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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, 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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