Note: Each chapter concludes with Review Exercises and P.S. Problem Solving. P. Prerequisites P.1 Solving Equations P.2 Solving Inequalities P.3 Graphical Representation of Data P.4 Graphs of Equations P.5 Linear Equations in Two Variables | |
Functions and Their Graphs | |
Functions | |
Analyzing Graphs of Functions | |
Shifting, Reflecting, and Stretching Graphs | |
Combinations of Functions | |
Inverse Functions | |
Mathematical Modeling | |
Polynomial and Rational Functions | |
Quadratic Functions | |
Polynomial Functions of Higher Degree | |
Polynomial and Synthetic Division | |
Complex Numbers | |
Zeros of Polynomial Functions | |
Rational Functions | |
Limits and Their Properties | |
A Preview of Calculus | |
Finding Limits Graphically and Numerically | |
Evaluating Limits Analytically | |
Continuity and One-Sided Limits | |
Infinite Limits | |
Differentiation | |
The Derivative and the Tangent Line Problem | |
Basic Differentiation Rules and Rates of Change | |
The Product and Quotient Rules and Higher-Order Derivatives | |
The Chain Rule | |
Implicit Differentiation | |
Related Rates | |
Applications of Differentiation | |
Extrema on an Interval | |
Rolle's Theorem and the Mean Value Theorem | |
Increasing and Decreasing Functions and the First Derivative Test | |
Concavity and the Second Derivative Test | |
Limits at Infinity | |
A Summary of Curve Sketching | |
Optimization Problems | |
Differentials | |
Integration | |
Antiderivatives and Indefinite Integration | |
Area | |
Riemann Sums and Definite Integrals | |
The Fundamental Theorem of Calculus | |
Integration by Substitution | |
Numerical Integration | |
Exponential and Logarithmic Functions | |
Exponential Functions and Their Graphs | |
Logarithmic Functions and Their Graphs | |
Properties of Logarithms | |
Exponential and Logarithmic Equations | |
Exponential and Logarithmic Models | |
Exponential and Logarithmic Functions and Calculus | |
Exponential Functions: Differentiation and Integration | |
Logarithmic Functions and Differentiation | |
Logarithmic Functions and Integration | |
Differential Equations: Growth and Decay | |
Trigonometric Functions | |
Radian and Degree Measure | |
Trigonometric Functions: The Unit Circle | |
Right Triangle Trigonometry | |
Trigonometric Functions of Any Angle | |
Graphs of Sine and Cosine Functions | |
Graphs of Other Trigonometric Functions | |
Inverse Trigonometric Functions | |
Applications and Models | |
Analytic Trigonometry | |
Using Fundamental Identities | |
Verifying Trigonometric Identities | |
Solving Trigonometric Equations | |
Sum and Difference Formulas | |
Multiple-Angle and Product-Sum Formulas | |
Trigonometric Functions and Calculus | |
Limits of Trigonometric Functions | |
Trigonometric Functions: Differentiation | |
Trigonometric Functions: Integration | |
Inverse Trigonometric Functions: Differentiation | |
Inverse Trigonometric Functions: Integration | |
Hyperbolic Functions | |
Additional Topics in Trigonometry | |
Law of Sines | |
Law of Cosines | |
Vectors in the Plane | |
Vectors and Dot Products | |
Trigonometric Form of a Complex Number | |
Systems of Equations and Matrices | |
Systems of Linear Equations in Two Variables | |
Multivariable Linear Systems | |
Systems of Inequalities | |
Matrices and Systems of Equations | |
Operations with Matrices | |
The Inverse of a Square Matrix | |
The Determinant of a Square Matrix | |
Topics in Analytic Geometry | |
Introduction to Conics: Parabolas | |
Ellipses and Implicit Differentiation | |
Hyperbolas and Implicit Differentiation | |
Parametric Equations | |
Polar Coordinates | |
Graphs of Polar Equations | |
Polar Equations of Conics | |
Proofs of Selected Theorems Answers to Odd-Numbered Exercises | |
Index of Applications | |
Index | |
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