Mathematical methods with applications to problems in the physical sciences:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Wiley
1984
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 702 S. graph. Darst. |
| ISBN: | 0471886394 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mathematical methods with applications to problems in the physical sciences |
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Record in the Search Index
| _version_ | 1804117807789506560 |
|---|---|
| adam_text | Contents
1 Linear Equations: An Introduction to
Matrices and Determinants
1. Vector Addition 1
2. Examples of Linear Algebraic
Equations 3
3. The Matrix Concept 7
4. The Permutation Symbol 13
5. Determinants 15
6. Linear Dependence and
Independence 22
7. The Rank of a Matrix 23
8. Consistency of Linear Algebraic
Equations 24
9. A Linear Mechanical System 28
10. The Inverse of a Matrix 30
2 Vectors and Tensors in a Cartesian Space
1. Vector Spaces 34
2. Orthogonal Transformations 35
3. Differentiation of Vectors 39
4. The Dot Product 41
5. Solid Angle and Gauss Law 47
6. Tensors 51
7. Isotropic Tensors 55
8. The Cross Product 58
9. Angular Momentum and Rigid
Body Motion 63
10. The Eigenvalue Problem 71
3 Vector Fields
1. The Gravitational Field of a Point
Mass 78
2. The Gradient of a Scalar Function 80
3. Review of Some Topics From
Calculus 82
4. Gradient and Directional
Derivative 83
5. The Divergence of a Vector 86
6. Heat Conduction and Diffusion 90
7. Line Integrals 93
8. Circulation and Curl 98
9. Differential and Integral Vector
Identities 104
10. Electrostatics 108
11. Magnetostatics 114
12. Maxwell s Equations 120
4 Curvilinear Coordinates
1. Rectangular, Cylindrical, and
Spherical Coordinates 127
2. Electric Dipoles 132
3. Admissible Coordinate
Transformations and Jacobians 134
4. Vectors and Tensors 139
5. Differential Geometry 143
6. Basis Vectors and Reciprocal
Basis Vectors 145
7. Dot and Cross Products 147
8. The Gradient Operator 149
9. Velocity and Acceleration 152
10. Divergence, Curl, and Laplacian 157
11. Magnetic Dipoles 159
12. Spheroidal Coordinates 161
13. Lagrange s Equations 167
14. Linear Vibrations 174
15. Euler Angles and Rigid
Body Dynamics 181
5 Complex Numbers and Variables
1. The Group Concept 188
2. Number Fields 191
3. The Complex Number Field 193
4. Review of Infinite Series 196
5. Infinite Series of Functions 204
6. Projectile Motion 214
7. Analytic Functions 216
8. Complex Infinite Series 219
9. The Exponential Function 223
10. Diffraction Grating 225
11. Capacitance and Inductance 229
12. Second Order Linear Differential
Equations 233
13. Linear Driven Systems 239
14. Trigonometric and Hyperbolic
Functions 246
15. Logarithms and Exponents 249
16. Inverse Functions 255
17. Two Dimensional Potential
Problems 259
18. Integration in the Complex Plane 267
19. Taylor and Laurent Expansions 272
20. Improper Integrals 279
21. Applications of the Residue
Theorem 284
22. Gamma and Beta Functions 291
23. Asymptotic Series 296
6 Probability, Statistics, and Experimental Errors
1. The Probability Concept 303
2. The Binomial Distribution 307
3. Poisson and Normal Distributions 312
4. Maximum Likelihood 317
5. Method of Least Squares 322
6. Lagrange Multipliers 326
7. Maxwell Boltzmann Statistics 329
7 Introduction to Hilbert Space and
Eigenvalue Problems
1. Periodic Systems With / Degrees
of Freedom 337
2. Vibrating String 345
3. Vibrating Membrane 356
4. Electromagnetic Waves in Metallic
Conductors 362
5. Electromagnetic Waves in
Hollow Conductors 367
6. The Schrodinger Wave Equation 374
7. Potential Barrier 380
8. Particle in a Box 384
9. One Dimensional Waves in
Elastic Media 388
10. The Sturm Liouville Eigenvalue
Problem 391
11. Hilbert Spaces and Unitary Spaces 398
12. Hermitian and Unitary Matrices 402
13. The Heisenberg Uncertainty
Relation 410
14. The Cayley Hamilton Theorem 412
15. Spectral Theorem 416
8 Fourier Series and Integrals
1. Definition and Convergence of
Fourier Series 425
2. Examples of Fourier Series 430
3. Periodic Solutions of Nonlinear
Differential Equations 437
4. Classical Central Force Problem 444
5. The Fourier Integral 450
6. The Free Particle in Quantum
Mechanics 455
7. Solution of the Wave Equation 459
8. The Laplace Transform 465
9 Partial Differential Equations and
Special Functions
1. Series Solutions of Ordinary
Differential Equations 472
2. The Harmonic Oscillator 477
3. Algebra of Angular Momentum 490
4. Orbital Angular Momentum and
Spherical Harmonics 495
5. Quantum Central Force Problem 500
