9780130255273

Technical Mathematics with Calculus

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  • ISBN13:

    9780130255273

  • ISBN10:

    0130255270

  • Edition: CD
  • Format: Paperback
  • Copyright: 2005-01-01
  • Publisher: Pearson College Div
  • View Upgraded Edition

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Summary

For courses in Technical Mathematics with Calculus. This text provides students in technology and pre-engineering with the necessary comprehensive mathematics skills required including practical calculus. With basic mathematics concepts presented through algebra, trigonometry, analytic geometry and calculus, the text is written in an intuitive manner, with technical applications integrated whenever possible.

Table of Contents

Fundamental Concepts
1(76)
The Real Number System
1(4)
Zero and Order of Operations
5(4)
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(16)
Chapter Summary
65(5)
Review
70(4)
Precision-Machined Computer Disks
74(2)
Right-Triangle Trigonometry
76(34)
The Trigonometric Ratios
76(10)
Values of the Trigonometric Ratios
86(6)
Solving Right Triangles
92(5)
Applications of the Right Triangle
97(13)
Chapter Summary
105(1)
Review
106(2)
The Global Positioning System
108(2)
Equations and Their Graphs
110(32)
Functions
110(5)
Graphing Equations
115(9)
The Straight Line
124(7)
Parallel and Perpendicular Lines
131(4)
The Distance and Midpoint Formulas
135(7)
Chapter Summary
138(2)
Review
140(2)
Factoring and Algebraic Fractions
142(32)
Special Products
142(3)
Factoring Algebraic Expressions
145(6)
Other Forms of Factoring
151(3)
Equivalent Fractions
154(3)
Multiplication and Division of Algebraic Fractions
157(3)
Addition and Subtraction of Algebraic Fractions
160(4)
Complex Fractions
164(3)
Equations with Fractions
167(7)
Chapter Summary
171(2)
Review
173(1)
Systems of Linear Equations
174(48)
Solving a System of Two Linear Equations
174(10)
Other Systems of Equations
184(2)
Solving a System of Three Linear Equations
186(6)
Determinants
192(5)
Properties of Determinants
197(3)
Solving a System of Linear Equations Using Determinants
200(6)
Partial Fractions
206(16)
Chapter Summary
213(4)
Review
217(3)
Solar Cell Technology
220(2)
Quadratic Equations
222(17)
Solving a Quadratic Equation by Factoring
222(3)
Solving Quadratic Equations by Completing the Square
225(3)
The Quadratic Formula
228(4)
Applications
232(7)
Chapter Summary
236(1)
Review
237(2)
Exponents and Radicals
239(25)
Integral Exponents
239(4)
Fractional Exponents
243(3)
Simplest Radical Form
246(6)
Addition and Subtraction of Radicals
252(2)
Multiplication and Division of Radicals
254(3)
Equations with Radicals
257(3)
Equations in Quadratic Form
260(4)
Chapter Summary
262(1)
Review
263(1)
Exponentials and Logarithms
264(42)
The Exponential Function
264(4)
The Logarithm
268(3)
Properties of Logarithms
271(4)
Common Logarithms
275(4)
Natural Logarithms
279(6)
Solving Exponential Equations
285(3)
Solving Logarithmic Equations
288(2)
Applications: Solving Exponential and Logarithmic Equations
290(4)
Data Along a Straight Line
294(12)
Chapter Summary
300(2)
Review
302(2)
Airbags
304(2)
Trigonometric Functions
306(27)
The Trigonometric Functions
306(8)
Trigonometric Functions of Any Angle
314(5)
Radian Measure
319(7)
Use of Radian Measure
326(7)
Chapter Summary
330(1)
Review
331(2)
Oblique Triangles and Vectors
333(44)
Law of Sines
333(6)
The Ambiguous Case
339(4)
Law of Cosines
343(4)
Applications of Oblique Triangles
347(5)
Addition of Vectors: Graphical Methods
352(5)
Addition of Vectors: Trigonometric Methods
357(3)
Vector Components
360(6)
Vector Applications
366(11)
Chapter Summary
373(1)
Review
374(3)
Graphing the Trigonometric Functions
377(23)
Graphing the Sine and Cosine Functions
