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Technical Mathematics with Calculus, Canadian Edition
by
Calter, Michael A., University of Rochester; Calter, Paul A., Vermont Technical College
Publisher: John Wiley & Sons Canada, Ltd.
Publishing Date: 2010/10/01
eText ISBN-10
0-470-16143-4
eText ISBN-13
978-0-470-16143-2
Print ISBN-10
0-470-15539-6
Print ISBN-13
978-0-470-15539-4
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Technical Mathematics with Calculus, Canadian Edition
by
Calter, Michael A., University of Rochester; Calter, Paul A., Vermont Technical College
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Copyright, iv
About the Authors, v
Preface, vii
1. Numerical Computation,...
2. Introduction to Algebr...
3. Simple Equations and W...
4. Functions, 108
5. Graphs, 126
6. Geometry, 142
7. Right Triangles and Ve...
8. Factors and Factoring,...
9. Fractions and Fraction...
10. Systems of Linear Equ...
11. Determinants, 279
12. Matrices, 301
13. Exponents and Radical...
14. Quadratic Equations, ...
15. Oblique Triangles and...
16. Radian Measure, Arc L...
17. Graphs of the Trigono...
18. Trigonometric Identit...
19. Ratio, Proportion, an...
20. Exponential and Logar...
21. Complex Numbers, 565
22. Analytic Geometry, 59...
23. Binary, Hexadecimal, ...
24. Inequalities and Line...
25. Sequences, Series, an...
26. Introduction to Stati...
27. Derivatives of Algebr...
28. Graphical Application...
29. More Applications of ...
30. Integration, 856
31. Applications of the I...
32. More Applications of ...
33. Derivatives of Trigon...
34. Methods of Integratio...
35. Differential Equation...
36. Solving Differential ...
37. Infinite Series, 1086
Appendices, A-1
Indexes, I-1
Table of Contents
Copyright, iv
About the Authors, v
Preface, vii
1. Numerical Computation, 1
1-1. The Real Numbers, 2
1-2. Addition and Subtraction, 6
1-3. Multiplication, 11
1-4. Division, 16
1-5. Powers and Roots, 19
1-6. Combined Operations, 22
1-7. Scientific Notation, 25
1-8. Units of Measurement, 30
1-9. Substituting into Equations and Formulas, 37
1-10. Percentage, 39
Chapter 1 Review Problems, 46
2. Introduction to Algebra, 51
2-1. Algebraic Expressions, 52
2-2. Addition and Subtraction of Algebraic Expressions, 55
2-3. Integral Exponents, 58
2-4. Multiplication of Algebraic Expressions, 65
2-5. Division of Algebraic Expressions, 73
Chapter 2 Review Problems, 80
3. Simple Equations and Word Problems, 83
3-1. Solving First-Degree Equations, 84
3-2. Solving Word Problems, 90
3-3. Financial Problems, 96
3-4. Mixture Problems, 98
3-5. Statics Problems, 102
Chapter 3 Review Problems, 104
4. Functions, 108
4-1. Functions and Relations, 109
4-2. Functional Notation, 114
4-3. Composite Functions and Inverse Functions, 121
Chapter 4 Review Problems, 124
5. Graphs, 126
5-1. Rectangular Coordinates, 127
5-2. The Graph of a Function, 129
5-3. Graphing the Straight Line, 131
5-4. Graphing Empirical Data, Formulas, and Parametric Equations, 135
5-5. Graphical Solution of Equations, 138
Chapter 5 Review Problems, 140
6. Geometry, 142
6-1. Straight Lines and Angles, 143
6-2. Triangles, 146
6-3. Quadrilaterals, 153
6-4. The Circle, 154
6-5. Volumes and Areas of Solids, 158
Chapter 6 Review Problems, 161
7. Right Triangles and Vectors, 163
7-1. Angles and Their Measures, 164
7-2. The Trigonometric Functions, 166
7-3. Finding the Angle When the Trigonometric Function Is Given, 171
7-4. Solution of Right Triangles, 172
7-5. Applications of the Right Triangle, 176
7-6. Vectors, 181
7-7. Applications of Vectors, 186
Chapter 7 Review Problems, 189
8. Factors and Factoring, 191
8-1. Common Factors, 192
8-2. Difference of Two Squares, 195
8-3. Factoring Trinomials, 197
8-4. Factoring by Grouping, 202
8-5. The General Quadratic Trinomial, 203
8-6. The Perfect Square Trinomial, 206
8-7. Sum or Difference of Two Cubes, 207
Chapter 8 Review Problems, 209
9. Fractions and Fractional Equations, 212
9-1. Simplification of Fractions, 213
9-2. Multiplication and Division of Fractions, 218
9-3. Addition and Subtraction of Fractions, 222
9-4. Complex Fractions, 228
9-5. Fractional Equations, 231
9-6. Word Problems Leading to Fractional Equations, 234
9-7. Literal Equations and Formulas, 239
Chapter 9 Review Problems, 246
10. Systems of Linear Equations, 249
10-1. Systems of Two Linear Equations, 250
