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Essential Calculus

 

Chapter 1: Functions, Models and Graphs

Click to Expand/Collapse! 1.1 Real Numbers and Number Lines
Click to Expand/Collapse! 1.2 Integer Exponents
Click to Expand/Collapse! 1.3 Fractional Exponents and Radicals
Click to Expand/Collapse! 1.4 Polynomials
Click to Expand/Collapse! 1.5 Lines and Their Graphs
Click to Expand/Collapse! 1.6a An Introduction to Functions
Click to Expand/Collapse! 1.6b Operations with Functions
Click to Expand/Collapse! 1.7 Functions and Their Graphs: A Calculator Section
Click to Expand/Collapse! 1.8 Functions and Models

Chapter 2: Limits, Slopes, and the Derivative

Click to Expand/Collapse! 2.1a Left and Right-Hand Limits
Click to Expand/Collapse! 2.1b Limits
Click to Expand/Collapse! 2.2a Average Rate of Change
Click to Expand/Collapse! 2.2b Instantaneous Rate of Change and Interpreting Graphs
Click to Expand/Collapse! 2.3a Definition of the Derivative and Power Rule
Click to Expand/Collapse! 2.3b Slope and Rate of Change Considered Algebraically
Click to Expand/Collapse! 2.4 Applications: Marginal Analysis
Click to Expand/Collapse! 2.5a More About Limits
Click to Expand/Collapse! 2.5b More about Continuity

Chapter 3: Algebraic Differentiation Rules

Chapter 4: Applications of the Derivative

Chapter 5: Exponential and Logarithmic Functions

Click to Expand/Collapse! 5.1 Exponential Functions
Click to Expand/Collapse! 5.2 The Algebra of the Natural Logarithm Function
Click to Expand/Collapse! 5.3 Differentiation of Logarithmic Functions
Click to Expand/Collapse! 5.4 Differentiation of Exponential Functions
Click to Expand/Collapse! 5.5a Applications of Exponential Functions: Growth and Decay
Click to Expand/Collapse! 5.5b Logarithmic Differentiation and Elasticity of Demand

Chapter 6: Integration with Applications

Chapter 7: Additional Integration Topics

Click to Expand/Collapse! 7.1 Integration by Parts
Click to Expand/Collapse! 7.2 Annuities and Income Streams
Click to Expand/Collapse! 7.3 Tables of Integrals
Click to Expand/Collapse! 7.4 Improper Integrals
Click to Expand/Collapse! 7.5 Probability
Click to Expand/Collapse! 7.6 Volume

Chapter 8: Multivariable Calculus

Click to Expand/Collapse! 8.1 Functions of Several Variables
Click to Expand/Collapse! 8.2 Partial Derivatives
Click to Expand/Collapse! 8.3 Local Extrema for Functions of Two Variables
Click to Expand/Collapse! 8.4 Lagrange Multipliers
Click to Expand/Collapse! 8.5 The Method of Least Squares
Click to Expand/Collapse! 8.6 Double Integrals

Chapter 9: The Trigonometric Functions

Click to Expand/Collapse! 9.1 The Trigonometric Functions
Click to Expand/Collapse! 9.2 Derivatives of the Trigonometric Functions
Click to Expand/Collapse! 9.3 Integration of the Trigonometric Functions
Click to Expand/Collapse! 9.4 Inverse Trigonometric Functions

Chapter 10: Sequences, Taylor Polynomials, and Power Series

Click to Expand/Collapse! 10.1 Infinite Sequences
Click to Expand/Collapse! 10.2 Taylor Polynomials
Click to Expand/Collapse! 10.3 Taylor Series, Infinite Expressions, and Their Applications