Review of Numerical Computation 1 | |

The Real Numbers 2 | |

Addition and Subtraction 8 | |

Multiplication 12 | |

Division 16 | |

Powers and Roots 20 | |

Combined Operations 24 | |

Scientific Notation and Engineering Notation 27 | |

Units of Measurement 34 | |

Percentage 43 | |

Review Problems 50 | |

Introduction to Algebra 54 | |

Algebraic Expressions 55 | |

Adding and Subtracting | |

Polynomials 59 2-3 Laws of Exponents 63 | |

Product of Two Monomials 69 | |

Product of a Multinomial and a Monomial 72 | |

Product of Two Binomials 73 | |

Product of Two Multinomials 74 | |

Powers of Multinomials 76 | |

Removing Symbols of Grouping 78 | |

Quotient of Two Monomials 80 | |

Dividing a Polynomial by a Monomial 83 | |

Quotient of Two Polynomials 85 | |

Review Problems 87 | |

Simple Equations and Word Problems | |

Solving First-Degree Equations 92 | |

Solving Word Problems 99 | |

Uniform Motion 104 | |

Financial 108 | |

Mixtures 110 | |

Statics 113 | |

Work, Fluid Flow, and Energy Flow 116 | |

Review Problems 119 | |

•4 Functions | |

Functions and Relations, 124 | |

More on Functions | |

Review Problems | |

Graphs | |

Rectangular Coordinates | |

Graphing an Equation | |

Graphing a Function by Calculator | |

The Straight Line | |

Solving an Equation Graphically | |

Review Problems 148 | |

Geometry 152 | |

Straight Lines and Angles | |

Triangles 156 | |

Quadrilaterals 162 | |

The Circle 164 | |

Volumes and Areas of Solids 169 | |

Review Problems 174 | |

Right Triangles and Vectors 178 | |

The Trigonometric Functions 179 | |

Solution of Right Triangles 182 | |

Applications of the Right Triangle 186 | |

Introduction to Vectors 190 | |

Applications of Vectors 192 | |

Review Problems 195 | |

Oblique Triangles and Vectors 198 | |

Trigonometric Functions of Any Angle 199 | |

Finding the Angle When the Trigonometric Function Is Kown | |

Law of Sines 208 | |

Law of Cosines 214 | |

Applications 218 | |

Resultants of Nonperpendicular Vectors 222 | |

Review Problems 226 | |

Systems of Linear Equations 229 | |

Systems of Two Linear Equations 230 | |

Other Systems of Equations 235 | |

Applications 240 | |

Systems of Three Linear Equations 246 | |

Review Problems 252 | |

Matrices and Determinants 256 | |

Introduction to Matrices 257 | |

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

Second-Order Determinants 265 | |

Higher-Order Determinants 271 | |

Review Problems 277 | |

Factoring and Fractions 281 | |

Common Factors 282 | |

Difference of Two Squares 285 | |

Factoring Trinomials | |

Other Factorable Expressions 293 | |

Simplification of Fractions | |

Multiplication and Division of Fractions 300 | |

Addition and Subtraction of Fractions 303 | |

Complex Fractions 307 | |

Fractional Equations 310 | |

Literal Equations and Formulas 312 | |

Review Problems 317 | |

Quadratic Equations 20 | |

Solving a Quadratic Equation by Calculator 321 | |

Solving a Quadratic by Formula 325 | |

Applications 328 | |

Review Problems 332 | |

Exponents and Radicals 335 | |

Integral Exponents 336 | |

Simplification of Radicals 341 | |

Operations with Radicals 3 | |

Radical Equations 352 | |

Review Problems 356 | |

Radian Measure, Arc Length, and Rotation 359 | |

Radian Measure 360 | |

Arc Length 366 | |

Uniform Circular Motion 370 | |

Review Problems 372 | |

Trigonometric, Parametric, and Polar Graphs 375 | |

Graphing the Sine Wave by Calculator 376 | |

Manual Graphing of the Sine Wave 383 | |

The Sine Wave as a Function of Time 387 | |

Graphs of the Other Trigonometric Functions 394 | |

Graphing Parametric Equations 400 | |

Graphing in Polar Coordinates 404 | |

Review Problems 410 | |

Trigonometric Identities and Equations 414 | |

Fundamental Identities 416 | |

Sum or Difference of Two Angles 421 | |

Functions of Double Angles and Half-Angles 426 | |

Evaluating Trigonometric Expressions 432 | |

Solving Trigonometric Equations 435 | |

Review Problems 439 | |

Ratio, Proportion, and Variation 442 | |

Ratio and Proportion 443 | |

Similar Figures 446 | |

Direct Variation 450 | |

The Power Function 453 | |

