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Washington Basic Technical Mathematics with Calculus, Ninth Edition Contents CHAPTER 1 Basic Algebraic Operations 1 1.1 Numbers 2 1.2 Fundamental Operations of Algebra 6 1.3 Calculators and Approximate Numbers 11 1.4 Exponents 16 1.5 Scientific Notation 21 1.6 Roots and Radicals 24 1.7 Addition and Subtraction of Algebraic Expressions 26 1.8 Multiplication of Algebraic Expressions 30 1.9 Division of Algebraic Expressions 32 1.10 Solving Equations 35 1.11 Formulas and Literal Equations 38 1.12 Applied Word Problems 41 Chapter Equations, Review Exercises, and Practice Test 45 CHAPTER 2 Geometry 49 2.1 Lines and Angles 50 2.2 Triangles 53 2.3 Quadrilaterals 60 2.4 Circles 63 2.5 Measurement of Irregular Areas 67 2.6 Solid Geometric Figures 71 Chapter Equations, Review Exercises, and Practice Test 75 CHAPTER 3 Functions and Graphs 80 3.1 Introduction to Functions 81 3.2 More about Functions 84 3.3 Rectangular Coordinates 89 3.4 The Graph of a Function 91 3.5 Graphs on the Graphing Calculator 96 3.6 Graphs of Functions Defined by Tables of Data 101 Review Exercises and Practice Test 105 CHAPTER 4 The Trigonometric Functions 108 4.1 Angles 109 4.2 Defining the Trigonometric Functions 112 4.3 Values of the Trigonometric Functions 115 4.4 The Right Triangle 119 4.5 Applications of Right Triangles 124 Chapter Equations, Review Exercises, and Practice Test 129 CHAPTER 5 Systems of Linear Equations; Determinants 134 5.1 Linear Equations 135 5.2 Graphs of Linear Functions 138 5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically 142 5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically 146 5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants 153 5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically 158 5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants 163 Chapter Equations, Review Exercises, and Practice Test 168 CHAPTER 6 Factoring and Fractions 173 6.1 Special Products 174 6.2 Factoring: Common Factor and Difference of Squares 177 6.3 Factoring Trinomials 182 6.4 The Sum and Differences of Cubes 188 6.5 Equivalent Fractions 189 6.6 Multiplication and Division of Fractions 194 6.7 Addition and Subtraction of Fractions 195 6.8 Equations Involving Fractions 204 Chapter Equations, Review Exercises, and Practice Test 208 CHAPTER 7 Quadratic Equations 212 7.1 Quadratic Equations; Solution by Factoring 213 7.2 Completing the Square 217 7.3 The Quadratic Formula 220 7.4 The Graph of the Quadratic Function 224 Chapter Equations, Review Exercises, and Practice Test 228 CHAPTER 8 Trigonometric Functions of Any Angle 231 8.1 Signs of the Trigonometric Functions 232 8.2 Trigonometric Functions of Any Angle 234 8.3 Radians 240 8.4 Applications of Radian Measure 244 Chapter Equations, Review Exercises, and Practice Test 250 CHAPTER 9 Vectors and Oblique Triangles 254 9.1 Introduction to Vectors 255 9.2 Components of Vectors 259 9.3 Vector Addition by Components 263 9.4 Applications of Vectors 268 9.5 Oblique Triangles, the Law of Sines 273 9.6 The Law of Cosines 280a Chapter Equations, Review Exercises, and Practice Test 284 CHAPTER 10 Graphs of the Trigonometric Functions 288 10.1 Graphs of y = a sin x and y = a cos x 289 10.2 Graphs of y = a sin bx and y = a cos bx 292 10.3 Graphs of y = a sin (bx + c) and y = a cos (bx + c) 295 10.4 Graphs of y = tan x, y = cot x, y = sec x, y = csc x 299 10.5 Applications of the Trigonometric Graphs 301 10.6 Composite Trigonometric Curves 304 Chapter Equations, Review Exercises, and Practice Test 309 CHAPTER 11 Exponents and Radicals 312 11.1 Simplifying Expressions with Integral Exponents 313 11.2 Fractional Exponents 317 11.3 Simplest Radical Form 321 11.4 Addition and Subtraction of Radicals 324 11.5 Multiplication and Division of Radicals 327 Chapter Equations, Review Exercises, and Practice