Mathematical methods for engineering and science students:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Arnold
1987
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 610 S. |
| ISBN: | 0713135255 |
Staff View
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| adam_text | Preface Hi
1 Vector Algebra 1
1.1 Vector Quantities 1
1.2 Components 5
1.3 The Scalar Product 9
1.4 The Vector Product 12
1.5 Triple Products 15
1.6 Vector Equations 18
1.7 Matrix Representation of Vector Algebra 19
Answers to Exercises 20
Further Exercises on Chapter 1 21
2 Solid Geometry: Planes and Curves 23
2.1 Surfaces 23
2.2 The Equation of a Plane 24
2.3 The Equations of a Line 26
2.4 Intersection of a Line and a Plane 30
2.5 Intersection of Two Lines 31
2.6 The Equations of a Curve 34
2.7 Intersections with Curves 36
Answers to Exercises 39
Further Exercises on Chapter 2 40
3 Functions 45
3.1 Basic Concepts 45
3.2 The Power Function 49
3.3 Hyperbolic Functions 50
3.4 Functions Relating Several Variables 55
3.5 Sequences 61
3.6 Bounded Functions 63
Answers to Exercises 69
Further Exercises on Chapter 3 69
4 Limits 73
4.1 The Concept of Limit asx a 73
4.2 The Concept of Limit as x oo 80
4.3 Theorems on Limits 82
4.4 Techniques for Evaluating Limits 85
Table of Limits 91
viii Contents
Answers to Exercises 91
Further Exercises on Chapter 4 92
5 Continuity 95
5.1 Continuous Functions 95
5.2 Properties of Continuous Functions 98
Answers to Exercises 101
Further Exercises on Chapter 5 102
6 Differentiatior, Inequalities, and Curve Sketching 105
6.1 Definitions, Notation, and Rules 105
6.2 Logarithmic Differentiation 112
6.3 Higher Derivatives 114
6.4 Vector Functions 118
6.5 Functions Defined Parametrically 120
6.6 Functions Defined Implicitly 124
6.7 The Mean Value Theorem 127
6.8 Curve Sketching 131
6.9 Inequalities 139
6.10 Partial Derivatives 145
6.11 Complex Functions 148
Answers to Exercises 152
Table of Derivatives 154
Further Exercises on Chapter 6 155
7 Numerical Solution of Equations 161
7.1 Newton s Method 161
7.2 Errors 168
7.3 The Bisection Method 171
7.4 Direct Iteration 173
7.5 Summaries of Methods for Finding a Root r of f(x) = 0 176
Answers to Exercises 177
Further Exercises on Chapter 7 178
8 Series 179
8.1 Convergence of Series 179
8.2 Notation 185
8.3 The Comparison Tests 187
8.4 Absolute Convergence 189
Answers to Exercises 191
Further Exercises on Chapter 8 192
Table of Series 195
9 The Integral Calculus 197
9.1 Definition of the Riemann Integral 197
9.2 Applications 199
9.3 Properties of the Riemann Integral 205
9.4 The Fundamental Theorem 209
Contents ix
9.5 Evaluation of Riemann Integrals 213
9.6 Vector Functions and Complex Functions 216
Answers to Exercises 218
Further Exercises on Chapter 9 219
10 Antiderivatives 225
10.1 Standard Results 225
10.2 Substitution, or Change of Variable 226
10.3 Integration by Parts 230
10.4 Rational Functions 235
10.5 Reduction Formulas 240
10.6 Systematic Integration 244
10.7 Improper Integrals 247
Answers to Exercises 252
Table of Antiderivatives 253
Table of Reduction Formulas 254
Further Exercises on Chapter 10 254
11 Line Integrals and Double Integrals 259
11.1 Length of a Space Curve given Parametrically 259
11.2 Work done during Motion along a Curve 263
11.3 Further Techniques for Line Integrals 266
11.4 Alternative Derivation of the Work Formula 270
11.5 Integrals of Functions of Two Variables 271
11.6 Specification of Regions 277
11.7 Evaluation of Double Integrals 280
Answers to Exercises 287
Further Exercises on Chapter 11 289
12 Complex Algebra and Functions 293
12.1 De Moivre s Theorem 293
12.2 Powers of Complex Numbers 296
12.3 Solution of Polynomial Equations 299
12.4 Complex Functions as Mappings between Complex Planes 301
12.5 The Complex Exponential Function 306
