Technical Mathematics with Calculus, 6th Edition

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  • Edition: 6th
  • Format: Hardcover
  • Copyright: 2011-04-01
  • Publisher: Wiley

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This textbook has been in constant use since 1980, and this edition represents the first major revision of this text since the second edition. It was time to select, make hard choices of material, polish, refine, and fill in where needed. Much has been rewritten to be even cleaner and clearer, new features have been introduced, and some peripheral topics have been removed.The authors continue to provide real-world, technical applications that promote intuitive reader learning. Numerous fully worked examples and boxed and numbered formulas give students the essential practice they need to learn mathematics. Computer projects are given when appropriate, including BASIC, spreadsheets, computer algebra systems, and computer-assisted drafting. The graphing calculator has been fully integrated and calculator screens are given to introduce computations. Everything the technical student may need is included, with the emphasis always on clarity and practical applications.

Table of Contents

Review of Numerical Computation 1
The Real Numbers 2
Addition and Subtraction 8
Multiplication 12
Division 16
Powers and Roots 20
Combined Operations 24
Scientific Notation and Engineering Notation 27
Units of Measurement 34
Percentage 43
Review Problems 50
Introduction to Algebra 54
Algebraic Expressions 55
Adding and Subtracting
Polynomials 59 2-3 Laws of Exponents 63
Product of Two Monomials 69
Product of a Multinomial and a Monomial 72
Product of Two Binomials 73
Product of Two Multinomials 74
Powers of Multinomials 76
Removing Symbols of Grouping 78
Quotient of Two Monomials 80
Dividing a Polynomial by a Monomial 83
Quotient of Two Polynomials 85
Review Problems 87
Simple Equations and Word Problems
Solving First-Degree Equations 92
Solving Word Problems 99
Uniform Motion 104
Financial 108
Mixtures 110
Statics 113
Work, Fluid Flow, and Energy Flow 116
Review Problems 119
•4 Functions
Functions and Relations, 124
More on Functions
Review Problems
Rectangular Coordinates
Graphing an Equation
Graphing a Function by Calculator
The Straight Line
Solving an Equation Graphically
Review Problems 148
Geometry 152
Straight Lines and Angles
Triangles 156
Quadrilaterals 162
The Circle 164
Volumes and Areas of Solids 169
Review Problems 174
Right Triangles and Vectors 178
The Trigonometric Functions 179
Solution of Right Triangles 182
Applications of the Right Triangle 186
Introduction to Vectors 190
Applications of Vectors 192
Review Problems 195
Oblique Triangles and Vectors 198
Trigonometric Functions of Any Angle 199
Finding the Angle When the Trigonometric Function Is Kown
Law of Sines 208
Law of Cosines 214
Applications 218
Resultants of Nonperpendicular Vectors 222
Review Problems 226
Systems of Linear Equations 229
Systems of Two Linear Equations 230
Other Systems of Equations 235
Applications 240
Systems of Three Linear Equations 246
Review Problems 252
Matrices and Determinants 256
Introduction to Matrices 257
Solving Systems of Equations by the Unit Matrix Method 260
Second-Order Determinants 265
Higher-Order Determinants 271
Review Problems 277
Factoring and Fractions 281
Common Factors 282
Difference of Two Squares 285
Factoring Trinomials
Other Factorable Expressions 293
Simplification of Fractions
Multiplication and Division of Fractions 300
Addition and Subtraction of Fractions 303
Complex Fractions 307
Fractional Equations 310
Literal Equations and Formulas 312
Review Problems 317
Quadratic Equations 20
Solving a Quadratic Equation by Calculator 321
Solving a Quadratic by Formula 325
Applications 328
Review Problems 332
Exponents and Radicals 335
Integral Exponents 336
Simplification of Radicals 341
Operations with Radicals 3
Radical Equations 352
Review Problems 356
Radian Measure, Arc Length, and Rotation 359
Radian Measure 360
Arc Length 366
Uniform Circular Motion 370
Review Problems 372
Trigonometric, Parametric, and Polar Graphs 375
Graphing the Sine Wave by Calculator 376
