Calculus Basic Partial Differential Equations by D. Bleecker and G. Csordas

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"Basic Partial Differential Equations" by David Bleecker and George Csordas is a comprehensive introductory text that covers essential topics in PDEs, making it accessible for beginners. The book begins with a review of ordinary differential equations and progresses to generalities about PDEs, including first-order linear PDEs and their applications. Key sections include detailed discussions on the heat equation, wave equation, and Laplace's equation, emphasizing derivations, uniqueness, and boundary conditions. The text also introduces Fourier series and transforms, providing foundational knowledge for solving PDEs. Numerical methods are briefly covered, offering insights into approximations and error considerations. The book is recommended as a secondary textbook for those new to the subject, praised for its clarity and structured approach.

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Table of Contents:
Code:
[LIST]
[*] Preface
[*] Review and Introduction
[LIST]
[*] A Review of Ordinary Differential Equations
[*] Generalities about PDEs
[*] General Solutions and Elementary Techniques
[/LIST]
[*] First-Order PDEs
[LIST]
[*] First-Order Linear PDEs (Constant Coefficients)
[*] Variable Coefficients
[*] Higher Dimensions, Quasi-linearity, Applications
[*] Supplement on General Nonlinear First-Order PDEs (Optional
[/LIST]
[*] The Heat Equation
[LIST]
[*] Derivation of the Heat Equation and Solutions of the Standard Initial/Boundary-Value Problems
[*] Uniqueness and the Maximum Principle
[*] Time-Independent Boundary Conditions
[*] Time-Dependent Boundary Conditions and Duhamel's Principle for Inhomogeneous Heat Equations
[/LIST]
[*] Fourier Series and Sturm-Liouville Theory
[LIST]
[*] Orthogonality and the Definition of Fourier Series
[*] Convergence Theorems for Fourier Series
[*] Sine and Cosine Series and Applications
[*] Sturm-Liouville Theory
[/LIST]
[*] The Wave Equation
[LIST]
[*] The Wave Equation - Derivation and Uniqueness
[*] D'Alambert's Solution of Wave Problems
[*] Other Boundary Conditions and Inhomogeneous Wave Equations
[/LIST]
[*] Laplace's Equation
[LIST]
[*] General Orientation
[*] The Dirichlet Problem for a Rectangle
[*] The Dirichlet Problem for Annuli and Disks
[*] The Maximum Principle and Uniqueness for the Dirichlet Problem
[*] Complex Variable Theory with Applications
[/LIST]
[*] Fourier Transforms
[LIST]
[*] Complex Fourier Series
[*] Basic Properties of Fourier Transforms
[*] The Inversion Theorem and Parseval's Equality
[*] Fourier Transform Methods for PDEs
[*] Applications to Problems on Finite and Semi-Finite Intervals
[/LIST]
[*] Numerical Solutions of PDEs - An Introduction
[LIST]
[*] The O Symbol and Approximations of Derivatives
[*] The Explicit Difference Method and the Heat Equation
[*] Difference Equations and Round-off Errors
[*] An Overview of Some Other Numerical Methods for PDEs (Optional)
[/LIST]
[*] PDEs in Higher Dimensions
[LIST]
[*] Higher-Dimensional PDEs - Rectangular Coordinates
[*] The Eigenfunction Viewpoint
[*] PDEs in Spherical Coordinates
[*] Spherical Harmonics, Laplace Series and Applications
[*] Special Functions and Applications
[*] Solving PDEs on Manifolds
[/LIST]
[*] Appendix
[LIST]
[*] The Classification Theorem
[*] Fubini's Theorem
[*] Leibniz's Rule
[*] The Maximum/Minimum Theorem
[*] A Table of Fourier Transforms
[*] Bessel Functions
[/LIST]
[*] References
[*] Selected Answers
[*] Index of Notation
[*] Notation
[/LIST]
 
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I've tried to use many PDE books over the years but have found this intro book very accessible. It's a nice read, not too complicated, not too many proof, and works very well for an intro course. It goes over first orders briefly, then second orders (of two varables) in detail. It then briefly introduces the student to PDE of more than three variables, and then presents a very nice section on numerical methods.

I highly recommend this text as a secondary textbook for anyone just starting with PDEs.
 
The book is fascinating. If your education includes a typical math degree curriculum, with Lebesgue integration, functional analysis, etc, it teaches QFT with only a passing acquaintance of ordinary QM you would get at HS. However, I would read Lenny Susskind's book on QM first. Purchased a copy straight away, but it will not arrive until the end of December; however, Scribd has a PDF I am now studying. The first part introduces distribution theory (and other related concepts), which...
I've gone through the Standard turbulence textbooks such as Pope's Turbulent Flows and Wilcox' Turbulent modelling for CFD which mostly Covers RANS and the closure models. I want to jump more into DNS but most of the work i've been able to come across is too "practical" and not much explanation of the theory behind it. I wonder if there is a book that takes a theoretical approach to Turbulence starting from the full Navier Stokes Equations and developing from there, instead of jumping from...

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