377(5)
Phase Shift
382(4)
Graphing the Other Trigonometric Functions
386(3)
Graphing Composite Curves
389(2)
Simple Harmonic Motion
391(9)
Chapter Summary
395(1)
Review
396(2)
Improving Color Television
398(2)
Trigonometric Formulas and Identities
400(35)
Basic Trigonometric Identities
400(6)
Formulas for the Sum and the Difference of Two Angles
406(5)
Double- and Half-Angle Formulas
411(6)
Trigonometric Equations
417(3)
Inverse Trigonometric Relations
420(5)
Inverse Trigonometric Functions
425(10)
Chapter Summary
431(2)
Review
433(2)
Complex Numbers
435(21)
Complex Numbers in Rectangular Form
435(6)
Trigonometric and Exponential Forms of Complex Numbers
441(3)
Multiplication and Division of Complex Numbers in Exponential and Trigonometric Forms
444(4)
Powers and Roots
448(8)
Chapter Summary
453(2)
Review
455(1)
Matrices
456(24)
Basic Operations
456(5)
Multiplication of Matrices
461(4)
Finding the Inverse of a Matrix
465(8)
Solving a System of Equations by a Matrix Method
473(7)
Chapter Summary
477(1)
Review
478(2)
Polynomials of Higher Degree
480(16)
Polynomial Functions
480(5)
Real Solutions of Polynomial Equations
485(3)
Complex Solutions of Polynomial Equations
488(8)
Chapter Summary
491(1)
Review
492(2)
Matrices Used to Encode Information
494(2)
Inequalities and Absolute Value
496(20)
Inequalities
496(8)
Equations and Inequalities Involving Absolute Value
504(3)
Other Types of Inequalities
507(4)
Inequalities in Two Variables
511(5)
Chapter Summary
513(1)
Review
514(2)
Progressions and the Binomial Theorem
516(16)
Arithmetic Progressions
516(3)
Geometric Progressions
519(4)
The Binomial Theorem
523(9)
Chapter Summary
525(1)
Review
526(2)
Statistics in the Manufacturing Process
528(4)
Statistics for Process Control
532(29)
Graphic Presentation of Data
532(5)
Measures of Central Tendency
537(3)
Measures of Dispersion
540(4)
The Normal Distribution
544(3)
Fitting Curves to Data Sets
547(5)
Statistical Process Control
552(9)
Chapter Summary
557(1)
Review
558(3)
Analytic Geometry
561(52)
The Circle
561(5)
The Parabola
566(9)
The Ellipse
575(4)
The Hyperbola
579(6)
Translation of Axes
585(5)
The General Second-Degree Equation
590(2)
Systems of Quadratic Equations
592(3)
Polar Coordinates
595(8)
Graphs in Polar Coordinates
603(10)
Chapter Summary
609(2)
Review
611(2)
The Derivative
613(47)
Motion
613(6)
The Limit
619(8)
The Slope of a Tangent Line to a Curve
627(3)
The Derivative
630(4)
Differentiation of Polynomials
634(5)
Derivatives of Products and Quotients
639(4)
The Derivative of a Power
643(4)
Implicit Differentiation
647(3)
Proofs of Derivative Formulas
650(3)
Higher Derivatives
653(7)
Chapter Summary
656(2)
Review
658(2)
Applications of the Derivative
660(40)
Curve Sketching
660(10)
Using Derivatives in Curve Sketching
670(4)
More on Curve Sketching
674(7)
Maximum and Minimum Problems
681(7)
Related Rates
688(4)
Differentials
692(8)
Chapter Summary
695(3)
Review
698(2)
Derivatives of Transcendental Functions
700(24)
Derivatives of Sine and Cosine Functions
700(5)
Derivatives of Other Trigonometric Functions
705(5)
Derivatives of Inverse Trigonometric Functions
710(2)
Derivatives of Logarithmic Functions
712(4)
Derivatives of Exponential Functions
716(2)
Applications
718(6)
Chapter Summary
722(1)
Review
722(2)
The Integral
724(23)
The Indefinite Integral
724(7)
The Constant of Integration
731(4)
Area Under a Curve
735(6)
The Definite Integral
741(6)
Chapter Summary
745(1)
Review
745(2)
Applications of Integration
747(58)
Area Between Curves
747(7)
Volumes of Revolution: Disk Method
754(8)
Volumes of Revolution: Shell Method
762(4)
Center of Mass of a System of Particles
766(4)
Center of Mass of Continuous Mass Distributions
770(12)
Moments of Inertia
782(7)
