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Review of Numerical Computation 1 | |

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The Real Numbers 2 | |

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Addition and Subtraction 8 | |

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Multiplication 12 | |

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Division 16 | |

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Powers and Roots 20 | |

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Combined Operations 24 | |

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Scientific Notation and Engineering Notation 27 | |

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Units of Measurement 34 | |

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Percentage 43 | |

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Review Problems 50 | |

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Introduction to Algebra 54 | |

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Algebraic Expressions 55 | |

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Adding and Subtracting | |

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Polynomials 59 2-3 Laws of Exponents 63 | |

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Product of Two Monomials 69 | |

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Product of a Multinomial and a Monomial 72 | |

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Product of Two Binomials 73 | |

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Product of Two Multinomials 74 | |

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Powers of Multinomials 76 | |

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Removing Symbols of Grouping 78 | |

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Quotient of Two Monomials 80 | |

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Dividing a Polynomial by a Monomial 83 | |

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Quotient of Two Polynomials 85 | |

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Review Problems 87 | |

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Simple Equations and Word Problems | |

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Solving First-Degree Equations 92 | |

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Solving Word Problems 99 | |

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Uniform Motion 104 | |

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Financial 108 | |

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Mixtures 110 | |

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Statics 113 | |

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Work, Fluid Flow, and Energy Flow 116 | |

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Review Problems 119 | |

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•4 Functions | |

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Functions and Relations, 124 | |

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More on Functions | |

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Review Problems | |

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Graphs | |

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Rectangular Coordinates | |

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Graphing an Equation | |

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Graphing a Function by Calculator | |

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The Straight Line | |

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Solving an Equation Graphically | |

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Review Problems 148 | |

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Geometry 152 | |

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Straight Lines and Angles | |

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Triangles 156 | |

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Quadrilaterals 162 | |

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The Circle 164 | |

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Volumes and Areas of Solids 169 | |

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Review Problems 174 | |

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Right Triangles and Vectors 178 | |

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The Trigonometric Functions 179 | |

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Solution of Right Triangles 182 | |

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Applications of the Right Triangle 186 | |

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Introduction to Vectors 190 | |

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Applications of Vectors 192 | |

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Review Problems 195 | |

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Oblique Triangles and Vectors 198 | |

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Trigonometric Functions of Any Angle 199 | |

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Finding the Angle When the Trigonometric Function Is Kown | |

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Law of Sines 208 | |

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Law of Cosines 214 | |

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Applications 218 | |

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Resultants of Nonperpendicular Vectors 222 | |

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Review Problems 226 | |

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Systems of Linear Equations 229 | |

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Systems of Two Linear Equations 230 | |

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Other Systems of Equations 235 | |

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Applications 240 | |

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Systems of Three Linear Equations 246 | |

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Review Problems 252 | |

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Matrices and Determinants 256 | |

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Introduction to Matrices 257 | |

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Solving Systems of Equations by the Unit Matrix Method 260 | |

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Second-Order Determinants 265 | |

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Higher-Order Determinants 271 | |

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Review Problems 277 | |

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Factoring and Fractions 281 | |

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Common Factors 282 | |

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Difference of Two Squares 285 | |

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Factoring Trinomials | |

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Other Factorable Expressions 293 | |

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Simplification of Fractions | |

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Multiplication and Division of Fractions 300 | |

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Addition and Subtraction of Fractions 303 | |

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Complex Fractions 307 | |

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Fractional Equations 310 | |

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Literal Equations and Formulas 312 | |

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Review Problems 317 | |

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Quadratic Equations 20 | |

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Solving a Quadratic Equation by Calculator 321 | |

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Solving a Quadratic by Formula 325 | |

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Applications 328 | |

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Review Problems 332 | |

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Exponents and Radicals 335 | |

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Integral Exponents 336 | |

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Simplification of Radicals 341 | |

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Operations with Radicals 3 | |

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Radical Equations 352 | |

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Review Problems 356 | |

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Radian Measure, Arc Length, and Rotation 359 | |

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Radian Measure 360 | |

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Arc Length 366 | |

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Uniform Circular Motion 370 | |

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Review Problems 372 | |

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Trigonometric, Parametric, and Polar Graphs 375 | |

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Graphing the Sine Wave by Calculator 376 | |

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Manual Graphing of the Sine Wave 383 | |

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The Sine Wave as a Function of Time 387 | |

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Graphs of the Other Trigonometric Functions 394 | |

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Graphing Parametric Equations 400 | |

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Graphing in Polar Coordinates 404 | |

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Review Problems 410 | |

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Trigonometric Identities and Equations 414 | |

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Fundamental Identities 416 | |

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Sum or Difference of Two Angles 421 | |

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Functions of Double Angles and Half-Angles 426 | |

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Evaluating Trigonometric Expressions 432 | |

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Solving Trigonometric Equations 435 | |

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Review Problems 439 | |

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Ratio, Proportion, and Variation 442 | |

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Ratio and Proportion 443 | |