6. Spin and Quaternions 510
7. Angular Momentum and Rotation 514
8. Spin Particle in a Magnetic Field 520
9. Laplace s Equation in Spherical
Coordinates 524
10. Examples of Solutions of
Laplace s Equation 531
11. Problems in Magnetostatics 537
12. Addition Theorem for Spherical
Harmonics 546
13. Introduction to Bessel Functions 555
14. Contour Integral Solution of
Bessel s Equation 563
15. Saddle Point Method 570
16. Applications of Bessel Functions 581
17. Spherical Bessel Functions 589
18. Hankel Transforms 598
19. Green Functions 602
20. Green s Function Expansions 606
10 The Calculus of Variations
1. The Brachistochrone Problem 616
2. Surfaces of Revolution of
Minimum Area 622
3. Variation of End Points 629
4. Isoperimetric Problems 632
5. Hamilton s Principle 636
6. Geodesies 639
7. Continuous Systems 641
8. Variational Aspects of the
Eigenvalue Problem 646
11 Numerical Methods
1. The Matrix as an Array of Numbers 653
2. Exchange of Rows in an Array 654
3. Multiplication of a Row by a Factor 654
4. Addition of a Multiple of
One Row to Another Row 655
5. Transpose of an Array 655
6. Matrix Multiplication 655
7. Orthogonal Transformation of
a Vector 656
8. Second Rank Tensor Transformation 657
9. Matrix Inverse 658
10. Matrix Eigenvalues 659
11. Schmidt Orthogonalization 662
12. The Eigenvalues of a
Symmetric Matrix 664
13. The Characteristic Function
of a Matrix 667
14. Finding the Roots of a Function 669
15. Maxima and Minima 670
16. Determinants 671
17. Arrays with More Than
Two Subscripts 672
18. The Permutation Symbol 672
19. Numerical Integration 673
20. The Runge Kutta Method 674
21. Summing Series 675
22. Computing with Recurrence
Formulas 677
Bibliography 686
Index 689
|
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| dewey-ones | 530 - Physics |
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| dewey-sort | 3530.1 15 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T16:00:17Z |
| institution | BVB |
| isbn | 0471886394 |
| language | English |
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| physical | IX, 702 S. graph. Darst. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
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| publisher | Wiley |
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| spelling | Bradbury, Ted. C. Verfasser aut Mathematical methods with applications to problems in the physical sciences New York u.a. Wiley 1984 IX, 702 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathématiques Physique mathématique Physique mathématique ram Mathematik Mathematische Physik Mathematical physics Mathematics Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Physik (DE-588)4045956-1 s Mathematische Methode (DE-588)4155620-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002191778&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bradbury, Ted. C. Mathematical methods with applications to problems in the physical sciences Mathématiques Physique mathématique Physique mathématique ram Mathematik Mathematische Physik Mathematical physics Mathematics Mathematische Methode (DE-588)4155620-3 gnd Physik (DE-588)4045956-1 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4045956-1 (DE-588)4143389-0 |
| title | Mathematical methods with applications to problems in the physical sciences |
| title_auth | Mathematical methods with applications to problems in the physical sciences |
| title_exact_search | Mathematical methods with applications to problems in the physical sciences |
| title_full | Mathematical methods with applications to problems in the physical sciences |
| title_fullStr | Mathematical methods with applications to problems in the physical sciences |
| title_full_unstemmed | Mathematical methods with applications to problems in the physical sciences |
| title_short | Mathematical methods with applications to problems in the physical sciences |
| title_sort | mathematical methods with applications to problems in the physical sciences |
| topic | Mathématiques Physique mathématique Physique mathématique ram Mathematik Mathematische Physik Mathematical physics Mathematics Mathematische Methode (DE-588)4155620-3 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Mathématiques Physique mathématique Mathematik Mathematische Physik Mathematical physics Mathematics Mathematische Methode Physik Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002191778&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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