9780130488220

Technical Mathematics with Calculus

by ; ;
  • ISBN13:

    9780130488220

  • ISBN10:

    0130488224

  • Edition: 2nd
  • Format: Paperback
  • Copyright: 2004-06-22
  • Publisher: Pearson

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Summary

//-->4882B-1, 0-13-048822-4, Ewen, Dale, Gary, Joan S., Trefzger, James E., Technical Mathematics with Calculus, 2/E//-->This book provides readers with necessary mathematics skills, including practical calculus. Mathematics provides the essential framework for and is the basic language of all the technologies. Mathematical, problem-solving, and critical thinking skills are crucial to understanding the changing face of technology.It presents the following major areas: fundamental concepts and measurement; fundamental algebraic concepts; exponential and logarithmic functions; right-triangle trigonometry; the trigonometric functions with formulas and identities; complex numbers; matrices; polynomial and rational functions; basic statistics; analytic geometry; differential and integral calculus with applications; partial derivatives and double integrals; series; and differential equations. An excellent learning aid and resource tool for engineers, especially computer software, hardware, and peripheral manufacturers. Its comprehensive appendices make this an excellent desktop reference.

Table of Contents

Fundamental Concepts
1(76)
Introduction
1(1)
The Real Number System
1(5)
Zero and Order of Operations
6(3)
Scientific Notation and Powers of 10
9(5)
Measurement
14(3)
Operations with Measurements
17(4)
Algebraic Expressions
21(5)
Exponents and Radicals
26(5)
Multiplication of Algebraic Expressions
31(4)
Division of Algebraic Expressions
35(3)
Linear Equations
38(4)
Formulas
42(3)
Substitution of Data into Formulas
45(5)
Applications Involving Linear Equations
50(5)
Ratio and Proportion
55(5)
Variation
60(17)
Summary
65(5)
Review
70(3)
Special NASA Application: Spare Parts for the Space Shuttle
73(2)
Application: Precision-Machined Computer Disks
75(2)
Review of Geometry
77(37)
Introduction
77(1)
Angles and Lines
77(5)
Triangles
82(8)
Quadrilaterals
90(5)
Circles
95(5)
Geometric Solids: Areas and Volumes
100(14)
Summary
107(3)
Review
110(2)
Special NASA Application: Window-to-Wall Ratio
112(2)
Right-Triangle Trigonometry
114(31)
Introduction
114(1)
The Trigonometric Ratios
114(10)
Values of the Trigonometric Ratios
124(6)
Solving Right Triangles
130(4)
Applications of the Right Triangle
134(11)
Summary
142(1)
Review
143(2)
Equations and Their Graphs
145(35)
Introduction
145(1)
Functions
145(5)
Graphing Equations
150(9)
The Straight Line
159(7)
Parallel and Perpendicular Lines
166(4)
The Distance and Midpoint Formulas
170(10)
Summary
173(1)
Review
174(2)
Special NASA Application: The Space Shuttle Landing, Part I
176(4)
Factoring and Algebraic Fractions
180(32)
Introduction
180(1)
Special Products
180(3)
Factoring Algebraic Expressions
183(6)
Other Forms of Factoring
189(3)
Equivalent Fractions
192(3)
Multiplication and Division of Algebraic Fractions
195(3)
Addition and Subtraction of Algebraic Fractions
198(4)
Complex Fractions
202(3)
Equations with Fractions
205(7)
Summary
209(2)
Review
211(1)
Systems of Linear Equations
212(49)
Introduction
212(1)
Solving a System of Two Linear Equations