Manual Graphing of the Sine Wave 383
The Sine Wave as a Function of Time 387
Graphs of the Other Trigonometric Functions 394
Graphing Parametric Equations 400
Graphing in Polar Coordinates 404
Review Problems 410
Trigonometric Identities and Equations 414
Fundamental Identities 416
Sum or Difference of Two Angles 421
Functions of Double Angles and Half-Angles 426
Evaluating Trigonometric Expressions 432
Solving Trigonometric Equations 435
Review Problems 439
Ratio, Proportion, and Variation 442
Ratio and Proportion 443
Similar Figures 446
Direct Variation 450
The Power Function 453
Inverse Variation 457
Functions of More Than One Variable 461
Review Problems 466
Exponential and Logarithmic Functions 469
The Exponential Function 470
Logarithms 478
Properties of Logarithms 483
Exponential Equations 490
Solving Logarithmic Equations 497
Review Problems 500
Complex Numbers 504
Complex Numbers in Rectangular Form 505
Complex Numbers in Polar Form 509
Complex Numbers on the Calculator 513
Vector Operations Using Complex Numbers 515
Alternating Current Applications 519
Review Problems 524
Sequences, Series, and the Binomial Theorem 527
Sequences and Series 528
Arithmetic and Harmonic Progressions 534
Geometric Progressions 540
Infinite Geometric Progressions 544
The Binomial Theorem 546
Review Problems 553
Introduction to Statistics and Probability
Definitions and Terminology
Frequency Distributions
Numerical Description of Data
Introduction to Probability
The Normal Curve
Standard Errors
Process Control
Review Problems
Analytic Geometry 557
The Straight Line 558
Equation of a Straight Line 565
The Circle 572
The Parabola 579
The Ellipse 587
The Hyperbola 597
Review Problems 605
Derivatives of Algebraic Functions 610
Limits 611
Rate of Change and the Tangent 618
The Derivative 622
Rules for Derivatives 630
Derivative of a Function Raised to a Power 636
Derivatives of Products and Quotients 640
Other Variables, Implicit Relations, and Differentials 646
Higher-Order Derivatives 652
Review Problems 653
Graphical Applications of the Derivative 656
Equations of Tangents and Normals 657
Maximum, Minimum, and Inflection Points 661
Sketching, Verifying, and Interpreting Graphs 670
Review Problems 675
More Applications of the Derivative 677
Rate of Change 678
Motion of a Point 683
Related Rates 690
Optimization 696
Review Problems 705
Integration 708
The Indefinite Integral 709
Rules for Finding Integrals 718
Simple Differential Equations 726
The Definite Integral 730
Approximate Area under a Curve 734
Exact Area under a Curve 738
Review Problems 742
Applications of the Integral 744
Applications to Motion 745
Applications to Eletric Circuits 750
Finding Areas by Integration 753
Volumes by Integration 764
Review Problems 771
More Applications of the Integral 774
Length of Arc 775
Area of Surface of
Revolution 779
Centroids 782
Fluid Pressure 789
Work 792
Moment of Inertia 796
Review Problems 801
Trigonometric, Logarithmic, and Exponential Functions 804
Derivatives of the Sine and Cosine Functions
Derivatives of the Other Trigonometric Functions 813
Derivatives of the Inverse Trigonometric Functions 817
Derivatives of Logarithmic Functions 819
Derivatives of the Exponential Functions 825
Integrals of the Exponential and Logarithmic Functions 831
Integrals of the Trigonometric Functions 835
Average and Root Mean Square Values 839
Review Problems 841
First-Order Differential Equations 844
Definitions 845
Solving a DE by Calculator, Graphically, and Numerically 848
First-Order DE: Variables Separable 853
Exact First-Order DE 856
First-Order Homogeneous DE 859
First-Order Linear DE 861
Geometric Applications of First-Order DE 866
Exponential Growth and Decay 870
Series RL and RC Circuits 872
Review Problems 877
Second-Order Differential Equations
Second-Order DE 881
Constant Coefficients and Right Side Zero 882
Right Side Not Zero 889
Mechanical Vibrations 894
RLC Circuits 899
Review Problems 907
Summary of Facts and Formulas A-1
Conversion Factors A-27
Table of Integrals
Answers to Selected Problems
Index to Applications
General Index
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