10-2. Other Systems of Equations, 257
10-3. Word Problems with Two Unknowns, 262
10-4. Systems of Three Linear Equations, 270
Chapter 10 Review Problems, 277
11. Determinants, 279
11-1. Second-Order Determinants, 280
11-2. Third-Order Determinants, 285
11-3. Higher-Order Determinants, 293
Chapter 11 Review Problems, 298
12. Matrices, 301
12-1. Definitions, 302
12-2. Operations with Matrices, 306
12-3. The Inverse of a Matrix, 318
12-4. Solving a System of Linear Equations by Matrix Inversion, 322
Chapter 12 Review Problems, 324
13. Exponents and Radicals, 327
13-1. Integral Exponents, 328
13-2. Simplification of Radicals, 333
13-3. Operations with Radicals, 340
13-4. Radical Equations, 345
Chapter 13 Review Problems, 348
14. Quadratic Equations, 351
14-1. Solving Quadratics by Factoring, 352
14-2. Solving Quadratics by Completing the Square, 357
14-3. Solving Quadratics by Formula, 359
14-4. Applications and Word Problems, 363
14-5. Graphing the Quadratic Function, 367
14-6. Equations of Quadratic Type, 370
14-7. Simple Equations of Higher Degree, 372
14-8. Systems of Quadratic Equations, 373
Chapter 14 Review Problems, 377
15. Oblique Triangles and Vectors, 380
15-1. Trigonometric Functions of Any Angle, 381
15-2. Law of Sines, 388
15-3. Law of Cosines, 393
15-4. Applications, 397
15-5. Addition of Vectors, 401
Chapter 15 Review Problems, 405
16. Radian Measure, Arc Length, and Rotation, 407
16-1. Radian Measure, 408
16-2. Arc Length, 414
16-3. Uniform Circular Motion, 417
Chapter 16 Review Problems, 420
17. Graphs of the Trigonometric Functions, 422
17-1. The Sine Curve, 423
17-2. The General Sine Wave, 427
17-3. Quick Sketching of the Sine Curve, 435
17-4. Graphs of More Trigonometric Functions, 437
17-5. The Sine Wave as a Function of Time, 442
17-6. Polar Coordinates, 451
17-7. Graphing Parametric Equations, 456
Chapter 17 Review Problems, 459
18. Trigonometric Identities and Equations, 462
18-1. Fundamental Identities, 463
18-2. Sum or Difference of Two Angles, 468
18-3. Functions of Double Angles, 474
18-4. Functions of Half-Angles, 477
18-5. Trigonometric Equations, 480
18-6. Inverse Trigonometric Functions, 487
Chapter 18 Review Problems, 489
19. Ratio, Proportion, and Variation, 491
19-1. Ratio and Proportion, 492
19-2. Direct Variation, 495
19-3. The Power Function, 499
19-4. Inverse Variation, 507
19-5. Functions of More Than One Variable, 511
Chapter 19 Review Problems, 515
20. Exponential and Logarithmic Functions, 519
20-1. The Exponential Function, 520
20-2. Exponential Growth and Decay, 524
20-3. Logarithms, 532
20-4. Properties of Logarithms, 536
20-5. Exponential Equations, 543
20-6. Logarithmic Equations, 549
20-7. Graphs on Logarithmic and Semilogarithmic Paper, 554
Chapter 20 Review Problems, 562
21. Complex Numbers, 565
21-1. Complex Numbers in Rectangular Form, 566
21-2. Graphing Complex Numbers, 571
21-3. Complex Numbers in Trigonometric and Polar Forms, 572
21-4. Complex Numbers in Exponential Form, 578
21-5. Vector Operations Using Complex Numbers, 580
21-6. Alternating Current Applications, 583
Chapter 21 Review Problems, 588
22. Analytic Geometry, 590
22-1. The Straight Line, 591
22-2. The Circle, 605
22-3. The Parabola, 612
22-4. The Ellipse, 620
22-5. The Hyperbola, 629
Chapter 22 Review Problems, 639
23. Binary, Hexadecimal, Octal, and BCD Numbers, 643
23-1. The Binary Number System, 644
23-2. The Hexadecimal Number System, 649
23-3. The Octal Number System, 652
23-4. BCD Codes, 653
Chapter 23 Review Problems, 655
24. Inequalities and Linear Programming, 656
24-1. Definitions, 657
24-2. Solving Inequalities, 661
24-3. Linear Programming, 669
Chapter 24 Review Problems, 673
25. Sequences, Series, and the Binomial Theorem, 676
25-1. Sequences and Series, 677
25-2. Arithmetic Progressions, 681
25-3. Geometric Progressions, 687
25-4. Infinite Geometric Progressions, 691
25-5. The Binomial Theorem, 695
Chapter 25 Review Problems, 704
26. Introduction to Statistics and Probability, 706
26-1. Definitions and Terminology, 707
26-2. Frequency Distributions, 710
26-3. Numerical Description of Data, 716
26-4. Introduction to Probability, 725
26-5. The Normal Curve, 734
26-6. Standard Errors, 740
26-7. Process Control, 746
26-8. Regression, 754
Chapter 26 Review Problems, 758
27. Derivatives of Algebraic Functions, 763
27-1. Limits, 764
27-2. The Derivative, 771
