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Electrical and Computer Engineering ECE3260 - Science of Sound, Spring 2004 ECE3640 - Signals and Systems, Spring 2006 ECE4660 - Communication Systems I, Spring 2006 ECE5660 - Communication Systems I, Spring 2006 ECE6010 - Stochastic Processes, Spring 2006 Instructional Technology & Learning Sciences INST4010 - Principles and Practices of Technology, Spring 2008 INST5240 - Producing Distance Education Resources, Spring 2005 INST5245 - Interactive Multimedia Production, Summer, 2008 INST5260 - Learn and Apply HTML, Spring 2005 INST5280 - Blogs, Wikis, New Media for Learning, Spring 2006 INST5400 - Computer Applications for Instruction and Training, Spring 2005 INST7150 - Advanced Topics in Learning Object Design and Reuse, Fall 2005 INST7150 - Introduction to Open Education, Fall 2007 INST7150 - Understanding Online Interaction, Spring 2005 INST7870 - Data Visualization Theory & Practice, Fall 2006 INST7870 - Instructional Games, Spring 2005 OER CPOR - Connecting People with Online Resources, Spring 2007 Conversation on Instructional Design EXT CS - CALFNES Spanish, Fall 2004 EXT LM01 - Landscape Management, Overview, Spring 1993 EXT LM02 - Climate and Landscapes, Spring 1993 EXT LM03 - Soils and Landscapes, Spring 1993 EXT LM04 - Plants and Landscapes, Spring 1993 EXT LM05 - Annuals and Perennials, Spring 1993 EXT LM06 - Transplanting, Spring 1993 EXT LM07 - Turf Management, Spring 1993 EXT LM08 - Pruning, Spring 1993 EXT LM09 - Water in Landscapes, Spring 1993 EXT LM10 - Irrigation, Fall 1993 EXT LM11 - Fertilization, Fall 1993 EXT LM12 - Calculating Rates, Fall 1993 EXT LM13 - Weed Control, Fall 1993 EXT LM14 - Landscape Problems, Fall 1993 EXT LM15 - Cost Estimation, Fall 1993 EXT LSM - Lambing and Sheep Management Food Safety, Storage and Allergies |
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Copyright ® 2008 Atlantic International University . All rights reserved.
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Linear Methods of Applied Mathematics
Orthogonal series, boundary-value problems, and integral operators
Evans M. Harrell II and James V. Herod
Orthogonal series, boundary-value problems, and integral operators
Evans M. Harrell II and James V. Herod
© Copyright 1994,1995,1996, 1997, 2000 by Evans M. Harrell II and James V. Herod. All rights reserved.
This is a WWW textbook written by Evans M. Harrell II and James V. Herod, both of Georgia Tech. It is suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations. Students are expected to have completed two years of calculus and an introduction to ordinary differential equations and vector spaces. For recommended 10-week and 15-week syllabuses, read the preface.
This text concentrates on mathematical concepts rather than on details of calculations, which are often done with software, such as Maple or Mathematica. It is not necessary to have experience with Maple or Mathematica in order to read this text, nor is it the goal of this text to teach software, but there are links in the text to Maple worksheets and Mathematica notebooks, which perform calculations and provide some supplementary instructive material. The supplementary material exists both in a "flat" form, which can be read with Netscape, and also in an active form, requiring mathematical software.
If you have access to mathematical software, you may wish to take this opportunity to set up the latest version of Netscape to launch Mathematica or Maple automatically when appropriate.
You are welcome to browse, but if you make more than casual use, such as downloading files or using them as study materials, certain restrictions and fees apply. Before proceeding, please read this copyright notice.
.
Contents
Preface
Diagnostic quiz
Please take this before embarking on a course from this book.
Links to review materials on ordinary differential equations and linear algebra
Also available in an Adobe Acrobat version
The red syllabus and the yellow syllabus continue with Chapter III
The green syllabus continues with Chapter XIII
Also available in an Adobe Acrobat version (without links)
A test at this stage.
Also available in an Adobe Acrobat version (without links)
The red syllabus continues with Chapter VI
The yellow syllabus continues with Chapter XIII
Also available in an Adobe Acrobat version (without links)
Also available in an Adobe Acrobat version (without links)
A test at this stage.
