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Course Search Results
Course Title Details Source Language Relevance
18.014 Calculus with Theory I, Fall 2002 (MIT) Details Massachusetts Institute of Technology English
 
15.414 Financial Management, Summer 2003 (MIT) Details Massachusetts Institute of Technology English
 
2.004 Modeling Dynamics and Control II, Spring 2003 (MIT) Details Massachusetts Institute of Technology English
 
24.962 Advanced Phonology, Spring 2005 (MIT) Details Massachusetts Institute of Technology English
 
11.434J Advanced Topics in Real Estate Finance, Spring 2007 (MIT) Details Massachusetts Institute of Technology English
 
24.901 Language and its Structure I: Phonology, Fall 2002 (MIT) Details Massachusetts Institute of Technology English
 
15.997 Practice of Finance: Advanced Corporate Risk Management, Spring 2009 (MIT) Details Massachusetts Institute of Technology English
 
11.432J Real Estate Capital Markets, Spring 2007 (MIT) Details Massachusetts Institute of Technology English
 
18.156 Differential Analysis, Spring 2004 (MIT) Details Massachusetts Institute of Technology English
 
Cálculo Infinitesimal Details Universidad Politecnica Madrid Spanish
 
6.253 Convex Analysis and Optimization, Spring 2004 (MIT) Details Massachusetts Institute of Technology English
 
16.100 Aerodynamics, Fall 2005 (MIT) Details Massachusetts Institute of Technology English
 
1.061 Transport Processes in the Environment, Fall 2008 (MIT) Details Massachusetts Institute of Technology English
 
2.154 Maneuvering and Control of Surface and Underwater Vehicles (13.49), Fall 2004 (MIT) Details Massachusetts Institute of Technology English
 
Fundamentos Matemáticos I (2009) Details Universidad de Cantabria Spanish
 
Fundamentos Matemáticos (2008) Details Universidad de Cantabria Spanish
 
Capital Markets (NIRI) Details University of California, Irvine English
 
Calculus III Details University of Massachusetts Boston English
 
Calculus I Details University of Massachusetts Boston English
 
HST.525J Tumor Pathophysiology and Transport Phenomena, Fall 2005 (MIT) Details Massachusetts Institute of Technology English
 
16.333 Aircraft Stability and Control, Fall 2004 (MIT) Details Massachusetts Institute of Technology English
 
These: Deroulage du peuplier : effets cultivars et stataions sur la qualite des produits derives Details Paris Tech French
 
18.02 Multivariable Calculus, Fall 2007 (MIT) Details Massachusetts Institute of Technology English
 
Curso Cero de Matemáticas para Estudiantes de Empresariales Details Universidad de Zaragoza Spanish
 
8.512 Theory of Solids II, Spring 2009 (MIT) Details Massachusetts Institute of Technology English
 
16.885J Aircraft Systems Engineering, Fall 2004 (MIT) Details Massachusetts Institute of Technology English
 
Ampliación de Matemáticas II Details Universidad Carlos III de Madrid Spanish
 
Industrias de la lengua Details Universidad Carlos III de Madrid Spanish
 
Introduction to Free/Open-Source Software Details University of Puerto Rico Spanish
 
Inferencia Estadística Details Universidad Icesi English
 
3.60 Symmetry, Structure, and Tensor Properties of Materials, Fall 2005 (MIT) Details Massachusetts Institute of Technology English
 
Economía financiera Details Universidad Carlos III de Madrid Spanish
 
20.102 Macroepidemiology (BE.102), Spring 2005 (MIT) Details Massachusetts Institute of Technology English
 
ANÁLISIS MATEMÁTICO Details Universidad Politecnica de Valencia Spanish
 
12.810 Dynamics of the Atmosphere, Spring 2008 (MIT) Details Massachusetts Institute of Technology English
 
ESD.86 Models, Data and Inference for Socio-Technical Systems, Spring 2007 (MIT) Details Massachusetts Institute of Technology English
 