27-3. Rules for Derivatives, 782
27-4. Derivative of a Function Raised to a Power, 787
27-5. Derivatives of Products and Quotients, 791
27-6. Derivatives of Implicit Relations, 797
27-7. Higher-Order Derivatives, 802
Chapter 27 Review Problems, 803
28. Graphical Applications of the Derivative, 806
28-1. Tangents and Normals, 807
28-2. Maximum, Minimum, and Inflection Points, 810
28-3. Sketching, Verifying, and Interpreting Graphs, 819
28-4. Approximate Solution of Equations by Newton’s Method, 823
Chapter 28 Review Problems, 826
29. More Applications of the Derivative, 827
29-1. Rate of Change, 828
29-2. Motion of a Point, 831
29-3. Related Rates, 838
29-4. Optimization, 844
Chapter 29 Review Problems, 854
30. Integration, 856
30-1. The Indefinite Integral, 857
30-2. Rules for Finding Integrals, 864
30-3. Constant of Integration, 870
30-4. The Definite Integral, 873
30-5. Approximate Area Under a Curve, 875
30-6. Exact Area Under a Curve, 880
Chapter 30 Review Problems, 883
31. Applications of the Integral, 885
31-1. Applications to Motion, 886
31-2. Applications to Electric Circuits, 889
31-3. Finding Areas by Means of the Definite Integral, 892
31-4. Volumes by Integration, 902
Chapter 31 Review Problems, 909
32. More Applications of the Integral, 911
32-1. Length of Arc, 912
32-2. Area of Surface of Revolution, 915
32-3. Centroids, 918
32-4. Fluid Pressure, 927
32-5. Work, 930
32-6. Moment of Inertia, 933
Chapter 32 Review Problems, 940
33. Derivatives of Trigonometric, Logarithmic, and Exponential Functions, 942
33-1. Derivatives of the Sine and Cosine Functions, 943
33-2. Derivatives of the Tangent, Cotangent, Secant, and Cosecant Functions, 949
33-3. Derivatives of the Inverse Trigonometric Functions, 954
33-4. Derivatives of Logarithmic Functions, 956
33-5. Derivatives of the Exponential Function, 962
Chapter 33 Review Problems, 966
34. Methods of Integration, 968
34-1. Integrals of Exponential and Logarithmic Functions, 969
34-2. Integrals of the Trigonometric Functions, 972
34-3. Average and Root Mean Square Values, 975
34-4. Integration by Parts, 977
34-5. Integrating Rational Fractions, 980
34-6. Integrating by Algebraic Substitution, 987
34-7. Integrating by Trigonometric Substitution, 989
34-8. Improper Integrals, 993
34-9. Approximate Value of a Definite Integral, 996
Chapter 34 Review Problems, 1002
35. Differential Equations, 1005
35-1. Definitions, 1006
35-2. Graphical and Numerical Solution of Differential Equations, 1008
35-3. First-Order Differential Equation, Variables Separable, 1013
35-4. Exact First-Order Differential Equations, 1016
35-5. First-Order Homogeneous Differential Equations, 1019
35-6. First-Order Linear Differential Equations, 1021
35-7. Geometric Applications of First-Order Differential Equations, 1026
35-8. Exponential Growth and Decay, 1030
35-9. Series
RL
and
RC
Circuits, 1032
35-10. Second-Order Differential Equations, 1037
35-11. Second-Order Differential Equations with Constant Coefficients and Right Side Zero, 1038
35-12. Second-Order Differential Equations with Right Side Not Zero, 1044
35-13.
RLC
Circuits, 1049
Chapter 35 Review Problems, 1057
36. Solving Differential Equations by the Laplace Transform and by Numerical Methods, 1059
36-1. The Laplace Transform of a Function, 1060
36-2. Inverse Transforms, 1066
36-3. Solving Differential Equations by the Laplace Transform, 1068
36-4. Electrical Applications, 1072
36-5. Numerical Solution of First-Order Differential Equations, 1077
36-6. Numerical Solution of Second-Order Differential Equations, 1081
Chapter 36 Review Problems, 1083
37. Infinite Series, 1086
37-1. Convergence and Divergence of Infinite Series, 1087
37-2. Maclaurin Series, 1090
37-3. Taylor Series, 1097
37-4. Operations with Power Series, 1100
37-5. Fourier Series, 1104
37-6. Waveform Symmetries, 1111
37-7. Waveforms with Period of
2L
, 1116
37-8. A Numerical Method for Finding Fourier Series, 1119
Chapter 37 Review Problems, 1122
Appendices, A-1
A. Summary of Facts and Formulas, A-1
B. Conversion Factors, A-39
C. Table of Integrals, A-44
D. Answers to Selected Problems, A-48
E. Graphing Calculator and Computer Applications, A-87
Indexes, I-1
Index to Applications, I-1
Index to Writing Questions, I-6
Index to Team Projects, I-7
General Index, I-8
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