Also available in an Adobe Acrobat version (without links)
- PDEs in space. (includes potential equations)
Also available in an Adobe Acrobat version (without links)
A test at this stage.
End of the red syllabus.
- Geometry and integral operators.
- Solving Y = KY + f.
A test at this stage.
- Ordinary differential operators.
- Finding Green functions for ODEs.
A test at this stage.
- Green functions, Fourier series, and eigenfunctions.
- Partial differential operators - classification and adjoints.
- The free Green function and the method of images
A test at this stage.
- The fundamental solution of the heat equation
- Using conformal mapping to construct Green functions.
- Some advanced topics.
APPENDICES
- Biographical and historical notes.
- Geometry without an Inner Product
- Derivation of the
heat equation
wave equation for the vibrating string
wave equation for electromagnetic waves
- Properties of solutions to potential equations (mean-value theorem and maximum principle)
- Filtering and signal processing.
- Green functions in Rn (a review of matrices)
- Legendre polynomials and spherical harmonics
- Ordinary differential equations (A review as a Maple worksheet)
- Thermal properties of common materials (table)
- Vector calculus (summary)
EXTERNAL LINKS
(We do not maintain these and cannot guarantee their content)
Univ. of Arizona Math 322, which has animations and Maple worksheets
Index and glossary.
A test at this stage.
A test at this stage.
A test at this stage.
- Biographical and historical notes.
- Geometry without an Inner Product
- Derivation of the
heat equation
wave equation for the vibrating string
wave equation for electromagnetic waves - Properties of solutions to potential equations (mean-value theorem and maximum principle)
- Filtering and signal processing.
- Green functions in Rn (a review of matrices)
- Legendre polynomials and spherical harmonics
- Ordinary differential equations (A review as a Maple worksheet)
- Thermal properties of common materials (table)
- Vector calculus (summary)
(We do not maintain these and cannot guarantee their content)
- Univ. of Arizona Math 322, which has animations and Maple worksheets
Index and glossary.
Link to
- the beginning of the Contents
- Evans Harrell's home page
- Jim Herod's home page
- Jim Herod's lecture notes on partial differential equations and the method of characteristics (copyright 1994,1995, James V. Herod). These are not systematically marked for hypertext.
- Mathphysics.com's consulting fees begin at US$90.00 or Euro 100/hour, one hour minimum paid in advance. Click here to make inquiries.
Evans M. Harrell II (send message)
James V. Herod (send message)
Unabridged Version of Sean's Applied Math Book
Download. Latest Build: January 24, 2004
Please note that the unabridged version of the text may not be used by Caltech students in ACM 95/100.
You can download the text in the following formats by saving the link to your computer. The PDF versions are better for viewing on your computer; they are hyperlinked. Get the postscript version if you are going to print the text.
- PDF, (Portable Document Format), suitable for viewing on the computer. This version has a page layout with smaller margins, larger fonts and a lower aspect ratio. 9.7 megabytes.
- PDF This version is in letter format. 8.9 megabytes.
- zipped postscript. 5.8 megabytes.
- zip archive 8.3 megabytes.
- gzip'ed tarball 7.7 megabytes.
Mathematica Notebooks
Some of the exercises in the text are solved in Mathematica notebooks. These exercises are labeled with the name of the notebook. Below is a list of these notebooks. You can download files to your computer and open them in Mathematica. You can also download all the notebooks in a tarball. (I have also written a set of tutorial Mathematica notebooks that I have used in teaching a Mathematica class.)
- Calculus
- Differential Calculus
- Definition of Differentiation, definition.nb
- Rules of Differentiation, rules.nb
- Implicit Differentiation, implicit.nb
- Maxima and Minima, maxima.nb
- Mean Value Theorems, taylor.nb
- L'Hospital's Rule, lhospitals.nb
- Integral Calculus
- Fundamental Integration Formulas, fundamental.nb
- Integration by Parts, parts.nb
- Partial Fractions, partial.nb
- Definite Integrals, definite.nb
- Improper Integrals, improper.nb
- Taylor Series, taylor.nb
- Differential Calculus
- Functions of a Complex Variable
- Series and Convergence
- Series of Constants, constants.nb
- Series and Convergence
- Ordinary Differential Equations
- First Order Differential Equations
- First Order Systems of Differentials Equations
- First Order Systems, systems.nb
- Techniques for Linear Differential Equations
- Constant Coefficient Equations, constant.nb
- Euler Equations, euler.nb
- Inhomogeneous Differential Equations
- Undetermined Coefficients, undetermined.nb
- Variation of Parameters, variation.nb
- Series Solutions of Differential Equations
- Series Solutions, series.nb
- The Laplace Transform
- Laplace Transform, laplace.nb
Status of the Text
- Algebra
- Sets and Functions - Very preliminary.
