change Considered Algebraically
2.4 Applications: Marginal Analysis
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- Bonus 1: Applications: Marginal Analysis
2.5a More About Limits
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- Bonus 1: More About Limits
2.5b More about Continuity
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- Bonus 1: More about Continuity
4.1a Higher Order Derivatives and Concavity
4.1b Higher Order Derivatives: the Second Derivative Test
4.2 Curve Sketching: Polynomial Functions
4.3 Curve Sketching: Rational Functions
4.4 Business Applications
4.5 Other Applications
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- Bonus 1: Other Applications
4.6 Differentials
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- Bonus 1: Differentials
5.1 Exponential Functions
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- Bonus 1: Exponential Functions
5.2 The Algebra of the Natural Logarithm Function
5.3 Differentiation of Logarithmic Functions
5.4 Differentiation of Exponential Functions
5.5a Applications of Exponential Functions: Growth and Decay
5.5b Logarithmic Differentiation and Elasticity of Demand
7.1 Integration by Parts
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- Bonus 1: Integration by Parts
7.2 Annuities and Income Streams
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- Bonus 1: Annuities and Income Streams
7.3 Tables of Integrals
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- Bonus 1: Tables of Integrals
7.4 Improper Integrals
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- Bonus 1: Improper Integrals
7.5 Probability
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- Bonus 1: Probability
7.6 Volume
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- Bonus 1: Volume
8.1 Functions of Several Variables
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- Bonus 1: Functions of Several Variables
8.2 Partial Derivatives
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- Bonus 1: Partial Derivatives
8.3 Local Extrema for Functions of Two Variables
8.4 Lagrange Multipliers
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- Bonus 1: Lagrange Multipliers
8.5 The Method of Least Squares
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- Bonus 1: The Method of Least Squares
8.6 Double Integrals
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- Bonus 1: Double Integrals