Geografía General Details Universidad Nacional de Educacion Spanish
 
9.520 Statistical Learning Theory and Applications, Spring 2003 (MIT) Details Massachusetts Institute of Technology English
 
6.801 Machine Vision, Fall 2004 (MIT) Details Massachusetts Institute of Technology English
 
Ampliación de Cálculo Numérico (2009) Details Universidad de Murcia Spanish
 
22.615 MHD Theory of Fusion Systems, Spring 2007 (MIT) Details Massachusetts Institute of Technology English
 
22.921 Nuclear Power Plant Dynamics and Control, January (IAP) 2006 (MIT) Details Massachusetts Institute of Technology English
 
Nuevos materiales, soportes y poéticas pictóricas (2008) Details Universidad de Murcia Spanish
 
9.520 Statistical Learning Theory and Applications, Spring 2006 (MIT) Details Massachusetts Institute of Technology English
 
8.811 Particle Physics II, Fall 2005 (MIT) Details Massachusetts Institute of Technology English
 
SISTEMAS OPERATIVOS - II Details Universidad Politecnica de Valencia Spanish
 
22.103 Microscopic Theory of Transport, Fall 2003 (MIT) Details Massachusetts Institute of Technology English
 
2.081J Plates and Shells, Spring 2007 (MIT) Details Massachusetts Institute of Technology English
 
2.57 Nano-to-Macro Transport Processes, Fall 2004 (MIT) Details Massachusetts Institute of Technology English
 
18.997 Topics in Combinatorial Optimization, Spring 2004 (MIT) Details Massachusetts Institute of Technology English
 
21L.701 Literary Interpretation: Beyond the Limits of the Lyric, Fall 2006 (MIT) Details Massachusetts Institute of Technology English
 
Macroeconomía III (2009) Details Universidad de Cantabria Spanish
 
10.37 Chemical and Biological Reaction Engineering, Spring 2007 (MIT) Details Massachusetts Institute of Technology English
 
24.919 Topics in Linguistics: Creole Languages and Caribbean Identities, Spring 2004 (MIT) Details Massachusetts Institute of Technology English
 
21L.449 End of Nature, Spring 2002 (MIT) Details Massachusetts Institute of Technology English
 
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Materials Science and Engineering

Combustion synthesis of fullerenes and fullerenic nanostructures. Courtesy Vander Sande Lab.


Students, professors, and researchers in the Department of Materials Science and Engineering explore the relationships between structure and properties in all classes of materials including metals, ceramics, electronic materials, and biomaterials. Read more about Materials Science and Engineering at MIT.

  • Lecture notes Lecture notes
  • Projects and examples Projects and examples
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  • Online textbooks Online textbooks
  • Assignments and solutions Assignments and solutions
  • Exams and solutions Exams and solutions
  • Multimedia content Multimedia content
  • Assignments (no solutions) Assignments (no solutions)
  • Exams (no solutions) Exams (no solutions)

Updated within the past 180 days

  Course # Course Title Term
 
Lecture notes
3.00 Thermodynamics of Materials Fall 2002
 
Lecture notesAssignments and solutionsExams and solutionsMultimedia content
3.012 Fundamentals of Materials Science Fall 2005
 
Image GalleriesMultimedia contentAssignments (no solutions)
3.014 Materials Laboratory Fall 2006
 
Selected lecture notesOnline textbooks
3.016 Mathematics for Materials Scientists and Engineers Fall 2005
NEW
  3.021J Introduction to Modeling and Simulation Spring 2008
 
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3.032 Mechanical Behavior of Materials Fall 2007
 
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3.034 Organic & Biomaterials Chemistry Fall 2005
 
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3.042 Materials Project Laboratory Spring 2008
 
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3.044 Materials Processing Spring 2005
 
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3.051J Materials for Biomedical Applications Spring 2006
 
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3.052 Nanomechanics of Materials and Biomaterials Spring 2007
 
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3.053J Molecular, Cellular, and Tissue Biomechanics Fall 2006
 
