Fundamental math and physics for scientists and engineers:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2015
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 447 S. Ill., graph. Darst. |
| ISBN: | 9780470407844 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804153196761841664 |
|---|---|
| adam_text | CONTENTS
1
Introduction
1
2 Problem
Solving
3
2.1
Analysis
3
2.2
Test-Taking Techniques
4
2.2.1
Dimensional Analysis
5
3
Scientific Programming
6
3.1
Language Fundamentals
6
3.1.1
Octave Programming
7
4
Elementary Mathematics
12
4.1
Algebra
12
4.1.1
Equation Manipulation
12
4.1.2
Linear Equation Systems
13
4.1.3
Factoring
14
4.1.4
Inequalities
15
4.1.5
Sum Formulas
16
4.1.6
Binomial Theorem
17
4.2
Geometry
17
4.2.1
Angles
18
4.2.2
Triangles
18
4.2.3
Right Triangles
19
4.2.4
Polygons
20
4.2.5
Circles
20
vii
iu
CONTENTS
4.3
Exponential, Logarithmic Functions, and Trigonometry
21
4.3.1
Exponential Functions
21
4.3.2
Inverse Functions and Logarithms
21
4.3.3
Hyperbolic Functions
22
4.3.4
Complex Numbers and Harmonic Functions
23
4.3.5
Inverse Harmonic and Hyperbolic Functions
25
4.3.6
Trigonometric Identities
26
4.4
Analytic Geometry
28
4.4.1
Lines and Planes
28
4.4.2
Conic Sections
29
4.4.3
Areas, Volumes, and Solid Angles
31
5
Vectors and Matrices
32
5.1
Matrices and Matrix Products
32
5.2
Equation Systems
34
5.3
Traces and Determinants
35
5.4
Vectors and Inner Products
38
5.5
Cross and Outer Products
40
5.6
Vector Identities
41
5.7
Rotations and Orthogonal Matrices
42
5.8
Groups and Matrix Generators
43
5.9
Eigenvalues and Eigenvectors
45
5.10
Similarity Transformations
48
6
Calculus of a Single Variable
50
6.1
Derivatives
50
6.2
Integrals
54
6.3
Series
60
7
Calculus of Several Variables
62
7.1
Partial Derivatives
62
7.2
Multidimensional Taylor Series and
Extrema
66
7.3
Multiple Integration
67
7.4
Volumes and Surfaces of Revolution
69
7.5
Change of Variables and Jacobians
70
8
Calculus of Vector Functions
72
8.1
Generalized Coordinates
72
8.2
Vector Differential Operators
77
8.3
Vector Differential Identities
81
8.4
Gauss s and Stokes Laws and
Green s Identities
82
8.5 Lagrange
Multipliers
83
CONTENTS
ІХ
9
Probability Theory and Statistics
85
9.1
Random Variables, Probability Density,
and Distributions
85
9.2
Mean, Variance, and Standard Deviation
86
9.3
Variable Transformations
86
9.4
Moments and Moment-Generating Function
86
9.5
Multivariate Probability Distributions,
Covariance, and Correlation
87
9.6
Gaussian, Binomial, and
Poisson
Distributions
87
9.7
Least Squares Regression
91
9.8
Error Propagation
92
9.9
Numerical Models
93
10
Complex Analysis
94
10.1
Functions of a Complex Variable
94
10.2
Derivatives, Analyticity, and
the Cauchy-Riemann Relations
95
10.3
Conformai
Mapping
96
10.4
Cauchy s Theorem and Taylor and Laurent Series
97
10.5
Residue Theorem
101
10.6
Dispersion Relations
105
10.7
Method of Steepest Decent
106
11 Differential
Equations
108
11.1
Linearity, Superposition, and Initial
and Boundary Values
108
11.2
Numerical Solutions
109
11.3
First-Order Differential Equations
112
11.4
Wronskian
114
11.5
Factorization
115
11.6
Method of Undetermined Coefficients
115
11.7
Variation of Parameters
116
11.8
Reduction of Order
118
11.9
Series Solution and Method of Frobenius
118
11.10
Systems of Equations, Eigenvalues,
and Eigenvectors
119
12
Transform Theory
122
12.1
Eigenfunctions and Eigenvectors
122
12.2
Sturm-Liouville Theory
123
12.3
Fourier Series
125
12.4
Fourier Transforms
127
12.5
Delta Functions
128
12.6
Green s Functions
131
x
CONTENTS
12.7
Laplace Transforms
135
12.8
z-Transforms
137
13
Partial Differential Equations and Special Functions
138
13.1
Separation of Variables and
Rectangular Coordinates
138
13.2
Legendre Polynomials
145
13.3
Spherical Harmonics
150
13.4
Bessel Functions
156
13.5
Spherical Bessel Functions
162
14
Integral Equations and the Calculus of Variations
166
14.
