Basic Technical Mathematics with Calculus

by Washington, Allyn J.

• ISBN13: 9780321131942
• ISBN10: 0321131940
• Edition: 9th
• Format: Hardcover
• Copyright: 2009-01-01
• Publisher: Prentice Hall

Summary

This tried-and-true text from the pioneer of the basic technical mathematics course now has Addison-Wesley's amazing math technologies MyMathLab and MathXL helping students to develop and maintain the math skills they will need in their technical careers.Technical mathematics is a course pioneered by Allyn Washington, and the eighth edition of this text preserves the author's highly regarded approach to technical math, while enhancing 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 in pursuit of 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 forty 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	(49)
Numbers	2	(4)
Fundamental Operations of Algebra	6	(5)
Calculators and Approximate Numbers	11	(5)
Exponents	16	(5)
Scientific Notation	21	(3)
Roots and Radicals	24	(2)
Addition and Subtraction of Algebraic Expressions	26	(4)
Multiplication of Algebraic Expressions	30	(2)
Division of Algebraic Expressions	32	(4)
Solving Equations	36	(3)
Formulas and Literal Equations	39	(3)
Applied Word Problems	42	(8)
Chapter Equations, Review Exercises, and Practice Test	46	(4)
Geometry	50	(31)
Lines and Angles	51	(3)
Triangles	54	(7)
Quadrilaterals	61	(3)
Circles	64	(4)
Measurement of Irregular Areas	68	(4)
Solid Geometric Figures	72	(9)
Chapter Equations, Review Exercises, and Practice Test	76	(5)
Functions and Graphs	81	(29)
Introduction to Functions	82	(3)
More about Functions	85	(5)
Rectangular Coordinates	90	(2)
The Graph of a Function	92	(6)
Graphs on the Graphing Calculator	98	(5)
Graphs of Functions Defined by Tables of Data	103	(7)
Review Exercises and Practice Test	107	(3)
The Trigonometric Functions	110	(27)
Angles	111	(3)
Defining the Trigonometric Functions	114	(4)
Values of the Trigonometric Functions	118	(4)
The Right Triangle	122	(5)
Applications of Right Triangles	127	(10)
Chapter Equations, Review Exercises, and Practice Test	132	(5)
Systems of Linear Equations; Determinants	137	(39)
Linear Equations	138	(3)
Graphs of Linear Functions	141	(4)
Solving Systems of Two Linear Equations in Two Unknowns Graphically	145	(4)
Solving Systems of Two Linear Equations in Two Unknowns Algebraically	149	(7)
Solving Systems of Two Linear Equations in Two Unknowns by Determinants	156	(5)
Solving Systems of Three Linear Equations in Three Unknowns Algebraically	161	(5)
Solving Systems of Three Linear Equations in Three Unknowns by Determinants	166	(10)
Chapter Equations, Review Exercises, and Practice Test	171	(5)
Factoring and Fractions	176	(40)
Special Products	177	(3)
Factoring: Common Factor and Difference of Squares	180	(5)
Factoring Trinomials	185	(6)
The Sum and Differences of Cubes	191	(2)
Equivalent Fractions	193	(5)
Multiplication and Division of Fractions	198	(4)
Addition and Subtraction of Fractions	202	(6)
Equations Involving Fractions	208	(8)
Chapter Equations, Review Exercises, and Practice Test	212	(4)
Quadratic Equations	216	(19)
Quadratic Equations; Solution by Factoring	217	(4)
Completing the Square	221	(3)
The Quadratic Formula	224	(4)
The Graph of the Quadratic Function	228	(7)
Chapter Equations, Review Exercises, and Practice Test	232	(3)
Trigonometric Functions of Any Angle	235	(23)
Signs of the Trigonometric Functions	236	(2)
Trigonometric Functions of Any Angle	238	(6)
Radians	244	(5)
Applications of Radian Measure	249	(9)
Chapter Equations, Review Exercises, and Practice Test	254	(4)
Vectors and Oblique Triangles	258	(34)
Introduction to Vectors	259	(4)
Components of Vectors	263	(4)
Vector Addition by Components	267	(5)
Applications of Vectors	272	(5)
Oblique Triangles, the Law of Sines	277	(7)
The Law of Cosines	284	(8)
Chapter Equations, Review Exercises, and Practice Test	289	(3)
Graphs of the Trigonometric Functions	292	(25)
Graphs of y = a sin x and y = a cos x	293	(3)
