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Preface | p. vii |
List of Supplements | p. xi |
Index of Applications | p. xv |
Equations, Inequalities, and Modeling | |
Equations in One Variable | p. 2 |
Equations and Graphs in Two Variables | p. 12 |
Scatter Diagrams and Curve Fitting | p. 23 |
Constructing Models to Solve Problems | p. 29 |
Quadratic Equations | p. 40 |
Linear and Absolute Value Inequalities | p. 55 |
Quadratic and Rational Inequalities | p. 67 |
Functions and Graphs | |
Functions | p. 85 |
Graphs of Relations and Functions | p. 98 |
Families of Functions: Transformations and Symmetry | p. 109 |
Operations with Functions | p. 124 |
Inverse Functions | p. 134 |
Constructing Functions with Variation | p. 146 |
Polynomial and Rational Functions | |
Linear Functions | p. 160 |
Quadratic Functions | p. 174 |
Complex Numbers | p. 185 |
Zeros of Polynomial Functions | p. 192 |
The Theory of Equations | p. 203 |
Graphs of Polynomial Functions | p. 212 |
Graphs of Rational Functions | p. 224 |
Exponential and Logarithmic Functions | |
Exponential Functions and Their Applications | p. 246 |
Logarithmic Functions and Their Applications | p. 261 |
Properties of Logarithms | p. 273 |
More Equations and Applications | p. 285 |
The Trigonometric Functions | |
Angles and Their Measurements | p. 303 |
The Sine and Cosine Functions | p. 318 |
The Graphs of the Sine and Cosine Functions | p. 331 |
The Other Trigonometric Functions and Their Graphs | p. 348 |
The Inverse Trigonometric Functions | p. 360 |
Right Triangle Trigonometry | p. 371 |
Trigonometric Identities and Conditional Equations | |
Basic Identities | p. 392 |
Verifying Identities | p. 400 |
Sum and Difference Identities | p. 407 |
Double-Angle and Half-Angle Identities | p. 416 |
Product and Sum Identities | p. 425 |
Conditional Trigonometric Equations | p. 434 |
Applications of Trigonometry | |
The Law of Sines | p. 453 |
The Law of Cosines | p. 465 |
Vectors | p. 474 |
Trigonometric Form of Complex Numbers | p. 487 |
Powers and Roots of Complex Numbers | p. 494 |
Polar Equations | p. 499 |
Parametric Equations | p. 509 |
Systems of Equations and Inequalities | |
Systems of Linear Equations in Two Variables | p. 521 |
Systems of Linear Equations in Three Variables | p. 532 |
Nonlinear Systems of Equations | p. 544 |
Partial Fractions | p. 552 |
Inequalities and Systems of Inequalities in Two Variables | p. 560 |
Linear Programming | p. 569 |
Matrices and Determinants | |
Solving Linear Systems Using Matrices | p. 580 |
Operations with Matrices | p. 594 |
Multiplication of Matrices | p. 600 |
Inverses of Matrices | p. 608 |
Solution of Linear Systems in Two Variables Using Determinants | p. 620 |
Solution of Linear Systems in Three Variables Using Determinants | p. 625 |
The Conic Sections | |
The Parabola | p. 639 |
The Ellipse and the Circle | p. 649 |
The Hyperbola | p. 662 |
Rotation of Axes | p. 675 |
Polar Equations of the Conics | p. 684 |
Sequences, Series, and Probability | |
Sequences | p. 695 |
Series | p. 705 |
Geometric Sequences and Series | p. 713 |
Counting and Permutations | p. 725 |
Combinations, Labeling, and the Binomial Theorem | p. 732 |
Probability | p. 741 |
Mathematical Induction | p. 751 |
Analytic Geometry and Vectors in Three Dimensions | |
Graphs in Space | p. 763 |
Vectors in Space | p. 768 |
Cross Product and Scalar Triple Product | p. 775 |
Equations of Lines and Planes in Space | p. 782 |
Limits | |
Finding Limits Numerically and Graphically | p. 796 |
Finding Limits Algebraically with Limit Theorems | p. 804 |
One-Sided Limits, Continuity, and Limits Involving Infinity | p. 811 |
Tangent Lines and the Derivative | p. 819 |
Appendix: Basic Algebra Review | p. 1 |
Real Numbers and Their Properties | p. 1 |
Exponents and Radicals | p. 8 |
Polynomials | p. 18 |
Factoring Polynomials | p. 23 |
Rational Expressions | p. 28 |
Appendix: Techniques for Solving Miscellaneous Equations | p. 35 |
Answers to Selected Exercises | p. 1 |
Credits | p. 1 |
Index | p. 1 |
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