# Alignment: Calculus • Early Transcendentals • Volume 1 • 3rd Edition

• 1 Precalculus Review
• 1.1 Real Numbers, Functions, and Graphs
• 1.2 Linear and Quadratic Functions
• 1.3 The Basic Classes of Functions
• 1.4 Trigonometric Functions
• 1.5 Inverse Functions
• 1.6 Exponential and Logarithmic Functions
• 1.7 Technology: Calculators and Computers
• 2 Limits
• 2.1 Limits, Rates of Change, and Tangent Lines
• 2.2 Limits: A Numerical and Graphical Approach
• 2.3 Basic Limit Laws
• 2.4 Limits and Continuity
• 2.5 Evaluating Limits Algebraically
• 2.6 Trigonometric Limits
• 2.7 Limits at Infinity
• 2.8 Intermediate Value Theorem
• 2.9 Formal Definition of Limit
• 3 Differentiation
• 3.1 Definition of Derivative
• 3.2 The Derivative as a Function
• 3.3 Product and Quotient Rules
• 3.4 Rates of Change
• 3.5 Higher Derivatives
• 3.6 Trigonometric Functions
• 3.7 The Chain Rule
• 3.8 Implicit Differentiation
• 3.9 Derivative of Exponential and Logarithmic Functions
• 3.10 Related Rates
• 4 Applications of the Derivative
• 4.1 Linear Approximation and Applications
• 4.2 Extreme Values
• 4.3 The Mean Value Theorem and Monotonicity
• 4.4 The Shape of a Graph
• 4.5 L’Hôpital’s Rule
• 4.6 Graph Sketching and Asymptotes
• 4.7 Applied Optimization
• 4.8 Newton’s Method
• 5 The Integral
• 5.1 Approximating and Computing Area
• 5.2 The Definite Integral
• 5.3 The Indefinite Integral
• 5.4 The Fundamental Theorem of Calculus, Part I
• 5.5 The Fundamental Theorem of Calculus, Part II
• 5.6 Net Change as the Integral of a Rate of Change
• 5.7 Substitution Method
• 5.8 Further Transcendental Functions
• 5.9 Exponential Growth and Decay
• 6 Applications of the Integral
• 6.1 Area between Two Curves
• 6.2 Setting up Integrals: Volume, Density, Average Value
• 6.3 Volumes of Revolution
• 6.4 The Method of Cylindrical Shells
• 6.5 Work and Energy
• 7 Techniques of Integration
• 7.1 Integration by Parts
• 7.2 Trigonometric Integrals
• 7.3 Trigonometric Substitution
• 7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
• 7.5 The Method of Partial Fractions
• 7.6 Strategies for Integration
• 7.7 Improper Integrals
• 7.8 Probability and Integration
• 7.9 Numerical Integration
• 8 Further Applications of the Integral and Taylor Polynomials
• 8.1 Arc Length and Surface Area
• 8.2 Fluid Pressure and Force
• 8.3 Center of Mass
• 8.4 Taylor Polynomials
• Appendices
• A The Language of Mathematics
• B Properties of Real Numbers
• C Induction and the Binomial Theorem