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What is included with this book?
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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