Table of Contents
Chapter P – PREPARATION FOR CALCULUS
- P.1 Graphs and Models
- P.2 Linear Models and Rates of Change
- P.3 Functions and Their Graphs
- P.4 Fitting Models to Data
Chapter 1 – LIMITS AND THEIR PROPERTIES
- 1.1 A Preview of Calculus
- 1.2 Finding Limits Graphically and Numerically
- 1.3 Evaluating Limits Analytically
- 1.4 Continuity and One-Sided Limits
- 1.5 Infinite Limits
Chapter 2 – DIFFERENTIATION
- 2.1 The Derivative and the Tangent Line Problem
- 2.2 Basic Differentiation Rules and Rates of Change
- 2.3 The Product and Quotient Rules and Higher-Order Derivatives
- 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 the Mean Value Theorem
- 3.3 Increasing and Decreasing Functions and the First Derivative Test
- 3.4 Concavity and the Second Derivative Test
- 3.5 Limits at Infinity
- 3.6 A Summary of Curve Sketching
- 3.7 Optimization Problems
- 3.8 Newton’s Method
- 3.9 Differentials
Chapter 4 – INTEGRATION
- 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
- 4.6 Numerical Integration
Chapter 5 – LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS
- 5.1 The Natural Logarithmic Function: Differentiation
- 5.2 The Natural Logarithmic Function: Integration
- 5.3 Inverse Functions
- 5.4 Exponential Functions: Differentiation and Integration
- 5.5 Bases Other than e and Applications
- 5.6 Inverse Trigonometric Functions: Differentiation
- 5.7 Inverse Trigonometric Functions: Integration
- 5.8 Hyperbolic Functions
Chapter 6 – DIFFERENTIAL EQUATIONS
- 6.1 Slope Fields and Euler’s Method
- 6.2 Differential Equations: Growth and Decay
- 6.3 Separation of Variables and the Logistic Equation
- 6.4 First-Order Linear Differential Equations
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