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Similar Figures 446 | |

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Direct Variation 450 | |

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The Power Function 453 | |

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Inverse Variation 457 | |

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Functions of More Than One Variable 461 | |

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Review Problems 466 | |

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Exponential and Logarithmic Functions 469 | |

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The Exponential Function 470 | |

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Logarithms 478 | |

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Properties of Logarithms 483 | |

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Exponential Equations 490 | |

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Solving Logarithmic Equations 497 | |

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Review Problems 500 | |

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Complex Numbers 504 | |

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Complex Numbers in Rectangular Form 505 | |

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Complex Numbers in Polar Form 509 | |

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Complex Numbers on the Calculator 513 | |

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Vector Operations Using Complex Numbers 515 | |

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Alternating Current Applications 519 | |

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Review Problems 524 | |

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Sequences, Series, and the Binomial Theorem 527 | |

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Sequences and Series 528 | |

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Arithmetic and Harmonic Progressions 534 | |

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Geometric Progressions 540 | |

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Infinite Geometric Progressions 544 | |

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The Binomial Theorem 546 | |

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Review Problems 553 | |

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Introduction to Statistics and Probability | |

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Definitions and Terminology | |

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Frequency Distributions | |

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Numerical Description of Data | |

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Introduction to Probability | |

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The Normal Curve | |

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Standard Errors | |

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Process Control | |

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Regression | |

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Review Problems | |

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Analytic Geometry 557 | |

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The Straight Line 558 | |

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Equation of a Straight Line 565 | |

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The Circle 572 | |

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The Parabola 579 | |

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The Ellipse 587 | |

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The Hyperbola 597 | |

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Review Problems 605 | |

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Derivatives of Algebraic Functions 610 | |

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Limits 611 | |

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Rate of Change and the Tangent 618 | |

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The Derivative 622 | |

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Rules for Derivatives 630 | |

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Derivative of a Function Raised to a Power 636 | |

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Derivatives of Products and Quotients 640 | |

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Other Variables, Implicit Relations, and Differentials 646 | |

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Higher-Order Derivatives 652 | |

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Review Problems 653 | |

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Graphical Applications of the Derivative 656 | |

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Equations of Tangents and Normals 657 | |

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Maximum, Minimum, and Inflection Points 661 | |

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Sketching, Verifying, and Interpreting Graphs 670 | |

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Review Problems 675 | |

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More Applications of the Derivative 677 | |

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Rate of Change 678 | |

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Motion of a Point 683 | |

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Related Rates 690 | |

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Optimization 696 | |

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Review Problems 705 | |

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Integration 708 | |

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The Indefinite Integral 709 | |

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Rules for Finding Integrals 718 | |

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Simple Differential Equations 726 | |

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The Definite Integral 730 | |

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Approximate Area under a Curve 734 | |

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Exact Area under a Curve 738 | |

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Review Problems 742 | |

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Applications of the Integral 744 | |

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Applications to Motion 745 | |

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Applications to Eletric Circuits 750 | |

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Finding Areas by Integration 753 | |

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Volumes by Integration 764 | |

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Review Problems 771 | |

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More Applications of the Integral 774 | |

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Length of Arc 775 | |

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Area of Surface of | |

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Revolution 779 | |

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Centroids 782 | |

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Fluid Pressure 789 | |

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Work 792 | |

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Moment of Inertia 796 | |

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Review Problems 801 | |

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Trigonometric, Logarithmic, and Exponential Functions 804 | |

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Derivatives of the Sine and Cosine Functions | |

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Derivatives of the Other Trigonometric Functions 813 | |

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Derivatives of the Inverse Trigonometric Functions 817 | |

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Derivatives of Logarithmic Functions 819 | |

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Derivatives of the Exponential Functions 825 | |

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Integrals of the Exponential and Logarithmic Functions 831 | |

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Integrals of the Trigonometric Functions 835 | |

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Average and Root Mean Square Values 839 | |

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Review Problems 841 | |

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First-Order Differential Equations 844 | |

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Definitions 845 | |

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Solving a DE by Calculator, Graphically, and Numerically 848 | |

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First-Order DE: Variables Separable 853 | |

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Exact First-Order DE 856 | |

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First-Order Homogeneous DE 859 | |

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First-Order Linear DE 861 | |

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Geometric Applications of First-Order DE 866 | |

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Exponential Growth and Decay 870 | |

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Series RL and RC Circuits 872 | |

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Review Problems 877 | |

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Second-Order Differential Equations | |

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Second-Order DE 881 | |

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Constant Coefficients and Right Side Zero 882 | |

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Right Side Not Zero 889 | |

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Mechanical Vibrations 894 | |

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RLC Circuits 899 | |

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Review Problems 907 | |

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Appendices | |

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Summary of Facts and Formulas A-1 | |

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Conversion Factors A-27 | |

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Table of Integrals | |

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Answers to Selected Problems | |

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Indexes | |

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Index to Applications | |

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General Index | |