Graphs of y = a sin bx and y = a cos bx	296	(4)
Graphs of y = a sin(bx + c) and y = a cos(bx + c)	300	(3)
Graphs of y = tan x, y = cot x, y = sec x, y = csc x	303	(3)
Applications of the Trigonometric Graphs	306	(3)
Composite Trigonometric Curves	309	(8)
Chapter Equations, Review Exercises, and Practice Test	313	(4)
Exponents and Radicals	317	(22)
Simplifying Expressions with Integral Exponents	318	(4)
Fractional Exponents	322	(5)
Simplest Radical Form	327	(3)
Addition and Subtraction of Radicals	330	(3)
Multiplication and Division of Radicals	333	(6)
Chapter Equations, Review Exercises, and Practice Test	337	(2)
Complex Numbers	339	(31)
Basic Definitions	340	(3)
Basic Operations with Complex Numbers	343	(3)
Graphical Representation of Complex Numbers	346	(3)
Polar Form of a Complex Number	349	(3)
Exponential Form of a Complex Number	352	(3)
Products, Quotients, Powers, and Roots of Complex Numbers	355	(6)
An Application to Alternating-Current (ac) Circuits	361	(9)
Chapter Equations, Review Exercises, and Practice Test	367	(3)
Exponential and Logarithmic Functions	370	(29)
Exponential Functions	371	(2)
Logarithmic Functions	373	(4)
Properties of Logarithms	377	(5)
Logarithms to the Base 10	382	(3)
Natural Logarithms	385	(3)
Exponential and Logarithmic Equations	388	(4)
Graphs on Logarithmic and Semilogarithmic Paper	392	(7)
Chapter Equations, Review Exercises, and Practice Test	396	(3)
Additional Types of Equations and Systems of Equations	399	(17)
Graphical Solution of Systems of Equations	400	(3)
Algebraic Solution of Systems of Equations	403	(4)
Equations in Quadratic Form	407	(3)
Equations with Radicals	410	(6)
Review Exercises and Practice Test	414	(2)
Equations of Higher Degree	416	(19)
The Remainder and Factor Theorems; Synthetic Division	417	(5)
The Roots of an Equation	422	(5)
Rational and Irrational Roots	427	(8)
Chapter Equations, Review Exercises, and Practice Test	433	(2)
Matrices	435	(23)
Definitions and Basic Operations	436	(4)
Multiplication of Matrices	440	(5)
Finding the Inverse of a Matrix	445	(5)
Matrices and Linear Equations	450	(8)
Chapter Equations, Review Exercises, and Practice Test	454	(4)
Inequalities	458	(30)
Properties of Inequalities	459	(4)
Solving Linear Inequalities	463	(5)
Solving Nonlinear Inequalities	468	(7)
Inequalities Involving Absolute Values	475	(3)
Graphical Solution of Inequalities with Two Variables	478	(3)
Linear Programming	481	(7)
Chapter Equations, Review Exercises, and Practice Test	485	(3)
Variation	488	(15)
Ratio and Proportion	489	(4)
Variation	493	(10)
Chapter Equations, Review Exercises, and Practice Test	499	(4)
Sequences and the Binomial Theorem	503	(21)
Arithmetic Sequences	504	(5)
Geometric Sequences	509	(4)
Infinite Geometric Series	513	(3)
The Binomial Theorem	516	(8)
Chapter Equations, Review Exercises, and Practice Test	521	(3)
Additional Topics in Trigonometry	524	(35)
Fundamental Trigonometric Identities	525	(7)
The Sum and Difference Formulas	532	(5)
Double-Angle Formulas	537	(4)
Half-Angle Formulas	541	(3)
Solving Trigonometric Equations	544	(5)
The Inverse Trigonometric Functions	549	(10)
Chapter Equations, Review Exercises, and Practice Test	555	(4)
Plane Analytic Geometry	559	(49)
Basic Definitions	560	(4)
The Straight Line	564	(6)
The Circle	570	(4)
The Parabola	574	(5)
The Ellipse	579	(5)
The Hyperbola	584	(6)
Translation of Axes	590	(3)
The Second-Degree Equation	593	(3)
Polar Coordinates	596	(4)
Curves in Polar Coordinates	600	(8)
Chapter Equations, Review Exercises, and Practice Test	603	(5)
Introduction to Statistics	608	(37)
Frequency Distributions	609	(4)
Measures of Central Tendency	613	(4)
Standard Deviation	617	(4)
Normal Distributions	621	(6)
Statistical Process Control	627	(5)
Linear Regression	632	(5)
Nonlinear Regression	637	(8)
Chapter Equations, Review Exercises, and Practice Test	641	(4)
The Derivative	645	(46)
Limits	646	(8)
The Slope of a Tangent to a Curve	654	(3)
The Derivative	657	(4)
The Derivative as an Instantaneous Rate of Change	661	(4)
