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Differential Equations A First Course on ODE and a Brief Introduction to PDE 1st Edition by Shair Ahmad, Antonio Ambrosetti ISBN 3110650037 9783110650037

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Differential Equations A First Course on ODE and a Brief Introduction to PDE 1st Edition Shair Ahmad Digital Instant Download

Author(s): Shair Ahmad, Antonio Ambrosetti
ISBN(s): 9783110650037, 3110650037
Edition: 1
File Details: PDF, 10.29 MB
Year: 2019
Language: english
SKU: EB-11047378 Category: Tags: ,

Differential Equations A First Course on ODE and a Brief Introduction to PDE 1st Edition by Shair Ahmad, Antonio Ambrosetti – Ebook PDF Instant Download/Delivery: 3110650037, 9783110650037
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Product details:

ISBN 10: 3110650037 
ISBN 13: 9783110650037
Author: Shair Ahmad, Antonio Ambrosetti

This book is mainly intended as a textbook for students at the Sophomore-Junior level, majoring in mathematics, engineering, or the sciences in general. The book includes the basic topics in Ordinary Differential Equations, normally taught in an undergraduate class, as linear and nonlinear equations and systems, Bessel functions, Laplace transform, stability, etc. It is written with ample exibility to make it appropriate either as a course stressing applications, or a course stressing rigor and analytical thinking. This book also offers sufficient material for a one-semester graduate course, covering topics such as phase plane analysis, oscillation, Sturm-Liouville equations, Euler-Lagrange equations in Calculus of Variations, first and second order linear PDE in 2D. There are substantial lists of exercises at the ends of chapters. A solutions manual, containing complete and detailed solutions to all the exercises in the book, is available to instructors who adopt the book for teaching their classes.

Differential Equations A First Course on ODE and a Brief Introduction to PDE 1st Table of contents:

Part I: Ordinary Differential Equations (ODEs)

  1. Introduction to Ordinary Differential Equations

    • Definition and Basic Terminology

    • Initial Value Problems and Boundary Value Problems

    • Types of Differential Equations

    • Importance of ODEs in Modeling Real-World Phenomena

  2. First-Order Differential Equations

    • Separable Equations

    • Linear First-Order Equations

    • Exact Equations and Integrating Factors

    • Applications to Population Dynamics, Physics, and Chemistry

  3. Second-Order Linear Differential Equations

    • Homogeneous Equations with Constant Coefficients

    • Non-Homogeneous Equations and the Method of Undetermined Coefficients

    • Variation of Parameters

    • Applications in Mechanical and Electrical Systems

  4. Higher-Order Linear Differential Equations

    • General Theory and Solution Techniques

    • Reduction of Order Method

    • Linear Independence and the Wronskian

    • Applications to Vibrations, Waves, and Heat Transfer

  5. Systems of Ordinary Differential Equations

    • Linear Systems of Equations

    • Eigenvalue and Eigenvector Methods

    • Phase Plane Analysis

    • Stability and Qualitative Behavior of Solutions

    • Applications to Ecology, Economics, and Engineering

  6. Series Solutions of Differential Equations

    • Power Series Methods

    • Frobenius Method

    • Special Functions (Bessel, Legendre, etc.)

    • Applications in Physics and Engineering

  7. Numerical Methods for ODEs

    • Euler’s Method

    • Runge-Kutta Methods

    • Stability and Error Analysis

    • Applications to Computational Science

Part II: Brief Introduction to Partial Differential Equations (PDEs)

  1. Introduction to Partial Differential Equations

    • Definition and Terminology

    • Types of PDEs: Parabolic, Elliptic, and Hyperbolic Equations

    • The Role of Boundary Conditions and Initial Conditions

  2. First-Order Partial Differential Equations

    • Linear and Nonlinear Equations

    • Method of Characteristics

    • Applications to Fluid Dynamics and Traffic Flow

  3. Second-Order Linear Partial Differential Equations

    • Classification of PDEs

    • Heat Equation

    • Wave Equation

    • Laplace and Poisson Equations

    • Separation of Variables

  4. Methods of Solving PDEs

    • Separation of Variables Technique

    • Fourier Series and Fourier Transforms

    • Laplace Transforms

    • Green’s Functions

    • Numerical Methods for PDEs

  5. Applications of PDEs

    • Heat Transfer and Diffusion

    • Wave Propagation

    • Fluid Mechanics

    • Electromagnetism and Potential Theory

Part III: Advanced Topics (Optional)

  1. Stability and Chaos in ODEs

    • Linear Stability Analysis

    • Nonlinear Dynamics and Chaos Theory

    • Bifurcation Theory

  2. Variational Methods and Functional Analysis

    • Euler-Lagrange Equations

    • Rayleigh-Ritz and Galerkin Methods

    • Applications in Mechanics and Optimization

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Tags: Shair Ahmad, Antonio Ambrosetti, Differential Equations, ODE