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Mathematical Methods for Physics Problems and Solutions.

This book presents mathematical tools to solve partial differential equations, typical of physical problems. It explains in a detailed manner the process of solving the problems that typically arise in the context of physics. Although there are a large number of textbooks on this topic, few go so de...

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Bibliographic Details
Main Author: Aliev, Farkhad G.
Corporate Author: Taylor & Francis
Other Authors: Lara, Antonio
Format: eBook
Language:English
Published: Milton : Jenny Stanford Publishing, 2023.
Subjects:
Mathematical physics.
Mathematical physics > Problems, exercises, etc.
Physique mathématique.
Physique mathématique > Problèmes et exercices.
SCIENCE / Mathematical Physics
SCIENCE / Physics
Electronic books.
Problems and exercises.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover
  • Half Title
  • Title Page
  • Copyright Page
  • Table of Contents
  • Preface
  • Chapter 1: Harmonic Oscillator and Green's Function
  • 1.1: Damped Harmonic Oscillator
  • 1.2: Properties of the Ordinary Linear Differential Equation for a Forced Oscillator
  • 1.3: General Definition of Green's Functions
  • 1.4: Expansion of Green's Function in a Series of Orthogonal Eigenfunctions
  • 1.5: Green's Function of an Oscillator with Friction
  • 1.6: Movement of an Oscillator under the Influence of a Constant Force, Solved by Two Methods
  • 1.7: Oscillator Forced by a Rectangular Hit, Solved with Green's Functions
  • 1.8: Movement of a Mass after an Instantaneous Exponential Hit
  • 1.9: Shape of a String in Mechanical Equilibrium, Solved by the Green's Function Method
  • 1.10: Case Study: Transversal Displacement of a Tense String Glued to an Elastic Plane
  • 1.11: Forced Harmonic Oscillator, Solved with Green's Functions
  • Chapter 2: Problems in One Dimension
  • 2.1: Closed String
  • 2.2: Sturm-Liouville Problem with Boundary Conditions of the Second and Third Kind
  • 2.3: Stationary String in a Gravitational Field
  • 2.4: Static String with Boundary Conditions of the Third Kind at Both Ends
  • 2.5: String with a Point Mass Hanging from One of Its Ends
  • 2.6: String with a Point Mass in Its Center and Second and Third Type Boundary Conditions
  • 2.7: Static Form of a String with a Mass
  • 2.8: Heat Conduction through a Semi-Insulated Bar
  • 2.9: Variation of the Temperature of a Thin Rod as a Function of Time
  • 2.10: Thermal Conduction in a Bar with Insulated Ends
  • 2.11: Variation of the Temperature of a Bar as a Function of Time
  • 2.12: Relaxation of Temperature in a Rod with a Local Heat Source
  • 2.13: Heat Transfer in an Insulated Bar According to Newton's Law
  • 2.14: Case Study: Heat Transfer in a Semi-Infinite 1D Bar: Periodically Varying Temperature
  • 2.15: Case Study: Vibrations of Two United Bars
  • 2.16: Distribution of Temperature in a Non-Homogeneous Bar
  • 2.17: Case Study: Variation in the Ion Concentration in a Rod with Flux across Its Ends
  • 2.18: Oscillations of a Non-Homogeneous String
  • 2.19: Forced Oscillations of a String
  • 2.20: Case Study: Oscillations of a String Subject to an External Force
  • 2.21: Case Study: Oscillations of the Gas in a Semi-Open Tube
  • 2.22: Variation of the Temperature in a Thin Rod Exchanging Heat through Its Surface
  • 2.23: Distribution of Temperature in a Thin Wire with Losses on Its Surface
  • 2.24: Oscillations of a Finite String with Friction
  • 2.25: Propagation of a Thermal Pulse in a Thin Bar with Insulated Ends
  • 2.26: Forced Oscillations of a Hanging String in a Gravitational Field
  • 2.27: Temperature Equilibrium in a Bar with Heat Sources
  • 2.28: Case Study: String under a Gravitational Field
  • 2.29: String with Oscillations Forced in One of Its Ends