- Vectors - Finished. An elementary treatment.
- Calculus
- Differential Calculus - Short, but done.
- Integral Calculus - Short, but done.
- Vector Calculus - Very preliminary.
- Functions of a Complex Variable
- Complex Numbers - Done.
- Functions of a Complex Variable - Done.
- Analytic Functions - Done.
- Analytic Continuation - Disorganized.
- Contour Integration and Cauchy's Formula - Done.
- Cauchy's Integral Formula - Done.
- Series and Convergence - Done.
- The Residue Theorem - Done.
- Ordinary Differential Equations
- First Order Differential Equations - Done.
- First Order Systems of Differentials Equations - Preliminary.
- Theory of Linear Ordinary Differential Equations - Done.
- Techniques for Linear Differential Equations - Done.
- Techniques for Nonlinear Differential Equations - Preliminary.
- Transformations and Canonical Forms - Preliminary.
- The Dirac Delta Function - Preliminary.
- Inhomogeneous Differential Equations - Done.
- Difference Equations - Preliminary.
- Series Solutions of Differential Equations - Done.
- Asymptotic Expansions - Preliminary.
- Hilbert Spaces - Very Preliminary.
- Self Adjoint Linear Operators - Very Preliminary.
- Self Adjoint Boundary Value Problems - Very Preliminary.
- Fourier Series - Done.
- Regular Sturm-Liouville Problems - Done.
- Integrals and Convergence - Preliminary.
- The Laplace Transform - Done.
- The Fourier Transform - Done.
- The Gamma Function - Preliminary.
- Bessel Functions - Preliminary.
- Partial Differential Equations - All the chapters are very preliminary.
- Calculus of Variations - No text, just some exercises and solutions.
- Nonlinear Differential Equations - No text, just some exercises and solutions.
http://www.its.caltech.edu/~sean/, at(sean,dot(caltech,edu)) / Last Modified: October 11, 2006
Math 848 Class Notes
Note: These are informal notes which are to be corrected and updatedregularly.
Math 848, Final Examination:
TBA
Prerequisite: Advanced Calculus, Linear Algebra, Analysis, suggested course to be taken in advance or concurrently: Math 828
Suggested additional references: J.Hale, Ordinary Differential Equations, L. Perko, Differential Equations and Dynamical Systems, P. Hartman, Ordinary Differential Equations
- 1. Introduction
- 2. Linear Transformations
- 3. General Properties of Differential Equations
- 4. Existence Uniqueness Theorem
- 5. Dependence of Solutions to Differential Equations onParameters
- 6. Dependence of Solutions to Differential Equations onParameters--Continued
- 7. Autonomous Differential Equations
- 8. Limit Sets
- 9. Two dimensional systems
- 9a Differential Equations on a Two dimensional Torus
- 9b Differential Equations on a Two dimensional Torus--alternate
- 10. Umlaufsatz
- 10a. Degree of Circle Maps
- 10b. Alternate version of Umlaufsatz
- 11. Another index formula
- 11a. Alternate treatment of Section 11
- 12. Linear Differential Equations
- 13. Linear Differential Equations with Constant Coefficients
- 14. Some examples
- Note that the following notes (14a, 14b, 14c, 14d) were taken from other sets of lecture notes, so the page numberings do not have the number 14 in in them. They involve 17 and 18.