Answers to Exercises 308
Further Exercises on Chapter 12 311
13 Differential Equations 315
13.1 Separable First Order Equations 315
13.2 First Order Linear Equations 320
13.3 Second Order Linear Equations 323
13.4 Linear Equations with Constant Coefficients 325
13.5 Reduction of Order 331
13.6 Change of Variable 333
13.7 The Use of Complex Functions 334
13.8 Some Applications of Differential Equations 338
Hints and/or Answers to Exercises 347
Further Exercises on Chapter 13 348
x Contents
14 Functions of Two Variables, Solid Geometry and Surfaces 355
14.1 Geometric Interpretation of Partial Derivatives 355
14.2 Tangent Planes 358
14.3 Differentials 361
14.4 Tangent Lines 365
14.5 Composite Functions 367
14.6 Maxima and Minima 368
Answers to Exercises 374
Further Exercises on Chapter 14 374
15 Numerical Integration 377
15.1 The Trapezoidal Rule 377
15.2 Simpson s Rule 381
15.3 Derivation of Bounds on the Trapezoidal Rule Error 384
15.4 General Integration Procedures 387
Answers to Exercises 391
Further Exercises on Chapter 15 392
16 Power Series and Fourier Series 395
16.1 Series of Functions 395
16.2 Properties of Power Series 396
16.3 Expansion of a Given Function 400
16.4 Taylor s Series 404
16.5 Errors 406
16.6 Evaluation of Limits 411
16.7 Fourier Series 414
16.8 Properties of Fourier Series 419
16.9 Fourier Series with only Sine or only Cosine Terms 424
16.10 Complex Series 429
Answers to Exercises 433
Further Exercises on Chapter 16 435
Table of Power Series 438
17 Linear Algebra 441
17.1 Geometrical Classification of Linear Equations 441
17.2 Solution by Gaussian Elimination 444
17.3 The Inverse of a Matrix 450
17.4 Determinants and Homogeneous Equations 454
17.5 Properties of Determinants 458
17.6 Applications of Determinants 461
Answers (or checks) for Exercises 467
Further Exercises on Chapter 17 468
18 Functions of Three Variables 473
18.1 Level Curves 473
18.2 Differentials and Directional Derivatives 476
18.3 Gradient Vector (Two dimensional) 477
18.4 Functions of Three Variables 479
Contents xi
18.5 Implicit Differentiation 481
18.6 Composite Functions 484
18.7 Conservative Functions 486
Answers to Exercises 490
Further Exercises on Chapter 18 491
19 Numerical Solution of Differential Equations 493
19.1 Introduction 493
19.2 Euler Formulas 494
19.3 Comparison of Formulas 496
19.4 Fourth Order Runge Formula 499
19.5 Computer Implementation 500
19.6 Second Order Equations 501
Answers to Exercises 504
Further Exercises on Chapter 19 505
20 Laplace Transforms 507
20.1 Definition of the Laplace Transform 507
20.2 Inversion of Transforms 509
20.3 Solution of Differential Equations using Laplace Transforms 511
Answers to Exercises 514
Table of Laplace Transforms and Inversions 515
Further Exercises on Chapter 20 515
Appendix A Complex Numbers 517
A.1 Introduction 517
A.2 Complex Algebra 518
A.3 Complex Conjugates 522
A.4 The Interpretation of Complex Numbers 523
A.5 Polar Form of Complex Numbers 526
A.6 Geometric Interpretation of Multiplication and Division 531
A.7 Sets of Points in the Complex Plane 534
Answers to Exercises 538
Appendix B Flow Diagrams or Summaries of Mathematical Procedures 543
Appendix C Computer Programs 549
Appendix D Formal Definitions of Limiting Processes 561
Appendix E Change of Variable in an Integral 569
Appendix F Answers (or checks) to Selected Exercises 571
Appendix G Table of Antiderivatives 595
Appendix H Formulas from Elementary Mathematics 597
Index 601
|
| adam_txt |
Preface Hi
1 Vector Algebra 1
1.1 Vector Quantities 1
1.2 Components 5
1.3 The Scalar Product 9
1.4 The Vector Product 12
1.5 Triple Products 15
1.6 Vector Equations 18
1.7 Matrix Representation of Vector Algebra 19
Answers to Exercises 20
Further Exercises on Chapter 1 21
2 Solid Geometry: Planes and Curves 23
