Fundamental Math and Physics for Scientists and Engineers E-Book

David Yevick

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 590

Veröffentlichungsjahr: 2014

Beschreibung

Provides a concise overview of the core undergraduate physics and applied mathematics curriculum for students and practitioners of science and engineering Fundamental Math and Physics for Scientists and Engineers summarizes college and university level physics together with the mathematics frequently encountered in engineering and physics calculations. The presentation provides straightforward, coherent explanations of underlying concepts emphasizing essential formulas, derivations, examples, and computer programs. Content that should be thoroughly mastered and memorized is clearly identified while unnecessary technical details are omitted. Fundamental Math and Physics for Scientists and Engineers is an ideal resource for undergraduate science and engineering students and practitioners, students reviewing for the GRE and graduate-level comprehensive exams, and general readers seeking to improve their comprehension of undergraduate physics. * Covers topics frequently encountered in undergraduate physics, in particular those appearing in the Physics GRE subject examination * Reviews relevant areas of undergraduate applied mathematics, with an overview chapter on scientific programming * Provides simple, concise explanations and illustrations of underlying concepts Succinct yet comprehensive, Fundamental Math and Physics for Scientists and Engineers constitutes a reference for science and engineering students, practitioners and non-practitioners alike.

Leseprobe

CONTENTS

Cover

Title page

Copyright page

Dedication

1 Introduction

2 Problem Solving

2.1 Analysis

2.2 Test-Taking Techniques

3 Scientific Programming

3.1 Language Fundamentals

4 Elementary Mathematics

4.1 Algebra

4.2 Geometry

4.3 Exponential, Logarithmic Functions, and Trigonometry

4.4 Analytic Geometry

5 Vectors and Matrices

5.1 Matrices and Matrix Products

5.2 Equation Systems

5.3 Traces and Determinants

5.4 Vectors and Inner Products

5.5 Cross and Outer Products

5.6 Vector Identities

5.7 Rotations and Orthogonal Matrices

5.8 Groups and Matrix Generators

5.9 Eigenvalues and Eigenvectors

5.10 Similarity Transformations

6 Calculus of a Single Variable

6.1 Derivatives

6.2 Integrals

6.3 Series

7 Calculus of Several Variables

7.1 Partial Derivatives

7.2 Multidimensional Taylor Series and Extrema

7.3 Multiple Integration

7.4 Volumes and Surfaces of Revolution

7.5 Change of Variables and Jacobians

8 Calculus of Vector Functions

8.1 Generalized Coordinates

8.2 Vector Differential Operators

8.3 Vector Differential Identities

8.4 Gauss’s and Stokes’ Laws and Green’s Identities

8.5 Lagrange Multipliers

9 Probability Theory and Statistics

9.1 Random Variables, Probability Density, and Distributions

9.2 Mean, Variance, and Standard Deviation

9.3 Variable Transformations

9.4 Moments and Moment-Generating Function

9.5 Multivariate Probability Distributions, Covariance, and Correlation

9.6 Gaussian, Binomial, and Poisson Distributions

9.7 Least Squares Regression

9.8 Error Propagation

9.9 Numerical Models

10 Complex Analysis

10.1 Functions of a Complex Variable

10.2 Derivatives, Analyticity, and the Cauchy–Riemann Relations

10.3 Conformal Mapping

10.4 Cauchy’s Theorem and Taylor and Laurent Series

10.5 Residue Theorem

10.6 Dispersion Relations

10.7 Method of Steepest Decent

11 Differential Equations

11.1 Linearity, Superposition, and Initial and Boundary Values

11.2 Numerical Solutions

11.3 First-Order Differential Equations

11.4 Wronskian

11.5 Factorization

11.6 Method of Undetermined Coefficients

11.7 Variation of Parameters

11.8 Reduction of Order

11.9 Series Solution and Method of Frobenius

11.10 Systems of Equations, Eigenvalues, and Eigenvectors

12 Transform Theory

12.1 Eigenfunctions and Eigenvectors

12.2 Sturm–Liouville Theory

12.3 Fourier Series

12.4 Fourier Transforms

12.5 Delta Functions

12.6 Green’s Functions

12.7 Laplace Transforms

12.8 z-Transforms

13 Partial Differential Equations and Special Functions

13.1 Separation of Variables and Rectangular Coordinates

13.2 Legendre Polynomials

13.3 Spherical Harmonics

13.4 Bessel Functions

13.5 Spherical Bessel Functions

14 Integral Equations and the Calculus of Variations

14.1 Volterra and Fredholm Equations

14.2 Calculus of Variations the Euler-Lagrange Equation

15 Particle Mechanics

15.1 Newton’s Laws

15.2 Forces

15.3 Numerical Methods

15.4 Work and Energy

15.5 Lagrange Equations

15.6 Three-Dimensional Particle Motion

15.7 Impulse

15.8 Oscillatory Motion

15.9 Rotational Motion About a Fixed Axis

15.10 Torque and Angular Momentum

15.11 Motion in Accelerating Reference Systems

15.12 Gravitational Forces and Fields

15.13 Celestial Mechanics

15.14 Dynamics of Systems of Particles