212(10)
Other Systems of Equations
222(2)
Solving a Systems of Three Linear Equations
224(6)
Determinants
230(5)
Properties of Determinants
235(3)
Solving a System of Linear Equations Using Determinants
238(6)
Partial Fractions
244(17)
Summary
251(4)
Review
255(2)
Application: Kirchhoff's Laws for Electric Circuits
257(4)
Quadratic Equations
261(17)
Introduction
261(1)
Solving Quadratic Equations by Factoring
261(3)
Solving Quadratic Equations by Completing the Square
264(3)
The Quadratic Formula
267(4)
Applications
271(7)
Summary
275(1)
Review
276(2)
Exponents and Radicals
278(26)
Introduction
278(1)
Integral Exponents
278(3)
Fractional Exponents
281(3)
Simplest Radical Form
284(7)
Addition and Subtraction of Radicals
291(2)
Multiplication and Division of Radicals
293(3)
Equations with Radicals
296(4)
Equations in Quadratic Form
300(4)
Summary
302(1)
Review
303(1)
Exponentials and Logarithms
304(43)
Introduction
304(1)
The Exponential Function
304(4)
The Logarithm
308(3)
Properties of Logarithms
311(4)
Common Logarithms
315(4)
Natural Logarithms
319(5)
Solving Exponential Equations
324(3)
Solving Logarithmic Equations
327(2)
Applications: Solving Exponential and Logarithmic Equations
329(6)
Data Along a Straight Line
335(12)
Summary
341(1)
Review
342(3)
Special NASA Application: The Space Shuttle Landing, Part II
345(2)
Trigonometric Functions
347(26)
Introduction
347(1)
The Trigonometric Functions
347(7)
Trigonometric Functions of Any Angle
354(6)
Radian Measure
360(6)
Use of Radian Measure
366(7)
Summary
370(1)
Review
371(2)
Oblique Triangles and Vectors
373(48)
Introduction
373(1)
Law of Sines
373(6)
The Ambiguous Case
379(4)
Law of Cosines
383(4)
Applications of Oblique Triangles
387(5)
Addition of Vectors: Graphical Methods
392(6)
Addition of Vectors: Trigonometric Methods
398(2)
Vector Components
400(6)
Vector Applications
406(15)
Summary
413(2)
Review
415(3)
Special NASA Application: Vector Analysis of Wind Changes Affecting Shuttle Launch
418(3)
Graphing the Trigonometric Functions
421(24)
Introduction
421(1)
Graphing the Sine and Cosine Functions
421(5)
Phase Shift
426(4)
Graphing the Other Trigonometric Functions
430(3)
Graphing Composite Curves
433(2)
Simple Harmonic Motion
435(10)
Summary
441(1)
Review
441(2)
Special NASA Application: Fitting a Sine Curve to Energy Use Data
443(2)
Trigonometric Formulas and Identities
445(31)
Introduction
445(1)
Basic Trigonometric Identities
445(6)
Formulas for the Sum and the Difference of Two Angles
451(5)
Double- and Half-Angle Formulas
456(6)
Trigonometric Equations
462(3)
Inverse Trigonometric Functions
465(11)
Summary
473(1)
Review
474(2)
Complex Numbers
476(22)
Introduction
476(1)
Complex Numbers in Rectangular Form
476(6)
Trigonometric and Exponential Forms of Complex Numbers
482(4)
Multiplication and Division of Complex Numbers in Exponential and Trigonometric Forms
486(4)
Powers and Roots
490(8)
Summary
495(2)
Review
497(1)
Matrices
498(28)
Introduction
498(1)
Basic Operations
498(5)
Multiplication of Matrices
503(5)
Finding the Inverse of a Matrix
508(8)
Solving a System of Equations by a Matrix Method
516(10)
Summary
520(1)
Review
521(3)
Application: Matrices Used to Encode Information
524(2)
Polynomials of Higher Degree
526(16)
Introduction
526(1)
Polynomial Functions
526(5)