2.1 Surfaces 23
2.2 The Equation of a Plane 24
2.3 The Equations of a Line 26
2.4 Intersection of a Line and a Plane 30
2.5 Intersection of Two Lines 31
2.6 The Equations of a Curve 34
2.7 Intersections with Curves 36
Answers to Exercises 39
Further Exercises on Chapter 2 40
3 Functions 45
3.1 Basic Concepts 45
3.2 The Power Function 49
3.3 Hyperbolic Functions 50
3.4 Functions Relating Several Variables 55
3.5 Sequences 61
3.6 Bounded Functions 63
Answers to Exercises 69
Further Exercises on Chapter 3 69
4 Limits 73
4.1 The Concept of Limit asx a 73
4.2 The Concept of Limit as x oo 80
4.3 Theorems on Limits 82
4.4 Techniques for Evaluating Limits 85
Table of Limits 91
viii Contents
Answers to Exercises 91
Further Exercises on Chapter 4 92
5 Continuity 95
5.1 Continuous Functions 95
5.2 Properties of Continuous Functions 98
Answers to Exercises 101
Further Exercises on Chapter 5 102
6 Differentiatior, Inequalities, and Curve Sketching 105
6.1 Definitions, Notation, and Rules 105
6.2 Logarithmic Differentiation 112
6.3 Higher Derivatives 114
6.4 Vector Functions 118
6.5 Functions Defined Parametrically 120
6.6 Functions Defined Implicitly 124
6.7 The Mean Value Theorem 127
6.8 Curve Sketching 131
6.9 Inequalities 139
6.10 Partial Derivatives 145
6.11 Complex Functions 148
Answers to Exercises 152
Table of Derivatives 154
Further Exercises on Chapter 6 155
7 Numerical Solution of Equations 161
7.1 Newton's Method 161
7.2 Errors 168
7.3 The Bisection Method 171
7.4 Direct Iteration 173
7.5 Summaries of Methods for Finding a Root r of f(x) = 0 176
Answers to Exercises 177
Further Exercises on Chapter 7 178
8 Series 179
8.1 Convergence of Series 179
8.2 Notation 185
8.3 The Comparison Tests 187
8.4 Absolute Convergence 189
Answers to Exercises 191
Further Exercises on Chapter 8 192
Table of Series 195
9 The Integral Calculus 197
9.1 Definition of the Riemann Integral 197
9.2 Applications 199
9.3 Properties of the Riemann Integral 205
9.4 The Fundamental Theorem 209
Contents ix
9.5 Evaluation of Riemann Integrals 213
9.6 Vector Functions and Complex Functions 216
Answers to Exercises 218
Further Exercises on Chapter 9 219
10 Antiderivatives 225
10.1 Standard Results 225
10.2 Substitution, or Change of Variable 226
10.3 Integration by Parts 230
10.4 Rational Functions 235
10.5 Reduction Formulas 240
10.6 Systematic Integration 244
10.7 Improper Integrals 247
Answers to Exercises 252
Table of Antiderivatives 253
Table of Reduction Formulas 254
Further Exercises on Chapter 10 254
11 Line Integrals and Double Integrals 259
11.1 Length of a Space Curve given Parametrically 259
11.2 Work done during Motion along a Curve 263
11.3 Further Techniques for Line Integrals 266
11.4 Alternative Derivation of the Work Formula 270
11.5 Integrals of Functions of Two Variables 271
11.6 Specification of Regions 277
11.7 Evaluation of Double Integrals 280
Answers to Exercises 287
Further Exercises on Chapter 11 289
12 Complex Algebra and Functions 293
12.1 De Moivre's Theorem 293
12.2 Powers of Complex Numbers 296
12.3 Solution of Polynomial Equations 299
12.4 Complex Functions as Mappings between Complex Planes 301
12.5 The Complex Exponential Function 306
Answers to Exercises 308
Further Exercises on Chapter 12 311
13 Differential Equations 315
13.1 Separable First Order Equations 315
13.2 First Order Linear Equations 320
13.3 Second Order Linear Equations 323
13.4 Linear Equations with Constant Coefficients 325
13.5 Reduction of Order 331
13.6 Change of Variable 333
13.7 The Use of Complex Functions 334
13.8 Some Applications of Differential Equations 338
Hints and/or Answers to Exercises 347
Further Exercises on Chapter 13 348
x Contents
14 Functions of Two Variables, Solid Geometry and Surfaces 355
14.1 Geometric Interpretation of Partial Derivatives 355