Derivatives of Polynomials	665	(5)
Derivatives of Products and Quotients of Functions	670	(5)
The Derivative of a Power of a Function	675	(6)
Differentiation of Implicit Functions	681	(2)
Higher Derivatives	683	(8)
Chapter Equations, Review Exercises, and Practice Test	687	(4)
Applications of the Derivative	691	(42)
Tangents and Normals	692	(3)
Newton's Method for Solving Equations	695	(3)
Curvilinear Motion	698	(5)
Related Rates	703	(4)
Using Derivatives in Curve Sketching	707	(6)
More on Curve Sketching	713	(5)
Applied Maximum and Minimum Problems	718	(7)
Differentials and Linear Approximations	725	(8)
Chapter Equations, Review Exercises, and Practice Test	729	(4)
Integration	733	(25)
Antiderivatives	734	(2)
The Indefinite Integral	736	(5)
The Area Under a Curve	741	(5)
The Definite Integral	746	(3)
Numerical Integration: The Trapezoidal Rule	749	(3)
Simpson's Rule	752	(6)
Chapter Equations, Review Exercises, and Practice Test	755	(3)
Applications of Integration	758	(39)
Applications of the Indefinite Integral	759	(5)
Areas by Integration	764	(6)
Volumes by Integration	770	(5)
Centroids	775	(7)
Moments of Inertia	782	(5)
Other Applications	787	(10)
Chapter Equations, Review Exercises, and Practice Test	792	(5)
Differentiation of Transcendental Functions	797	(34)
Derivatives of the Sine and Cosine Functions	798	(5)
Derivatives of the Other Trigonometric Functions	803	(3)
Derivatives of the Inverse Trigonometric Functions	806	(4)
Applications	810	(5)
Derivative of the Logarithmic Function	815	(4)
Derivative of the Exponential Function	819	(4)
Applications	823	(8)
Chapter Equations, Review Exercises, and Practice Test	827	(4)
Methods of Integration	831	(44)
The General Power Formula	832	(2)
The Basic Logarithmic Form	834	(4)
The Exponential Form	838	(3)
Basic Trigonometric Forms	841	(4)
Other Trigonometric Forms	845	(4)
Inverse Trigonometric Forms	849	(4)
Integration by Parts	853	(3)
Integration by Trigonometric Substitution	856	(3)
Integration by Partial Fractions: Nonrepeated Linear Factors	859	(4)
Integration by Partial Fractions: Other Cases	863	(5)
Integration by Use of Tables	868	(7)
Chapter Equations, Review Exercises, and Practice Test	871	(4)
Expansion of Functions in Series	875	(35)
Infinite Series	876	(4)
Maclaurin Series	880	(4)
Certain Operations with Series	884	(4)
Computations by Use of Series Expansions	888	(3)
Taylor Series	891	(3)
Introduction to Fourier Series	894	(7)
More about Fourier Series	901	(9)
Chapter Equations, Review Exercises, and Practice Test	906	(4)
Differential Equations	910	(51)
Solutions of Differential Equations	911	(2)
Separation of Variables	913	(4)
Integrating Combinations	917	(2)
The Linear Differential Equation of the First Order	919	(3)
Elementary Applications	922	(6)
Higher-Order Homogeneous Equations	928	(4)
Auxiliary Equations with Repeated or Complex Roots	932	(3)
Solutions of Nonhomogeneous Equations	935	(5)
Applications of Higher-Order Equations	940	(7)
Laplace Transforms	947	(5)
Solving Differential Equations by Laplace Transforms	952	(9)
Chapter Equations, Review Exercises, and Practice Test	956	(5)
Supplementary Topics	961
Higher-Order Determinants	961	(6)
Gaussian Elimination	967	(3)
Rotation of Axes	970	(4)
Functions of Two Variables	974	(3)
Curves and Surfaces in Three Dimensions	977	(6)
Partial Derivatives	983	(4)
Double Integrals	987	(4)
Numerical Solutions of Differential Equations	991
Appendix A Study Aids	1	(3)
A.1 Introduction	1	(1)
A.2 Suggestions for Study	2	(1)
A.3 Solving Word Problems	3	(1)
Appendix B Units of Measurement; The Metric System	4	(6)
B.1 Introduction	4	(3)
B.2 Reductions and Conversions	7	(3)
Appendix C The Graphing Calculator	10	(8)
C.1 Introduction	10	(1)
C.2 The Graphing Calculator	10	(4)
C.3 Graphing Calculator Programs	14	(4)
Appendix D Newton's Method	18	(1)
Appendix E Table of Integrals	19
Answers to Odd-Numbered Exercises	1	(1)
Solutions to Practice Test Problems	1	(1)
Index of Applications	1	(10)
Index of Writing Exercises	11	(2)
Index	13