Basic Technical Mathematics with Calculus : Metric Version

by Washington, Alyn J.

• ISBN13: 9780201356663
• ISBN10: 020135666X
• 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. The book is intended for a two or three semester course and is taught primarily to students who plan to pursue engineering or other 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 arranged easily to fit the needs of the instructor as well as the 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 = logb x	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 Equations	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 Equation, 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)
The Derivative	627	(47)
Limits	628	(8)
The Slope of a Tangent to a Curve	636	(4)
The Derivative	640	(4)
The Derivative as an Instantaneous Rate of Change	644	(4)
Derivatives of Polynomials	648	(5)
Derivatives of Products and Quotients of Functions	653	(5)
The Derivative of a Power of a Function	658	(6)
Differentiation of Implicit Functions	664	(2)
Higher Derivatives	666	(8)
Chapter Equations, Review Exercises, and Practice Test	670	(4)
Applications of the Derivative	674	(41)
Tangents and Normals	674	(4)
Newton's Method for Solving Equations	678	(3)
Curvilinear Motion	681	(5)
Related Rates	686	(4)
Using Derivatives in Curve Sketching	690	(6)
More on Curve Sketching	696	(4)
Applied Maximum and Minimum Problems	700	(6)
Differentials and Linear Approximations	706	(9)
Chapter Equations, Review Exercises, and Practice Test	711	(4)
Integration	715	(25)
Antiderivatives	715	(3)
The Indefinite Integral	718	(5)
The Area Under a Curve	723	(5)
The Definite Integral	728	(3)
Numerical Integration: The Trapezoidal Rule	731	(3)
Simpson's Rule	734	(6)
Chapter Equations, Review Exercises, and Practice Test	737	(3)
Applications of Integration	740	(38)
Applications of the Indefinite Integral	740	(6)
Areas by Integration	746	(6)
Volumes by Integration	752	(5)
Centroids	757	(7)
Moments of Inertia	764	(5)
Other Applications	769	(9)
Chapter Equations, Review Exercises, and Practice Test	774	(4)
Differentiation of Transcendental Functions	778	(33)
Derivatives of the Sine and Cosine Functions	778	(6)
Derivatives of the Other Trigonometric Functions	784	(3)
Derivatives of the Inverse Trigonometric Functions	787	(4)
Applications	791	(5)
Derivative of the Logarithmic Function	796	(4)
Derivative of the Exponential Function	800	(4)
Applications	804	(7)
Chapter Equations, Review Exercises, and Practice Test	807	(4)
Methods of Integration	811	(42)
The General Power Formula	811	(3)
The Basic Logarithmic Form	814	(4)
The Exponential Form	818	(2)
Basic Trigonometric Forms	820	(4)
Other Trigonometric Forms	824	(4)
Inverse Trigonometric Forms	828	(4)
Integration by Parts	832	(3)
Integration by Trigonometric Substitution	835	(3)
Integration by Partial Fractions: Nonrepeated Linear Factors	838	(4)
Integration by Partial Fractions: Other Cases	842	(5)
Integration by Use of Tables	847	(6)
Chapter Equations, Review Exercises, and Practice Test	850	(3)
Expansion of Functions in Series	853	(33)
Infinite Series	853	(5)
Maclaurin Series	858	(4)
Certain Operations with Series	862	(4)
Computations by Use of Series Expansions	866	(3)
Taylor Series	869	(3)
Introduction to Fourier Series	872	(7)
More about Fourier Series	879	(7)
Chapter Equations, Review Exercises, and Practice Test	883	(3)
Differential Equations	886	(51)
Solutions of Differential Equations	886	(3)
Separation of Variables	889	(4)
Integrating Combinations	893	(2)
The Linear Differential Equation of the First Order	895	(3)
Elementary Applications	898	(6)
Higher-Order Homogeneous Equations	904	(4)
Auxiliary Equations with Repeated or Complex Roots	908	(3)
Solutions of Nonhomogeneous Equations	911	(5)
Applications of Second-Order Equations	916	(6)
Laplace Transforms	922	(6)
Solving Differential Equations by Laplace Transforms	928	(9)
Chapter Equations, Review Exercises, and Practice Test	932	(5)
Supplementary Topics	937	(24)
S-1 Gaussian Elimination	937	(3)
S-2 Rotation of Axes	940	(4)
S-3 Functions of Two Variables	944	(3)
S-4 Curves and Surfaces in Three Dimensions	947	(6)
S-5 Partial Derivatives	953	(4)
S-6 Double Integrals	957	(4)
S-7 Numerical Solutions of Differential Equations	961
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 The Metric System (SI)	A-4
B-2 Changing Units	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
Appendix D Newton's Method	A-18
Appendix E A Table of Integrals	A-19
Answers to Odd-Numbered Exercises	B-1
Solutions to Practice Test Problems	C-1
Index of Applications	D-1
Index of Writing Exercises	D-12
Index	D-14