14.2 Tangent Planes 358
14.3 Differentials 361
14.4 Tangent Lines 365
14.5 Composite Functions 367
14.6 Maxima and Minima 368
Answers to Exercises 374
Further Exercises on Chapter 14 374
15 Numerical Integration 377
15.1 The Trapezoidal Rule 377
15.2 Simpson's Rule 381
15.3 Derivation of Bounds on the Trapezoidal Rule Error 384
15.4 General Integration Procedures 387
Answers to Exercises 391
Further Exercises on Chapter 15 392
16 Power Series and Fourier Series 395
16.1 Series of Functions 395
16.2 Properties of Power Series 396
16.3 Expansion of a Given Function 400
16.4 Taylor's Series 404
16.5 Errors 406
16.6 Evaluation of Limits 411
16.7 Fourier Series 414
16.8 Properties of Fourier Series 419
16.9 Fourier Series with only Sine or only Cosine Terms 424
16.10 Complex Series 429
Answers to Exercises 433
Further Exercises on Chapter 16 435
Table of Power Series 438
17 Linear Algebra 441
17.1 Geometrical Classification of Linear Equations 441
17.2 Solution by Gaussian Elimination 444
17.3 The Inverse of a Matrix 450
17.4 Determinants and Homogeneous Equations 454
17.5 Properties of Determinants 458
17.6 Applications of Determinants 461
Answers (or checks) for Exercises 467
Further Exercises on Chapter 17 468
18 Functions of Three Variables 473
18.1 Level Curves 473
18.2 Differentials and Directional Derivatives 476
18.3 Gradient Vector (Two dimensional) 477
18.4 Functions of Three Variables 479
Contents xi
18.5 Implicit Differentiation 481
18.6 Composite Functions 484
18.7 Conservative Functions 486
Answers to Exercises 490
Further Exercises on Chapter 18 491
19 Numerical Solution of Differential Equations 493
19.1 Introduction 493
19.2 Euler Formulas 494
19.3 Comparison of Formulas 496
19.4 Fourth Order Runge Formula 499
19.5 Computer Implementation 500
19.6 Second Order Equations 501
Answers to Exercises 504
Further Exercises on Chapter 19 505
20 Laplace Transforms 507
20.1 Definition of the Laplace Transform 507
20.2 Inversion of Transforms 509
20.3 Solution of Differential Equations using Laplace Transforms 511
Answers to Exercises 514
Table of Laplace Transforms and Inversions 515
Further Exercises on Chapter 20 515
Appendix A Complex Numbers 517
A.1 Introduction 517
A.2 Complex Algebra 518
A.3 Complex Conjugates 522
A.4 The Interpretation of Complex Numbers 523
A.5 Polar Form of Complex Numbers 526
A.6 Geometric Interpretation of Multiplication and Division 531
A.7 Sets of Points in the Complex Plane 534
Answers to Exercises 538
Appendix B Flow Diagrams or Summaries of Mathematical Procedures 543
Appendix C Computer Programs 549
Appendix D Formal Definitions of Limiting Processes 561
Appendix E Change of Variable in an Integral 569
Appendix F Answers (or checks) to Selected Exercises 571
Appendix G Table of Antiderivatives 595
Appendix H Formulas from Elementary Mathematics 597
Index 601 |
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| spelling | Englefield, M. J. Verfasser aut Mathematical methods for engineering and science students 1. publ. London [u.a.] Arnold 1987 XI, 610 S. txt rdacontent n rdamedia nc rdacarrier Mathématiques de l'ingénieur Physique mathématique Wiskunde gtt Mathematik Engineering mathematics Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Mathematik (DE-588)4037944-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015090073&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Englefield, M. J. Mathematical methods for engineering and science students Mathématiques de l'ingénieur Physique mathématique Wiskunde gtt Mathematik Engineering mathematics Mathematik (DE-588)4037944-9 gnd |
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| title | Mathematical methods for engineering and science students |
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