Basic Technical Mathematics

by Washington, Allyn J.

• ISBN13: 9780201356649
• ISBN10: 0201356643
• Edition: 7th
• Format: Hardcover
• Copyright: 2000-01-01
• Publisher: Addison Wesley

Summary

Technical mathematics is a course pioneered by Allyn Washington, and the seventh edition of this text preserves the author's highly regarded approach to technical math while improving on the integration of technology in the text. The book is intended for a two or three-semester course and is taught primarily to students who plan to pursue technical fields. The primary strength of the text is the heavy integration of technical applications, which aids the student pursuing a technical career by showing the importance of a strong foundation in algebraic and trigonometric math. Allyn Washington defined the technical math market when he wrote the first edition of Basic Technical Mathematics over thirty years ago. His continued vision is to provide highly accurate mathematical concepts based on technical applications. The course is designed to allow the student to be simultaneously enrolled in allied technical areas, such as physics or electronics. The material in the text can be easily rearranged to fit the needs of both instructor and students. Above all, the author's vision of this book is to continue to enlighten today's students that an understanding of elementary math is critical in many aspects of life.

Table of Contents

Basic Algebraic Operations	1	(47)
Numbers	2	(4)
Fundamental Operations of Algebra	6	(4)
Calculators and Approximate Numbers	10	(6)
Exponents	16	(5)
Scientific Notation	21	(3)
Roots and Radicals	24	(2)
Addition and Subtraction of Algebraic Expressions	26	(3)
Multiplication of Algebraic Expressions	29	(2)
Division of Algebraic Expressions	31	(3)
Solving Equations	34	(4)
Formulas and Literal Equations	38	(3)
Applied Word Problems	41	(7)
Chapter Equations, Review Exercises, and Practice Test	45	(3)
Geometry	48	(29)
Lines and Angles	48	(4)
Triangles	52	(6)
Quadrilaterals	58	(4)
Circles	62	(3)
Measurement of Irregular Areas	65	(4)
Solid Geometric Figures	69	(8)
Chapter Equations, Review Exercises, and Practice Test	73	(4)
Functions and Graphs	77	(27)
Introduction to Functions	77	(4)
More About Functions	81	(5)
Rectangular Coordinates	86	(2)
The Graph of a Function	88	(5)
Graphs on the Graphing Calculator	93	(4)
Graphs of Functions Defined by Tables of Data	97	(7)
Review Exercises and Practice Test	101	(3)
The Trigonometric Functions	104	(25)
Angles	104	(3)
Defining the Trigonometric Functions	107	(5)
Values of the Trigonometric Functions	112	(4)
The Right Triangle	116	(4)
Applications of Right Triangles	120	(9)
Chapter Equations, Review Exercises, and Practice Test	124	(5)
Systems of Linear Equations; Determinants	129	(37)
Linear Equations	129	(3)
Graphs of Linear Functions	132	(4)
Solving Systems of Two Linear Equations in Two Unknowns Graphically	136	(4)
Solving Systems of Two Linear Equations in Two Unknowns Algebraically	140	(7)
Solving Systems of Two Linear Equations in Two Unknowns by Determinants	147	(5)
Solving Systems of Three Linear Equations in Three Unknowns Algebraically	152	(5)
Solving Systems of Three Linear Equations in Three Unknowns by Determinants	157	(9)
Chapter Equations, Review Exercises, and Practice Test	162	(4)
Factoring and Fractions	166	(36)
Special Products	166	(4)
Factoring: Common Factor and Difference of Squares	170	(4)
Factoring Trinomials	174	(6)
The Sum and Difference of Cubes	180	(1)
Equivalent Fractions	181	(5)
Multiplication and Division of Fractions	186	(3)
Addition and Subtraction of Fractions	189	(6)
Equations Involving Fractions	195	(7)
Chapter Equations, Review Exercises, and Practice Test	199	(3)
Quadratic Equations	202	(19)
Quadratic Equations; Solution by Factoring	202	(5)
Completing the Square	207	(3)
The Quadratic Formula	210	(4)
The Graph of the Quadratic Function	214	(7)
Chapter Equations, Review Exercises, and Practice Test	218	(3)
Trigonometric Functions of Any Angle	221	(22)
Signs of the Trigonometric Functions	221	(3)
Trigonometric Functions of Any Angle	224	(6)
Radians	230	(5)
Applications of Radian Measure	235	(8)
Chapter Equations, Review Exercises, and Practice Test	240	(3)
Vectors and Oblique Triangles	243	(33)
Introduction to Vectors	243	(5)
Components of Vectors	248	(4)
Vector Addition by Components	252	(5)
Applications of Vectors	257	(4)
Oblique Triangles, the Law of Sines	261	(7)
The Law of Cosines	268	(8)
Chapter Equations, Review Exercises, and Practice Test	272	(4)
Graphs of the Trigonometric Functions	276	(24)