Real Solutions of Polynomial Equations
531(4)
Complex Solutions of Polynomial Equations
535(7)
Summary
540(1)
Review
541(1)
Inequalities and Absolute Value
542(19)
Introduction
542(1)
Inequalities
542(8)
Equations and Inequalities Involving Absolute Value
550(3)
Other Types of Inequalities
553(3)
Inequalities in Two Variables
556(5)
Summary
559(1)
Review
559(2)
Progressions and the Binomial Theorem
561(13)
Introduction
561(1)
Arithmetic Progressions
561(3)
Geometric Progressions
564(4)
The Binomial Theorem
568(6)
Summary
572(1)
Review
573(1)
Basic Statistics
574(34)
Introduction
574(1)
Graphical Presentation of Data
574(5)
Measures of Central Tendency
579(3)
Measures of Dispersion
582(4)
The Normal Distribution
586(3)
Fitting Curves to Data Sets
589(6)
Statistical Process Control
595(13)
Summary
600(1)
Review
601(3)
Application: Statistics in the Manufacturing Process
604(4)
Analytic Geometry
608(51)
Introduction
608(1)
The Circle
608(5)
The Parabola
613(8)
The Ellipse
621(4)
The Hyperbola
625(6)
Translation of Axes
631(5)
The General Second-Degree Equation
636(2)
Systems of Quadratic Equations
638(3)
Polar Coordinates
641(8)
Graphs in Polar Coordinates
649(10)
Summary
655(2)
Review
657(2)
The Derivative
659(47)
Introduction
659(1)
Motion
659(6)
The Limit
665(8)
The Slope of a Tangent Line to a Curve
673(3)
The Derivative
676(4)
Differentiation of Polynomials
680(6)
Derivatives of Products and Quotients
686(3)
The Derivative of a Power
689(5)
Implicit Differentiation
694(2)
Proofs of Derivative Formulas
696(3)
Higher Derivatives
699(7)
Summary
702(2)
Review
704(2)
Applications of the Derivative
706(50)
Introduction
706(1)
Curve Sketching
706(10)
Using Derivatives in Curve Sketching
716(4)
More on Curve Sketching
720(7)
Newton's Method for Improving Estimated Solutions
727(7)
Maximum and Minimum Problems
734(6)
Related Rates
740(4)
Differentials and Linear Approximations
744(12)
Summary
747(3)
Review
750(2)
Special NASA Application: The Space Shuttle Landing, Part III
752(4)
Derivatives of Transcendental Functions
756(30)
Introduction
756(1)
Derivatives of Sine and Cosine Functions
756(6)
Derivatives of Other Trigonometric Functions
762(4)
Derivatives of Inverse Trigonometric Functions
766(3)
Derivatives of Logarithmic Functions
769(4)
Derivatives of Exponential Functions
773(1)
L'Hospital's Rule
774(6)
Applications
780(6)
Summary
784(1)
Review
785(1)
The Integral
786(24)
Introduction
786(1)
The Indefinite Integral
786(7)
The Constant of Integration
793(5)
Area Under a Curve
798(6)
The Definite Integral
804(6)
Summary
808(1)
Review
809(1)
Applications of Integration
810(57)
Introduction
810(1)
Area Between Curves
810(7)
Volumes of Revolution: Disk Method
817(7)
Volumes of Revolution: Shell Method
824(5)
Center of Mass of a System of Particles
829(4)
Center of Mass of Continuous Mass Distributions
833(11)
Moments of Inertia
844(7)
Work, Fluid Pressure, and Average Value
851(16)
Summary
861(4)
Review
865(2)
Methods of Integration
867(58)
Introduction
867(1)
The General Power Formula
867(4)
Logarithmic and Exponential Forms
871(3)
Basic Trigonometric Forms
874(6)
Other Trigonometric Forms
880(3)
Inverse Trigonometric Forms
883(3)
Integration Using Partial Fractions
886(3)
Integration by Parts
889(5)
Integration by Trigonometric Substitution
894(4)
Integration Using Tables