1
Volterra and
Fredholm
Equations
166
14.2
Calculus of Variations the
Euler-Lagrange Equation
168
15
Particle Mechanics
170
15.1
Newton s Laws
170
15.2
Forces
171
15.3
Numerical Methods
173
15.4
Work and Energy
174
15.5
Lagrange Equations
176
15.6
Three-Dimensional Particle Motion
180
15.7
Impulse
181
15.8
Oscillatory Motion
181
15.9
Rotational Motion About a Fixed Axis
185
15.10
Torque and Angular Momentum
187
15.11
Motion in Accelerating Reference Systems
188
15.12
Gravitational Forces and Fields
189
15.13
Celestial Mechanics
191
15.14
Dynamics of Systems of Particles
193
15.15
Two-Particle Collisions and Scattering
197
15.16
Mechanics of Rigid Bodies
199
15.17
Hamilton s Equation and Kinematics
206
16
Fluid Mechanics
210
16.1
Continuity Equation
210
16.2
Euler
s
Equation
212
16.3
Bernoulli s Equation
213
17
Special Relativity
215
17.1
Four-Vectors and
Lorentz
Transformation
215
17.2
Length Contraction, Time Dilation, and Simultaneity
217
CONTENTS
ХІ
17.3 Covariant Notation 219
17.4 Casuality
and Minkowski Diagrams
221
17.5 Velocity Addition and
Doppler
Shift
222
17.6 Energy
and Momentum
223
18 Electromagnetism 227
18.1
Maxwell s Equations
227
18.2
Gauss s Law
233
18.3
Electric Potential
235
18.4
Current and Resistivity
238
18.5
Dipoles and Polarization
241
18.6
Boundary Conditions and
Green s Functions
244
18.7
Multipole Expansion
248
18.8
Relativistic Formulation of Electromagnetism,
Gauge Transformations, and Magnetic Fields
249
18.9
Magnetostatics
256
18.10
Magnetic Dipoles
259
18.11
Magnetization
260
18.12
Induction and Faraday s Law
262
18.13
Circuit Theory and
Kirchoffs
Laws
266
18.14
Conservation Laws and the Stress Tensor
270
18.15
Lienard-Wiec
hert
Potentials
274
18.16
Radiation from Moving Charges
275
19
Wave Motion
282
19.1
Wave Equation
282
19.2
Propagation of Waves
284
19.3
Planar Electromagnetic Waves
286
19.4
Polarization
287
19.5
Superposition and Interference
288
19.6
Multipole Expansion for Radiating Fields
292
19.7
Phase and Group Velocity
295
19.8
Minimum Time Principle and Ray Optics
296
19.9
Refraction and
Snelľ s
Law
297
19.10
Lenses
299
19.11
Mechanical Reflection
301
19.12
Doppler
Effect and Shock Waves
302
19.13
Waves in Periodic Media
303
19.14
Conducting Media
304
19.15
Dielectric Media
306
19.16
Reflection and Transmission
307
19.17
Diffraction
311
19.18
Waveguides and Cavities
313
CONTENTS
20 Quantum
Mechanics
318
20.1 Fundamental
Principles
318
20.2
Particle-Wave Duality
319
20.3
Interference of Quantum Waves
320
20.4 Schrödinger
Equation
321
20.5
Particle Flux and Reflection
322
20.6
Wave Packet Propagation
324
20.7
Numerical Solutions
326
20.8
Quantum Mechanical Operators
328
20.9 Heisenberg
Uncertainty Relation
331
20.10
Hubert Space Representation
334
20.11
Square Well and Delta Function Potentials
336
20.12
WKB Method
339
20.13
Harmonic Oscillators
342
20.14 Heisenberg
Representation
343
20.15
Translation Operators
344
20.16
Perturbation Theory
345
20.17
Adiabatic Theorem
351
21
Atomic Physics
353
21.1
Properties of
Fermions
353
21.2
Bohr Model
354
21.3
Atomic Spectra and X-Rays
356
21.4
Atomic Units
356
21.5
Angular Momentum
357
21.6
Spin
358
21.7
Interaction of Spins
359
21.8
Ну
drogenic Atoms
360
21.9
Atomic Structure
362
21.10
Spin-Orbit Coupling
362
21.11
Atoms in Static Electric and Magnetic Fields
364
21.12
Helium Atom and the tf2+ Molecule
368
21.13
Interaction of Atoms with Radiation
371
21.14
Selection Rules
373
21.15
Scattering Theory
374
22
Nuclear and Particle Physics
379
22.1
Nuclear Properties
379
22.2
Radioactive Decay
381
22.3
Nuclear Reactions
382
22.4
Fission and Fusion
383
22.5
