Advanced engineering mathematics:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a]
Wiley
1977
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 578 S. zahlr. graph. Darst. |
| ISBN: | 0471995215 0471995207 |
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MARC
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| 245 | 1 | 0 | |a Advanced engineering mathematics |c Avinash C. Bajpai ; Leslie R. Mustoe ; Dennis Walker* |
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Record in the Search Index
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| adam_text | Contents
CHAPTER ONE: LINEAR ALGEBRA
1.1 Introduction 1
1.2 Vector Spaces 1
1.3 Linear Transformations 8
1.4 The Solution of Simultaneous Linear Equations 14
1.5 Schemes for Solution of Linear Equations 19
1.6 Partitioned Matrices 27
CHAPTER TWO: EIGENVALUE PROBLEMS
2.1 Introduction 31
2.2 Case Study: Vibration of a Two Storey Frame 32
2.3 Algebraic Determination of Eigenvalues 37
2.4 Further Results on Eigenvalues 41
2.5 Quadratic Forms and their Reduction 48
2.6 Boundary—Value Problems 55
2.7 Iterative Method for finding the Eigenvalue of
Largest Modulus 59
2.8 Determination of Other Eigenvalues 67
2.9 Transformation Methods for Symmetric Matrices 71
2.10 Further Notes on Computation 75
CHAPTER THREE: OPTIMIZATION I LINEAR PROGRAMMING
3.1 Introduction 77
3.2 Graphical Solution 77
3.3 The Simplex Algorithm 81
3.4 General Formulation of the Simplex Algorithm 86
3.5 Other Features of Linear Programming 90
CHAPTER FOUR: OPTIMIZATION II NON LINEAR PROBLEMS
4.1 Introduction 96
4.2 Search Techniques in One Variable 99
4.3 Functions of Several Variables Direct Search Methods 106
viii
4.4 Calculus Approach to Functions of Several Variables 112
4.5 Methods using the Gradient of a Function 119
4.6 Least Squares Problems 128
4.7 Constrained Optimization Techniques 131
4.8 Practical Use of Algorithms 132
CHAPTER FIVE: ORDINARY DIFFERENTIAL EQUATIONS
5.1 Introduction 133
5.2 One step and Multistep Methods 133
5.3 Predictor — Corrector Methods 138
5.4 Linear Difference Equations 147
5.5 Stability of Numerical Procedures 151
5.6 Case Study: Surge Tank 153
5.7 Phase—Plane Diagrams 156
5.8 Boundary Value Problems: Shooting Methods 160
5.9 Boundary Value Problems: Finite Difference Methods 161
CHAPTER SIX: SPECIAL FUNCTIONS
6.1 Introduction: A Problem in Heat Transfer 166
6.2 Series Solution of Ordinary Differential Equations 168
6.3 The Gamma Function 178
6.4 Bessel Functions of the First and Second Kind 179
6.5 Modified Bessel Functions 184
6.6 Transformations of Bessel s Equation 185
6.7 Solution of Partial Differential Equations 187
6.8 An Introduction to Legendre Polynomials 189
6.9 The Error Function 194
CHAPTER SEVEN: APPROXIMATION OF FUNCTIONS
7.1 Introduction 195
7.2 Taylor Series Approximation 195
7.3 Mini—max Approximation 198
7.4 Periodic Phenomena an Introduction to Fourier Series 203
7.5 Odd and Even Functions; Half—Range Series 214
7.6 Further Features of Fourier Series 218
7.7 Trigonometric Series Approximation of Discrete Data 228
7.8 Cubic Spline Fitting 233
CHAPTER EIGHT: PARTIAL DIFFERENTIAL EQUATIONS
8.1 Introduction 238
8.2 Case Study: Steady State Temperature Distribution
in a Plate 238
8.3 Some Basic Ideas 245
8.4 Separation of Variables Method 248
8.5 Origin of some Partial Differential Equations 253
8.6 Parabolic Equations: Finite Difference Methods 269 f,
ix
8.7 Case Study: Forced Convection 277
8.8 Elliptic Equations 279
8.9 Case Study: Torsion of a Rectangular Prism 283
8.10 Characteristics 286
CHAPTER NINE: TRANSFORM METHODS
9.1 Introduction 291
9.2 Basic Results on the Laplace Transforms 292
9.3 Further Forcing Terms 294
9.4 Further Results on Laplace Transforms 303
9.5 Finite Fourier Transforms 305
9.6 Infinite Fourier Transforms 311
9.7 Solution of Heat Conduction Equation 317
9.8 Interpretation of Fourier Transforms 321
CHAPTER TEN: INTEGRATION
10.1 Introduction: A Brake Problem 324
10.2 Newton—Cotes Formulae 325
10.3 Romberg Integration 328
10.4 Gaussian Integration 331