Inverse Variation 457 | |

Functions of More Than One Variable 461 | |

Review Problems 466 | |

Exponential and Logarithmic Functions 469 | |

The Exponential Function 470 | |

Logarithms 478 | |

Properties of Logarithms 483 | |

Exponential Equations 490 | |

Solving Logarithmic Equations 497 | |

Review Problems 500 | |

Complex Numbers 504 | |

Complex Numbers in Rectangular Form 505 | |

Complex Numbers in Polar Form 509 | |

Complex Numbers on the Calculator 513 | |

Vector Operations Using Complex Numbers 515 | |

Alternating Current Applications 519 | |

Review Problems 524 | |

Sequences, Series, and the Binomial Theorem 527 | |

Sequences and Series 528 | |

Arithmetic and Harmonic Progressions 534 | |

Geometric Progressions 540 | |

Infinite Geometric Progressions 544 | |

The Binomial Theorem 546 | |

Review Problems 553 | |

Introduction to Statistics and Probability | |

Definitions and Terminology | |

Frequency Distributions | |

Numerical Description of Data | |

Introduction to Probability | |

The Normal Curve | |

Standard Errors | |

Process Control | |

Regression | |

Review Problems | |

Analytic Geometry 557 | |

The Straight Line 558 | |

Equation of a Straight Line 565 | |

The Circle 572 | |

The Parabola 579 | |

The Ellipse 587 | |

The Hyperbola 597 | |

Review Problems 605 | |

Derivatives of Algebraic Functions 610 | |

Limits 611 | |

Rate of Change and the Tangent 618 | |

The Derivative 622 | |

Rules for Derivatives 630 | |

Derivative of a Function Raised to a Power 636 | |

Derivatives of Products and Quotients 640 | |

Other Variables, Implicit Relations, and Differentials 646 | |

Higher-Order Derivatives 652 | |

Review Problems 653 | |

Graphical Applications of the Derivative 656 | |

Equations of Tangents and Normals 657 | |

Maximum, Minimum, and Inflection Points 661 | |

Sketching, Verifying, and Interpreting Graphs 670 | |

Review Problems 675 | |

More Applications of the Derivative 677 | |

Rate of Change 678 | |

Motion of a Point 683 | |

Related Rates 690 | |

Optimization 696 | |

Review Problems 705 | |

Integration 708 | |

The Indefinite Integral 709 | |

Rules for Finding Integrals 718 | |

Simple Differential Equations 726 | |

The Definite Integral 730 | |

Approximate Area under a Curve 734 | |

Exact Area under a Curve 738 | |

Review Problems 742 | |

Applications of the Integral 744 | |

Applications to Motion 745 | |

Applications to Eletric Circuits 750 | |

Finding Areas by Integration 753 | |

Volumes by Integration 764 | |

Review Problems 771 | |

More Applications of the Integral 774 | |

Length of Arc 775 | |

Area of Surface of | |

Revolution 779 | |

Centroids 782 | |

Fluid Pressure 789 | |

Work 792 | |

Moment of Inertia 796 | |

Review Problems 801 | |

Trigonometric, Logarithmic, and Exponential Functions 804 | |

Derivatives of the Sine and Cosine Functions | |

Derivatives of the Other Trigonometric Functions 813 | |

Derivatives of the Inverse Trigonometric Functions 817 | |

Derivatives of Logarithmic Functions 819 | |

Derivatives of the Exponential Functions 825 | |

Integrals of the Exponential and Logarithmic Functions 831 | |

Integrals of the Trigonometric Functions 835 | |

Average and Root Mean Square Values 839 | |

Review Problems 841 | |

First-Order Differential Equations 844 | |

Definitions 845 | |

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

First-Order DE: Variables Separable 853 | |

Exact First-Order DE 856 | |

First-Order Homogeneous DE 859 | |

First-Order Linear DE 861 | |

Geometric Applications of First-Order DE 866 | |

Exponential Growth and Decay 870 | |

Series RL and RC Circuits 872 | |

Review Problems 877 | |

Second-Order Differential Equations | |

Second-Order DE 881 | |

Constant Coefficients and Right Side Zero 882 | |

Right Side Not Zero 889 | |

Mechanical Vibrations 894 | |

RLC Circuits 899 | |

Review Problems 907 | |

Appendices | |

Summary of Facts and Formulas A-1 | |

Conversion Factors A-27 | |

Table of Integrals | |

Answers to Selected Problems | |

Indexes | |

Index to Applications | |

General Index | |

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