Graphs of y = a sin x and y = a cos x	276	(4)
Graphs of y = a sin bx and y = a cos bx	280	(3)
Graphs of y = a sin(bx + c) and y = a cos(bx + c)	283	(4)
Graphs of y = tan x, y = cot x, y = sec x, y = csc x	287	(3)
Applications of the Trigonometric Graphs	290	(3)
Composite Trigonometric Curves	293	(7)
Chapter Equations, Review Exercises, and Practice Test	297	(3)
Exponents and Radicals	300	(21)
Simplifying Expressions with Integral Exponents	300	(5)
Fractional Exponents	305	(4)
Simplest Radical Form	309	(3)
Addition and Subtraction of Radicals	312	(3)
Multiplication and Division of Radicals	315	(6)
Chapter Equations, Review Exercises, and Practice Test	319	(2)
Complex Numbers	321	(30)
Basic Definitions	321	(4)
Basic Operations with Complex Numbers	325	(3)
Graphical Representation of Complex Numbers	328	(2)
Polar Form of a Complex Number	330	(3)
Exponential Form of a Complex Number	333	(3)
Products, Quotients, Powers, and Roots of Complex Numbers	336	(6)
An Application to Alternating-Current (ac) Circuits	342	(9)
Chapter Equations, Review Exercises, and Practice Test	348	(3)
Exponential and Logarithmic Functions	351	(28)
The Exponential and Logarithmic Functions	351	(3)
Graphs of y = bx and y = logbx	354	(4)
Properties of Logarithms	358	(4)
Logarithms to the Base 10	362	(3)
Natural Logarithms	365	(3)
Exponential and Logarithmic Equations	368	(4)
Graphs on Logarithmic and Semilogarithmic Paper	372	(7)
Chapter Equations, Review Exercises, and Practice Test	376	(3)
Additional Types of Equations and Systems of Equations	379	(17)
Graphical Solution of Systems of Equations	379	(4)
Algebraic Solution of Systems of Equations	383	(3)
Equations in Quadratic Form	386	(4)
Equations with Radicals	390	(6)
Review Exercises and Practice Test	393	(3)
Equations of Higher Degree	396	(20)
The Remainder Theorem and the Factor Theorem	396	(3)
Synthetic Division	399	(4)
The Roots of an Equation	403	(5)
Rational and Irrational Roots	408	(8)
Chapter Equations, Review Exercises, and Practice Test	414	(2)
Determinants and Matrices	416	(33)
Determinants: Expansion by Minors	416	(6)
Some Properties of Determinants	422	(4)
Matrices: Definitions and Basic Operations	426	(4)
Multiplication of Matrices	430	(5)
Finding the Inverse of a Matrix	435	(5)
Matrices and Linear Equations	440	(9)
Chapter Equations, Review Exercises, and Practice Test	444	(5)
Inequalities	449	(26)
Properties of Inequalities	449	(5)
Solving Linear Inequalities	454	(5)
Solving Nonlinear Inequalities	459	(6)
Inequalities Involving Absolute Values	465	(3)
Graphical Solution of Inequalities with Two Variables	468	(7)
Chapter Equations, Review Exercises, and Practice Test	473	(2)
Variation	475	(14)
Ratio and Proportion	475	(5)
Variation	480	(9)
Chapter Equations, Review Exercises, and Practice Test	485	(4)
Sequences and the Binomial Theorem	489	(20)
Arithmetic Sequences	489	(6)
Geometric Sequences	495	(3)
Infinite Geometric Series	498	(4)
The Binomial Theorem	502	(7)
Chapter Equations, Review Exercises, and Practice Test	506	(3)
Additional Topics in Trigonometry	509	(34)
Fundamental Trigonometric Identities	510	(7)
The Sum and Difference Formulas	517	(5)
Double-Angle Formulas	522	(3)
Half-Angle Formulas	525	(4)
Solving Trigonometric Equations	529	(4)
The Inverse Trigonometric Functions	533	(10)
Chapter Equations, Review Exercises, and Practice Test	539	(4)
Plane Analytic Geometry	543	(48)
Basic Definitions	543	(5)
The Straight Line	548	(6)
The Circle	554	(4)
The Parabola	558	(5)
The Ellipse	563	(5)
The Hyperbola	568	(6)
Translation of Axes	574	(3)
The Second-Degree Equation	577	(3)
Polar Coordinates	580	(3)
Curves in Polar Coordinates	583	(8)
Chapter Equations, Review Exercises, and Practice Test	586	(5)
Introduction to Statistics	591	(36)
Frequency Distributions	592	(4)
Measures of Central Tendency	596	(4)
Standard Deviation	600	(4)
Normal Distributions	604	(5)
Statistical Process Control	609	(5)
Linear Regression	614	(5)
Nonlinear Regression	619	(8)
Chapter Equations, Review Exercises, and Practice Test	623	(4)
SUPPLEMENTARY TOPICS	627
S-1 Gaussian Elimination	627
S-2 Rotation of Axes	630
APPENDIX A STUDY AIDS	A-1
A-1 Introduction	A-1
A-2 Suggestions for Study	A-2
A-3 Solving Word Problems	A-3
APPENDIX B UNITS OF MEASUREMENT; THE METRIC SYSTEM	A-4
B-1 Introduction	A-4
B-2 Reductions and Conversions	A-7
APPENDIX C THE GRAPHING CALCULATOR	A-10
C-1 Introduction	A-10
C-2 The Graphing Calculator	A-10
C-3 Graphing Calculator Programs	A-14
Answers to Odd-Numbered Exercises	B-1
Solutions to Practice Test Problems	C-1
Index of Applications	D-1
Index of Writing Exercises	D-10
Index	D-12