Test 331 CHAPTER 12 Complex Numbers 333 12.1 Basic Definitions 334 12.2 Basic Operations with Complex Numbers 337 12.3 Graphical Representation of Complex Numbers 340 12.4 Polar Form of a Complex Number 342 12.5 Exponential Form of a Complex Number 344 12.6 Products, Quotients, Powers, and Roots of Complex Numbers 347 12.7 An Application to Alternating-Current (ac) Circuits 353 Chapter Equations, Review Exercises, and Practice Test 359 CHAPTER 13 Exponential and Logarithmic Functions 362 13.1 Exponential Functions 363 13.2 Logarithmic Functions 365 13.3 Properties of Logarithms 369 13.4 Logarithms to the Base 10 374 13.5 Natural Logarithms 377 13.6 Exponential and Logarithmic Equations 380 13.7 Graphs on Logarithmic and Semilogarithmic Paper 384 Chapter Equations, Review Exercises, and Practice Test 388 CHAPTER 14 Additional Types of Equations and Systems of Equations 391 14.1 Graphical Solution of Systems of Equations 392 14.2 Algebraic Solution of Systems of Equations 395 14.3 Equations in Quadratic Form 399 14.4 Equations with Radicals 402 Review Exercises and Practice Test 406 CHAPTER 15 Equations of Higher Degree 408 15.1 The Remainder and Factor Theorems; Synthetic Division 409 15.2 The Roots of an Equation 414 15.3 Rational and Irrational Roots 419 Chapter Equations, Review Exercises, and Practice Test 425 CHAPTER 16 Matrices; Systems of Linear Equations 427 16.1 Matrices: Definitions and Basic Operations 428 16.2 Multiplication of Matrices 432 16.3 Finding the Inverse of a Matrix 437 16.4 Matrices and Linear Equations 442 16.5 Gaussian Elimination 446 16.6 Higher Order Determinants 450 Chapter Equations, Review Exercises, and Practice Test 456 CHAPTER 17 Inequalities 460 17.1 Properties of Inequalities 461 17.2 Solving Linear Inequalities 465 17.3 Solving Nonlinear Inequalities 470 17.4 Inequalities Involving Absolute Values 477 17.5 Graphical Solution of Inequalities with Two Variables 480 17.6 Linear Programming 483 Chapter Equations, Review Exercises, and Practice Test 487 CHAPTER 18 Variation 490 18.1 Ratio and Proportion 491 18.2 Variation 495 Chapter Equations, Review Exercises, and Practice Test 501 CHAPTER 19 Sequences and the Binomial Theorem 505 19.1 Arithmetic Sequences 506 19.2 Geometric Sequences 511 19.3 Infinite Geometric Series 515 19.4 The Binomial Theorem 518 Chapter Equations, Review Exercises, and Practice Test 523 CHAPTER 20 Additional Topics in Trigonometry 526 20.1 Fundamental Trigonometric Identities 527 20.2 The Sum and Difference Formulas 533 20.3 Double-Angle Formulas 537 20.4 Half-Angle Formulas 541 20.5 Solving Trigonometric Equations 544 20.6 The Inverse Trigonometric Functions 548 Chapter Equations, Review Exercises, and Practice Test 554 CHAPTER 21 Plane Analytic Geometry 558 21.1 Basic Definitions 559 21.2 The Straight Line 563 21.3 The Circle 569 21.4 The Parabola 574 21.5 The Ellipse 578 21.6 The Hyperbola 583 21.7 Translation of Axes 589 21.8 The Second-Degree Equation 592 21.9 The Rotation of Axes 595 21.10 Polar Coordinates 599 21.11 Curves in Polar Coordinates 603 Chapter Equations, Review Exercises, and Practice Test 606 CHAPTER 22 Introduction to Statistics 612 22.1 Frequency Distributions 613 22.2 Measures of Central Tendency 617 22.3 Standard Deviation 621 22.4 Normal Distributions 625 22.5 Statistical Process Control 631 22.6 Linear Regression 636 22.7 Nonlinear Regression 641 Chapter Equations, Review Exercises, and Practice Test 645 CHAPTER 23 The Derivative 649 23.1 Limits 650 23.2 The Slope of a Tangent to a Curve 658 23.3 The Derivative 661 23.4 The Derivative as an Instantaneous Rate of Change 665 23.5 Derivatives of Polynomials 669 23.6 Derivatives of Products and Quotients of Functions 674 23.7 The Derivative of a Power of a Function 678 23.8 Differentiation of Implicit Functions 684 23.9 Higher Derivatives 687 Chapter Equations, Review