Work, Fluid Pressure, and Average Value
789(16)
Chapter Summary
800(3)
Review
803(2)
Methods of Integration
805(49)
The General Power Formula
805(4)
Logarithmic and Exponential Forms
809(3)
Basic Trigonometric Forms
812(6)
Other Trigonometric Forms
818(4)
Inverse Trigonometric Forms
822(2)
Integration Using Partial Fractions
824(3)
Integration by Parts
827(4)
Integration by Trigonometric Substitution
831(4)
Integration Using Tables
835(2)
Numerical Methods of Integration
837(8)
Areas in Polar Coordinates
845(9)
Chapter Summary
850(1)
Review
851(3)
Three-Space: Partial Derivatives and Double Integrals
854(30)
Functions in Three-Space
854(9)
Partial Derivatives
863(4)
Applications of Partial Derivatives
867(8)
Double Integrals
875(9)
Chapter Summary
880(2)
Review
882(2)
Series
884(39)
Series and Convergence
884(7)
Ratio and Integral Tests
891(4)
Alternating Series and Conditional Convergence
895(1)
Power Series
896(5)
Maclaurin Series
901(3)
Operations with Series
904(3)
Taylor Series
907(2)
Computational Approximations
909(2)
Fourier Series
911(12)
Chapter Summary
917(4)
Review
921(2)
First-Order Differential Equations
923(25)
Solving Differential Equations
923(3)
Separation of Variables
926(5)
Use of Integrating Factors
931(3)
Linear Equations of First Order
934(3)
Applications of First-Order Differential Equations
937(11)
Chapter Summary
943(1)
Review
944(2)
Differential Equations and the Gateway Arch
946(2)
Second-Order Differential Equations
948(35)
Higher-Order Homogeneous Differential Equations
948(5)
Repeated Roots and Complex Roots
953(4)
Nonhomogeneous Equations
957(5)
Applications of Second-Order Differential Equations
962(8)
The Laplace Transform
970(6)
Solutions by the Method of Laplace Transforms
976(7)
Chapter Summary
979(2)
Review
981(2)
APPENDIX A Review of Geometry 983(6)
A.1 Angles and Lines
983(1)
A.2 Triangles
984(2)
A.3 Quadrilaterals
986(1)
A.4 Circles
987(1)
A.5 Areas and Volumes of Solids
988(1)
APPENDIX B The Metric System 989(25)
B.1 Introduction
989(3)
B.2 Length
992(4)
B.3 Mass
996(2)
B.4 Volume and Area
998(5)
B.5 Temperature, Time, Current, and Power
1003(6)
B.6 Other Conversions
1009(3)
Appendix B Review
1012(2)
APPENDIX C Using a Graphing Calculator 1014(35)
C.1 Introduction to the TI-83 Keyboard
1014(3)
C.2 Computational Examples
1017(3)
C.3 Graphing Features
1020(2)
C.4 Examples of Graphing
1022(6)
C.5 Trigonometric Functions and Polar Coordinates
1028(4)
C.6 Equation-Solving and TABLE Features
1032(3)
C.7 The Numeric SOLVER
1035(2)
C.8 Matrix Features
1037(2)
C.9 LIST Features and Descriptive Statistics
1039(2)
C.10 The Line of Best Fit (Linear Regression)
1041(1)
C.11 Calculus Features
1042(4)
C.12 Sequences and Series
1046(3)
APPENDIX D Using an Advanced Graphing Calculator 1049(43)
D.1 Introduction to the TI-89 Keyboard
1049(3)
D.2 Variables and Editing
1052(1)
D.3 The Home Screen Menus
1053(2)
D.4 The Keyboard Menus
1055(5)
D.5 Graphing Functions
1060(2)
D.6 Examples of Graphing
1062(8)
D.7 Trig Functions and Polar Coordinates
1070(4)
D.8 Numerical GRAPH and TABLE Features
1074(3)
D.9 Sequences and Series
1077(1)
D.10 The Numeric Solver
1078(2)
D.11 Matrix Features
1080(1)
D.12 The Data Editor and Descriptive Statistics
1081(1)
D.13 The Line of Best Fit (Linear Regression)
1082(1)
D.14 Symbolic Algebra Features
1083(3)
D.15 Basic Calculus Features
1086(2)
D.16 Graphing in 3D
1088(2)
D.17 Advanced Calculus Features
1090(2)
APPENDIX E Tables 1092(11)
Table 1 English Weights and Measures
1092(1)
Table 2 Metric System Prefixes
1093(1)
Table 3 Conversion Tables
1094(2)
Table 4 Physical Quantities and Their Units
1096(1)
Table 5 Table of Integrals
1097(6)
Answers to Odd-Numbered Exercises and Chapter Reviews 1103(86)
Index 1189

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