10.5 Double Integration 336
10.6 Further Features of Double Integrals 347
10.7 Volumes of Interpenetration 357
10.8 Triple Integrals 361
CHAPTER ELEVEN: VECTOR FIELD THEORY
11.1 Introduction: Scalar and Vector Fields 366
11.2 Differentiation of Vectors 367
11.3 The Gradient of a Scalar Field 370
11.4 Divergence of a Vector Field 373
11.5 Line Integrals 375
11.6 Curl of a. Vector Field 383
11.7 Vector Identities 387
11.8 Surface Integrals: Stokes Theorem 388
11.9 Gauss Divergence Theorem 392
11.10 Miscellaneous Results 395
CHAPTER TWELVE: FUNCTIONS OF A COMPLEX VARIABLE
12.1 Introduction 397
12.2 Analytic Functions. The Cauchy Riemann Equations 397
12.3 Standard Functions of a Complex Variable 404
12.4 Complex Potential and Conformal Mapping 409
12.5 Further Conformal Mappings 417
12.6 Complex Integrals 424
12.7 Taylor and Laurent Series 433
X
12.8 The Residue Theorem 436
12.9 Evaluation of Real Integrals 438
12.10 Further Applications of Contour Integration 443
CHAPTER THIRTEEN: STATISTICAL TESTS OF SIGNIFICANCE
13.1 Introduction 446
13.2 Tests of Hypotheses 447
13.3 Mean of a Small Sample: the t Test 453
13.4 Test of Sample Variance: the x2 Distribution 457
13.5 Further Applications of x2: Inferences about Frequencies 461
13.6 Sample Variances: the F Test 479
13.7 Comparison of Sample Means 484
13.8 Introduction to Analysis of Variance 492
CHAPTER FOURTEEN: LINEAR REGRESSION
14.1 Introduction to Simple Regression 505
14.2 Scatter Diagrams and the Least Squares Model 507
14.3 Estimation of the Parameters of the Regression Line 508
14.4 Confidence Intervals for Predictions 514
14.5 Review Example 518
14.6 A Simple Introduction to Correlation 521
14.7 Variance Analysis Approach to Regression 524
14.8 Concluding Remarks 530
14.9 Introduction to Multiple Regression 533
APPENDIX
Differentiation under the Integral Sign 540
The Normal Probability Integral 544
Percentage points of the t Distribution 545
Percentage points of the x2 Distribution 546
Percentage points of the F Distribution 547
BIBLIOGRAPHY 549
ANSWERS 550
INDEX 574
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| dewey-full | 510/.2/462 |
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| discipline | Mathematik |
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| indexdate | 2024-07-09T15:43:20Z |
| institution | BVB |
| isbn | 0471995215 0471995207 |
| language | English |
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| spelling | Bajpai, Avinash C. Verfasser (DE-588)1013168275 aut Advanced engineering mathematics Avinash C. Bajpai ; Leslie R. Mustoe ; Dennis Walker* London [u.a] Wiley 1977 X, 578 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Engineering mathematics Analysis (DE-588)4001865-9 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 Mathematik (DE-588)4037944-9 s Ingenieurwissenschaften (DE-588)4137304-2 s Mustoe, L. R. Verfasser aut Walker, Dennis Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001499975&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bajpai, Avinash C. Mustoe, L. R. Walker, Dennis Advanced engineering mathematics Engineering mathematics Analysis (DE-588)4001865-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4137304-2 (DE-588)4037944-9 |
| title | Advanced engineering mathematics |
| title_auth | Advanced engineering mathematics |
| title_exact_search | Advanced engineering mathematics |
| title_full | Advanced engineering mathematics Avinash C. Bajpai ; Leslie R. Mustoe ; Dennis Walker* |
| title_fullStr | Advanced engineering mathematics Avinash C. Bajpai ; Leslie R. Mustoe ; Dennis Walker* |
| title_full_unstemmed | Advanced engineering mathematics Avinash C. Bajpai ; Leslie R. Mustoe ; Dennis Walker* |
| title_short | Advanced engineering mathematics |
| title_sort | advanced engineering mathematics |
| topic | Engineering mathematics Analysis (DE-588)4001865-9 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Engineering mathematics Analysis Ingenieurwissenschaften Mathematik |
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