Fundamental Properties of
Elementary Particles
383
CONTENTS xiii
23
Thermodynamics and Statistical Mechanics
386
23.1
Entropy
386
23.2
Ensembles
388
23.3
Statistics
391
23.4
Partition Functions
393
23.5
Density of States
396
23.6
Temperature and Energy
397
23.7
Phonons and Photons
400
23.8
The Laws of Thermodynamics
401
23.9
The
Legen
dre
Transformation and
Thermodynamic Quantities
403
23.10
Expansion of Gases
407
23.11
Heat Engines and the Carnot Cycle
409
23.12
Thermodynamic Fluctuations
410
23.13
Phase Transformations
412
23.14
The Chemical Potential and Chemical Reactions
413
23.15
The Fermi Gas
414
23.16
Bose-Einstein Condensation
416
23.17
Physical Kinetics and Transport Theory
417
24
Condensed Matter Physics
422
24.1
Crystal Structure
422
24.2
X Ray Diffraction
423
24.3
Thermal Properties
424
24.4
Electron Theory of Metals
425
24.5
Superconductors
426
24.6
Semiconductors
427
25
Laboratory Methods
430
25.1
Interaction of Particles with Matter
430
25.2
Radiation Detection and Counting Statistics
431
25.3
Lasers
432
Index
434
|
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| id | DE-604.BV042473088 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:22:46Z |
| institution | BVB |
| isbn | 9780470407844 |
| language | English |
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| physical | XIII, 447 S. Ill., graph. Darst. |
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| publisher | Wiley |
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| spelling | Yevick, David Verfasser aut Fundamental math and physics for scientists and engineers David Yevick ; Hannah Yevick Hoboken, NJ Wiley 2015 XIII, 447 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Technische Mathematik (DE-588)4827059-3 gnd rswk-swf Naturwissenschaften (DE-588)4041421-8 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Technische Mathematik (DE-588)4827059-3 s DE-604 Naturwissenschaften (DE-588)4041421-8 s Mathematische Methode (DE-588)4155620-3 s 2\p DE-604 Yevick, Hannah Verfasser aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027908217&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yevick, David Yevick, Hannah Fundamental math and physics for scientists and engineers Mathematische Methode (DE-588)4155620-3 gnd Technische Mathematik (DE-588)4827059-3 gnd Naturwissenschaften (DE-588)4041421-8 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4827059-3 (DE-588)4041421-8 (DE-588)4123623-3 |
| title | Fundamental math and physics for scientists and engineers |
| title_auth | Fundamental math and physics for scientists and engineers |
| title_exact_search | Fundamental math and physics for scientists and engineers |
| title_full | Fundamental math and physics for scientists and engineers David Yevick ; Hannah Yevick |
| title_fullStr | Fundamental math and physics for scientists and engineers David Yevick ; Hannah Yevick |
| title_full_unstemmed | Fundamental math and physics for scientists and engineers David Yevick ; Hannah Yevick |
| title_short | Fundamental math and physics for scientists and engineers |
| title_sort | fundamental math and physics for scientists and engineers |
| topic | Mathematische Methode (DE-588)4155620-3 gnd Technische Mathematik (DE-588)4827059-3 gnd Naturwissenschaften (DE-588)4041421-8 gnd |
| topic_facet | Mathematische Methode Technische Mathematik Naturwissenschaften Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027908217&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT yevickdavid fundamentalmathandphysicsforscientistsandengineers AT yevickhannah fundamentalmathandphysicsforscientistsandengineers |