898(2)
Numerical Methods of Integration
900(8)
Areas in Polar Coordinates
908(7)
Improper Integrals
915(10)
Summary
920(2)
Review
922(3)
Three-Space: Partial Derivatives and Double Integrals
925(28)
Introduction
925(1)
Functions in Three-Space
925(9)
Partial Derivatives
934(3)
Applications of Partial Derivatives
937(8)
Double Integrals
945(8)
Summary
950(2)
Review
952(1)
Series
953(43)
Introduction
953(1)
Series and Convergence
953(7)
Ratio and Integral Tests
960(4)
Alternating Series and Conditional Convergence
964(2)
Power Series
966(4)
Maclaurin Series
970(3)
Operations with Series
973(4)
Taylor Series
977(2)
Computational Approximations
979(3)
Fourier Series
982(14)
Summary
990(4)
Review
994(2)
First-Order Differential Equations
996(26)
Introduction
996(1)
Solving Differential Equations
996(3)
Separation of Variables
999(5)
Use of Exact Differentials
1004(3)
Linear Equations of First Order
1007(3)
Applications of First-Order Differential Equations
1010(12)
Summary
1016(1)
Review
1017(2)
Special NASA Application: Under the Sea: Carbon Dioxide Buildup
1019(3)
Second-Order Differential Equations
1022(38)
Introduction
1022(1)
Higher-Order Homogeneous Differential Equations
1022(5)
Repeated Roots and Complex Roots
1027(4)
Nonhomogeneous Equations
1031(5)
Applications of Second-Order Differential Equations
1036(8)
The Laplace Transform
1044(6)
Solutions by the Method of Laplace Transforms
1050(10)
Summary
1054(2)
Review
1056(2)
Application: Differential Equations and the Gateway Arch
1058(2)
APPENDIX A Tables
1060(4)
Table 1 U.S. Weights and Measures
1060(1)
Table 2 Conversion Tables
1061(2)
Table 3 Physical Quantities and Their Units
1063(1)
APPENDIX B The Metric System
1064(24)
B.1 Introduction
1064(3)
B.2 Length
1067(4)
B.3 Mass
1071(2)
B.4 Volume and Area
1073(5)
B.5 Temperature, Time, Current, and Power
1078(6)
B.6 Other Conversions
1084(4)
Appendix B Review
1086(2)
APPENDIX C Using a Graphing Calculator
1088(35)
C.1 Introduction to the TI-83 Plus Keyboard
1088(3)
C.2 Computational Examples
1091(3)
C.3 Graphing Features
1094(2)
C.4 Examples of Graphing
1096(6)
C.5 Trigonometric Functions and Polar Coordinates
1102(4)
C.6 Equation-Solving and Table Features
1106(3)
C.7 The Numeric Solver
1109(2)
C.8 Matrix Features
1111(2)
C.9 List Features and Descriptive Statistics
1113(2)
C.10 The Line of Best Fit (Linear Regression)
1115(1)
C.11 Calculus Features
1116(4)
C.12 Sequences and Series
1120(3)
APPENDIX D Using an Advanced Graphing Calculator
1123(43)
D.1 Introduction to the TI-89 Keyboard
1123(3)
D.2 Variables and Editing
1126(1)
D.3 The Home Screen Menus
1127(2)
D.4 The Keyboard Menus
1129(5)
D.5 Graphing Functions
1134(2)
D.6 Examples of Graphing
1136(8)
D.7 Trig Functions and Polar Coordinates
1144(4)
D.8 Numerical Graph and Table Features
1148(3)
D.9 Sequences and Series
1151(1)
D.10 The Numeric Solver
1152(2)
D.11 Matrix Features
1154(1)
D.12 The Data Editor and Descriptive Statistics
1155(1)
D.13 The Line of Best Fit (Linear Regression)
1156(1)
D.14 Symbolic Algebra Features
1157(3)
D.15 Basic Calculus Features
1160(2)
D.16 Graphing in 3D
1162(2)
D.17 Advanced Calculus Features
1164(2)
APPENDIX E Table of Integrals
1166(5)
Answers to Odd-Numbered Exercises and Chapter Reviews 1171(74)
Index 1245

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