- 14a. Further Examples and Properties-a
- 14b. Further Examples and Properties-b
- 14c. Further Examples and Properties-c
- 14d. Further Examples and Properties-d
- 15. Jordan Canonical Form
- 16. The Grobman-Hartman theorems
- 17. Proofs of the Grobman-Hartman theorems
- 18. Proofs of the Grobman-Hartman theorems -Continued
- 19. Hyperbolic Periodic Orbits and Lyapunov Stability
- 20. Hamiltonian Systems in $R^{2n}$
- 21. Hamiltonian Systems and Variational Problems
Exercises
- Exercise Set 1
- Exercise Set 2
- Exercise Set 3
- Exercise Set 4
- Exercise Set 4 supplement
- Some optional exercises on the Fundamental Group
Finite Difference and Spectral Methods
for Ordinary and Partial Differential Equations
Lloyd N. Trefethen
Available online -- see below
This 325-page textbook was written during 1985-1994 and used in graduate courses at MIT and Cornell on the numerical solution of partial differential equations.
The book has not been completed, though half of it got expanded into Spectral Methods in MATLAB. Nevertheless, the part of it that is written is in quite polished form, including many exercises, and is suitable for classroom use (and indeed has been used at quite a few universities). Copies are now available here for use by anyone who wishes. There is no restriction on this use, except that any copies must not alter the original text and must include the author's name.
The files currently online are missing some tables, figures, and text that are not available in PostScript or are in copyright; a list of some of these omissions is available.
Thanks to Darryl Yong of Harvey Mudd College for converting these PostScript files into searchable pdf files.
Front matter. Preface, Table of Contents, etc. (ps,pdf)
Chapter 1. Ordinary differential equations. (ps,pdf)
Chapter 2. Fourier analysis. (ps,pdf)
Chapter 3. Finite difference approximations. (ps,pdf)
Chapter 4. Accuracy, stability and convergence. (ps,pdf)
Chapter 5. Dissipation, dispersion, and group velocity. (ps,pdf)
Chapter 6. Boundary conditions. (ps,pdf)
Chapter 7. Fourier spectral methods. (ps,pdf)
Chapter 8. Chebyshev spectral methods. (ps,pdf)
References. (ps,pdf)
Perhaps a reasonable way to cite this book would be: Lloyd N. Trefethen, Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, unpublished text, 1996, available at http://www.comlab.ox.ac.uk/nick.trefethen/pdetext.html.
Return to L. N. Trefethen homepage
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Table of Contents [11–20 of 30 articles]
- Variational Iteration Decomposition Method for Solving Eighth-Order Boundary Value Problems, Muhammad Aslam Noor and Syed Tauseef Mohyud-Din
Volume 2007 (2007), Article ID 19529, 16 pages - A Note on Wave Equation and Convolutions, Adem Kılıçman and Hassan Eltayeb
Volume 2007 (2007), Article ID 49251, 13 pages - Optimal Control of Mechanical Systems, Vadim Azhmyakov
Volume 2007 (2007), Article ID 18735, 16 pages - Global Existence and Asymptotic Behavior of Solutions for a Class of Nonlinear Degenerate Wave Equations, Yaojun Ye
Volume 2007 (2007), Article ID 19685, 9 pages - Stochastic Finite Element Technique for Stochastic One-Dimension Time-Dependent Differential Equations with Random Coefficients, M. M. Saleh, I. L. El-Kalla, and M. M. Ehab
Volume 2007 (2007), Article ID 48527, 16 pages - Uniform Blow-Up Rates and Asymptotic Estimates of Solutions for Diffusion Systems with Nonlocal Sources, Zhoujin Cui and Zuodong Yang
Volume 2007 (2007), Article ID 87696, 16 pages - Numerical Effectiveness of Models and Methods of Integration of the Equations of Motion of a Car, Marek Szczotka, Szymon Tengler, and Stanislaw Wojciech
Volume 2007 (2007), Article ID 49157, 13 pages - A perturbation-based model for rectifier circuits, Vipin B. Vats and H. Parthasarathy
Volume 2006 (2006), Article ID 32675, 13 pages - Nonlinear elliptic problems with the method of finite volumes, Sanjay Kumar Khattri
Volume 2006 (2006), Article ID 31797, 16 pages - On a similarity solution of MHD boundary layer flow over a moving vertical cylinder, Maryem Amkadni and Adnane Azzouzi
Volume 2006 (2006), Article ID 52765, 9 pages
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