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Theoretical Physics : A Classical Approach

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概要 This introduction to classical theoretical physics emerged from a course for students in the third and fourth semester, which the authors have given several times at the University of Freiburg (German...y). The goal of the course is to give the student a comprehensive and coherent overview of the principal areas of classical theoretical physics. In line with this goal, the content, the terminology, and the mathematical techniques of theoret ical physics are all presented along with applications, to serve as a solid foundation for further courses in the basic areas of experimental and theoretical physics. In conceiving the course, the authors had four interdependent goals in mind: - the presentation of a consistent overview, even at this elementary level - the establishment of a well-balanced interactive relationship between phys ical content and mathematical methods - a demonstration of the important applications of physics, and - an acquisition of the most important mathematical techniques needed to solve specific problems. In relation to the first point, it was necessary to limit the amount of material treated. This introductory course was not intended to preempt a later, primarily On the other hand, we aimed for a certain completeness in theoretical, course.続きを見る
目次 1. Introduction
2. Newtonian Mechanics
2.1 Space and Time in Classical Mechanics
2.2 Newton's Laws
2.3 A Few Important Force Laws
2.4 The Energy of a Particle in a Force Field
2.5 Several Interacting Particles
2.6 Momentum and Momentum Conservation
2.7 Angular Momentum
2.8 The Two-Body Problem
2.9 The Kepler Problem
2.10 Scattering
2.11 The Scattering Cross-Section
2.12 The Virial Theorem
2.13 Mechanical Similarity
2.14 Some General Observations About the Many-Body Problem
Problems
3. Lagrangian Methods in Classical Mechanics
3.1 A Sketch of the Problem and Its Solution in the Case of a Pendulum
3.2 The Lagrangian Method of the First Type
3.3 The Lagrangian Method of the Second Type
3.4 The Conservation of Energy in Motions Which are Limited by Constraints
3.5 Non-holonomic Constraints
3.6 Invariants and Conservation Laws
3.7 The Hamiltonian
3.8 The Hamiltonian Principle of Stationary Action
Problems
4. Rigid Bodies
4.1 The Kinematics of the Rigid Body
4.2 The Inertia Tensor and the Kinetic Energy of a Rigid Body
4.3 The Angular Momentum of a Rigid Body, Euler's Equations
4.4 The Equations of Motion for the Eulerian Angles
Problems
5. Motion in a Noninertial System of Reference
5.1 Fictitious Forces in Noninertial Systems
5.2 Foucault's Pendulum
6. Linear Oscillations
6.1 Linear Approximations About a Point of Equilibrium
6.2 A Few General Remarks About Linear Differential Equations
6.3 Homogeneous Linear Systems with One Degree of Freedom and Constant Coefficients
6.4 Homogeneous Linear Systems with n Degrees of Freedom and Constant Coefficients
6.5 The Response of Linear Systems to External Forces
Problems
7. Classical Statistical Mechanics
7.1 Thermodynamic Systems and Distribution Functions
7.2 Entropy
7.3 Temperature, Pressure, and Chemical Potential
7.4 The Gibbs Equation and the Forms of Energy Exchange
7.5 The Canonical Ensemble and the Free Energy
7.6 Thermodynamic Potentials
7.7 Material Constants
7.8 Changes of State
7.9 The Transformation of Heat into Work, the Carnot Efficiency
7.10 The Laws of Thermodynamics
7.11 The Phenomenological Basis of Thermodynamics
7.12 Equilibrium and Stability Conditions
Problems
8. Applications of Thermodynamics
8.1 Phase Transformations and Phase Diagrams
8.2 The Latent Heat of Phase Transitions
8.3 Solutions
8.4 Henry's Law, Osmosis
8.5 Phase Transitions in Solutions
Problem
9. Elements of Fluid Mechanics
9.1 A Few Introductory Remarks About Fluid Mechanics
9.2 The General Balance Equation
9.3 Particular Balance Equations
9.4 Entropy Production, Generalized Forces, and Fluids
9.5 The Differential Equations of Fluid Mechanics
9.6 A Few Elementary Applications of the Navier-Stokes Equations
Problem
10. The Most Important Linear Partial Differential Equations of Physics
10.1 General Considerations
10.2 Solutions of the Wave Equation
10.3 Boundary Value Problems
10.4 The Helmholtz Equation in Spherical Coordinates, Spherical Harmonics, and Bessel Functions
Problems
11. Electrostatics
11.1 The Basic Equations of Electrostatics and Their First Consequences
11.2 Boundary Value Problems in Electrostatics, Green's Functions
11.3 The Calculation of Green's Functions, the Method of Images
11.4 The Calculation of Green's Functions, Expansion in Spherical Harmonics
11.5 Localized Charge Distributions, the Multipole Expansion
11.6 Electrostatic Potential Energy
Problems
12. Moving Charges, Magnetostatics
12.1 The Biot-Savart Law, the Fundamental Equations of Magnetostatics
12.2 Localized Current Distributions
13. Time Dependent Electromagnetic Fields
13.1 Maxwell's Equations
13.2 Potentials and Gauge Transformations
13.3 Electromagnetic Waves in a Vacuum, the Polarization of Transverse Waves
13.4 Electromagnetic Waves, the Influence of Sources
13.5 The Energy of the Electromagnetic Field
13.6 The Momentum of the Electromagnetic Field
14. Elements of the Electrodynamics of Continuous Media
14.1 The Macroscopic Maxwell Equations
14.2 Electrostatic Fields in Continuous Media
14.3 Magnetostatic Fields in Continuous Media
14.4 Plane Waves in Matter, Wave Packets
14.5 Reflection and Refraction at Plane Boundary Surfaces
Appendices
A. The ?-Function
B. Conic Sections
C. Tensors
D. Fourier Series and Fourier Integrals
D.1 Fourier Series
D.2 Fourier Integrals and Fourier Transforms
E. Distributions and Green's Functions
E.1 Distributions
E.2 Green's Functions
F. Vector Analysis and Curvilinear Coordinates
F.1 Vector Fields and Scalar Fields
F.2 Line, Surface, and Volume Integrals
F.3 Stokes's Theorem
F.4 Gauss's Theorem
F.5 Applications of the Integral Theorems
F.6 Curvilinear Coordinates
Problems
References.
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登録日 2020.06.27
更新日 2020.06.28