15.15 Two-Particle Collisions and Scattering

15.16 Mechanics of Rigid Bodies

15.17 Hamilton’s Equation and Kinematics

16 Fluid Mechanics

16.1 Continuity Equation

16.2 Euler’s Equation

16.3 Bernoulli’s Equation

17 Special Relativity

17.1 Four-Vectors and Lorentz Transformation

17.2 Length Contraction, Time Dilation, and Simultaneity

17.3 Covariant Notation

17.4 Casuality and Minkowski Diagrams

17.5 Velocity Addition and Doppler Shift

17.6 Energy and Momentum

18 Electromagnetism

18.1 Maxwell’s Equations

18.2 Gauss’s Law

18.3 Electric Potential

18.4 Current and Resistivity

18.5 Dipoles and Polarization

18.6 Boundary Conditions and Green’s Functions

18.7 Multipole Expansion

18.8 Relativistic Formulation of Electromagnetism, Gauge Transformations, and Magnetic Fields

18.9 Magnetostatics

18.10 Magnetic Dipoles

18.11 Magnetization

18.12 Induction and Faraday’s Law

18.13 Circuit Theory and Kirchoff’s Laws

18.14 Conservation Laws and the Stress Tensor

18.15 Lienard–Wiechert Potentials

18.16 Radiation from Moving Charges

19 Wave Motion

19.1 Wave Equation

19.2 Propagation of Waves

19.3 Planar Electromagnetic Waves

19.4 Polarization

19.5 Superposition and Interference

19.6 Multipole Expansion for Radiating Fields

19.7 Phase and Group Velocity

19.8 Minimum Time Principle and Ray Optics

19.9 Refraction and Snell’s Law

19.10 Lenses

19.11 Mechanical Reflection

19.12 Doppler Effect and Shock Waves

19.13 Waves in Periodic Media

19.14 Conducting Media

19.15 Dielectric Media

19.16 Reflection and Transmission

19.17 Diffraction

19.18 Waveguides and Cavities

20 Quantum Mechanics

20.1 Fundamental Principles

20.2 Particle–Wave Duality

20.3 Interference of Quantum Waves

20.4 Schrödinger Equation

20.5 Particle Flux and Reflection

20.6 Wave Packet Propagation

20.7 Numerical Solutions

20.8 Quantum Mechanical Operators

20.9 Heisenberg Uncertainty Relation

20.10 Hilbert Space Representation

20.11 Square Well and Delta Function Potentials

20.12 WKB Method

20.13 Harmonic Oscillators

20.14 Heisenberg Representation

20.15 Translation Operators

20.16 Perturbation Theory

20.17 Adiabatic Theorem

21 Atomic Physics

21.1 Properties of Fermions

21.2 Bohr Model

21.3 Atomic Spectra and X-Rays

21.4 Atomic Units

21.5 Angular Momentum

21.6 Spin

21.7 Interaction of Spins

21.8 Hydrogenic Atoms

21.9 Atomic Structure

21.10 Spin–Orbit Coupling

21.11 Atoms in Static Electric and Magnetic Fields

21.12 Helium Atom and the

Molecule

21.13 Interaction of Atoms with Radiation

21.14 Selection Rules

21.15 Scattering Theory

22 Nuclear and Particle Physics

22.1 Nuclear Properties

22.2 Radioactive Decay

22.3 Nuclear Reactions

22.4 Fission and Fusion

22.5 Fundamental Properties of Elementary Particles

23 Thermodynamics and Statistical Mechanics

23.1 Entropy

23.2 Ensembles

23.3 Statistics

23.4 Partition Functions

23.5 Density of States

23.6 Temperature and Energy

23.7 Phonons and Photons

23.8 The Laws of Thermodynamics

23.9 The Legendre Transformation and Thermodynamic Quantities

23.10 Expansion of Gases

23.11 Heat engines and the Carnot Cycle

23.12 Thermodynamic Fluctuations

23.13 Phase Transformations

23.14 The Chemical Potential and Chemical Reactions

23.15 The Fermi Gas

23.16 Bose–Einstein Condensation

23.17 Physical Kinetics and Transport Theory

24 Condensed Matter Physics

24.1 Crystal Structure

24.2 X-Ray Diffraction

24.3 Thermal Properties

24.4 Electron Theory of Metals

24.5 Superconductors

24.6 Semiconductors

25 Laboratory Methods

25.1 Interaction of Particles with Matter

25.2 Radiation Detection and Counting Statistics

25.3 Lasers

Index

End User License Agreement

List of Illustrations

Chapter 04

Figure 4.1 Corresponding angles.

Figure 4.2 Proof that the angles of a triangle sum to 180°.

Figure 4.3 Right angle triangle.

Figure 4.4 Hyperbolic functions.

Figure 4.5 Harmonic functions.

Figure 4.6 Geometric interpretation of a complex number.

Chapter 05

Figure 5.1 Addition of two vectors.

Chapter 07

Figure 7.1 Integration limits.

Chapter 08

Figure 8.1 Computation of curl.

Chapter 10

Figure 10.1 Contour for Cauchy’s theorem.

Figure 10.2 Laurent series contour.

Figure 10.3 Contour integration enclosing several singularities.

Figure 10.4 Integration contour.

Figure 10.5 Contour for principal part integration.

Chapter 11

Figure 11.1 Slope field.

Chapter 15

Figure 15.1 Two pulley system.

Figure 15.2 Infinitesimal rotation.

Figure 15.3 Euler angles.

Chapter 17

Figure 17.1 Light ray in a moving frame.

Figure 17.2 Minkowski diagram.

Chapter 19

Figure 19.1 Refraction at a dielectric interface for TM polarization.

Figure 19.2 Modal condition.

Chapter 23

Figure 23.1 Thermodynamic square.

Figure 23.2 Carnot cycle.

Guide

Cover

Table of Contents

Begin Reading

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FUNDAMENTAL MATH AND PHYSICS FOR SCIENTISTS AND ENGINEERS

DAVID YEVICK

HANNAH YEVICK