Exercises, and Practice Test 690 CHAPTER 24 Applications of the Derivative 694 24.1 Tangents and Normals 695 24.2 Newtonøs Method for Solving Equations 697 24.3 Curvilinear Motion 701 24.4 Related Rates 705 24.5 Using Derivatives in Curve Sketching 709 24.6 More on Curve Sketching 715 24.7 Applied Maximum and Minimum Problems 720 24.8 Differentials and Linear Approximations 727 Chapter Equations, Review Exercises, and Practice Test 731 CHAPTER 25 Integration 735 25.1 Antiderivatives 736 25.2 The Indefinite Integral 738 25.3 The Area Under a Curve 743 25.4 The Definite Integral 748 25.5 Numerical Integration: The Trapezoidal Rule 751 25.6 Simpsonøs Rule 754 Chapter Equations, Review Exercises, and Practice Test 757 CHAPTER 26 Applications of Integration 760 26.1 Applications of the Indefinite Integral 761 26.2 Areas by Integration 765 26.3 Volumes by Integration 771 26.4 Centroids 776 26.5 Moments of Inertia 782 26.6 Other Applications 787 Chapter Equations, Review Exercises, and Practice Test 792 CHAPTER 27 Differentiation of Transcendental Functions 797 27.1 Derivatives of the Sine and Cosine Functions 798 27.2 Derivatives of the Other Trigonometric Functions 802 27.3 Derivatives of the Inverse Trigonometric Functions 805 27.4 Applications 808 27.5 Derivative of the Logarithmic Function 813 27.6 Derivative of the Exponential Function 817 27.7 LøHospitaløs Rule 820 27.8 Applications 824 Chapter Equations, Review Exercises, and Practice Test 827 CHAPTER 28 Methods of Integration 832 28.1 The General Power Formula 833 28.2 The Basic Logarithmic Form 835 28.3 The Exponential Form 839 28.4 Basic Trigonometric Forms 842 28.5 Other Trigonometric Forms 846 28.6 Inverse Trigonometric Forms 850 28.7 Integration by Parts 854 28.8 Integration by Trigonometric Substitution 858 28.9 Integration by Partial Fractions: Nonrepeated Linear Factors 861 28.10 Integration by Partial Fractions: Other Cases 864 28.11 Integration by Use of Tables 869 Chapter Equations, Review Exercises, and Practice Test 872 CHAPTER 29 Partial Derivatives and Double Integrals 876 29.1 Functions of Two Variables 877 29.2 Curves and Surfaces in Three Dimensions 880 29.3 Partial Derivatives 886 29.4 Double Integrals 890 Chapter Equations, Review Exercises, and Practice Test 894 CHAPTER 30 Expansion of Functions in Series 896 30.1 Infinite Series 897 30.2 Maclaurin Series 901 30.3 Operations with Series 905 30.4 Computations by Use of Series Expansions 909 30.5 Taylor Series 912 30.6 Introduction to Fourier Series 915 30.7 More About Fourier Series 922 Chapter Equations, Review Exercises, and Practice Test 927 CHAPTER 31 Differential Equations 931 31.1 Solutions of Differential Equations 932 31.2 Separation of Variables 934 31.3 Integrating Combinations 937 31.4 The Linear Differential Equation of the First Order 939 31.5 Numerical Solutions of First-Order Equations 942 31.6 Elementary Applications 945 31.7 Higher-Order Homogeneous Equations 951 31.8 Auxiliary Equation with Repeated or Complex Roots 955 31.9 Solutions of Nonhomogeneous Equations 958 31.10 Applications of Higher-Order Equations 963 31.11 Laplace Transforms 970 31.12 Solving Differential Equations by Laplace Transforms 975 Chapter Equations, Review Exercises, and Practice Test 979 Appendix A Solving Word Problems A.1 Appendix B Units of Measurement; The Metric System A.2 B.1 Introduction A.2 B.2 Reductions and Conversions A.5 Appendix C The Graphing Calculator A.8 C.1 Introduction A.8 C.2 The Graphing Calculator A.8 C.3 Graphing Calculator Programs A.12 C.4 T he Advanced Graphing Calculator A.16 Appendix D Newtonøs Method A.24 Appendix E A Table of Integrals A.25 Answers to Odd-Numbered Exercises B.1 Solutions to Practice Test Problems C.1 Index of Applications D.1 Index of Writing Exercises D.11

Library of Congress Subject Headings for this publication:

Mathematics.