Table of contents for Basic technical mathematics with calculus / Allyn J. Washington.

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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.