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3.063 Polymer Physics Spring 2007
 
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3.064 Polymer Engineering Fall 2003
 
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3.080 Economic & Environmental Issues in Materials Selection Fall 2005
 
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3.091 Introduction to Solid State Chemistry Fall 2004
 
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3.093 Information Exploration: Becoming a Savvy Scholar Fall 2006
    3.094 Materials in Human Experience Spring 2004
 
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3.14 Physical Metallurgy Fall 2003
 
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3.15 Electrical, Optical & Magnetic Materials and Devices Fall 2006
 
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3.155J Micro/Nano Processing Technology Fall 2005
    3.172 Inventions and Patents Fall 2005
 
Lecture notesAssignments and solutionsExams and solutionsMultimedia content
3.185 Transport Phenomena in Materials Engineering Fall 2003
    3.986 The Human Past: Introduction to Archaeology Fall 2006
 
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3.987 Human Origins and Evolution Spring 2006
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3.A04 Modern Blacksmithing and Physical Metallurgy Fall 2008
    3.A08 Attraction and Repulsion: The Magic of Magnets Fall 2005
    3.A26 Freshman Seminar: The Nature of Engineering Fall 2005
 
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3.A27 Case Studies in Forensic Metallurgy Fall 2007
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Updated within the past 180 days

  Course # Course Title Term
 
Online textbooksMultimedia content
3.11 Mechanics of Materials Fall 1999
 
Assignments and solutionsExams and solutionsMultimedia content
3.20 Materials at Equilibrium (SMA 5111) Fall 2003
 
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3.205 Thermodynamics and Kinetics of Materials Fall 2006
 
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3.21 Kinetic Processes in Materials Spring 2006
 
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3.22 Mechanical Behavior of Materials Spring 2008
 
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3.225 Electronic and Mechanical Properties of Materials Fall 2007
 
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3.23 Electrical, Optical, and Magnetic Properties of Materials Fall 2007
 
Selected lecture notesMultimedia content
3.320 Atomistic Computer Modeling of Materials (SMA 5107) Spring 2005
 
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3.35 Fracture and Fatigue Fall 2003
 
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3.37 Welding and Joining Processes Fall 2002
 
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3.40J Physical Metallurgy Spring 2003
 
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3.40J Physical Metallurgy Spring 2004
 
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3.43J Integrated Microelectronic Devices Spring 2007
 
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3.45 Magnetic Materials Spring 2004
 
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3.46 Photonic Materials and Devices Spring 2006
 
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3.53 Electrochemical Processing of Materials Spring 2001
 
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3.56 Engineering Systems Analysis for Design Fall 2008
 
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3.560J Systems Perspectives on Industrial Ecology Spring 2006
 
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3.564J Sustainable Energy Spring 2005
 
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3.577 Engineering Risk-Benefit Analysis Spring 2007
 
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3.60 Symmetry, Structure, and Tensor Properties of Materials Fall 2005
    3.80J Proseminar in Manufacturing Fall 2005
 
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3.83J System Optimization and Analysis for Manufacturing Summer 2003
 
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3.91 Mechanical Behavior of Plastics Spring 2007
 
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3.961J Design of Medical Devices and Implants Spring 2006
 
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3.962J Molecular Principles of Biomaterials Spring 2006
 
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3.96J Biomaterials-Tissue Interactions (BE.441) Fall 2003
 
Selected lecture notes
3.97J Cell-Matrix Mechanics Spring 2004
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Mathematics

Surprising geometry emerges in the study of fluid jets. In this image, a vertical jet is deflected into a horizontal sheet by a horizontal impactor. At the sheet's edge, fluid flows outward along bounding rims that collide to create fluid chains. (Photo courtesty A.E. Hasha and J.W.M. Bush.)


An undergraduate degree in mathematics provides an excellent basis for graduate work in mathematics or computer science, or for employment in such mathematics-related fields as systems analysis, operations research, or actuarial science. Read more about Mathematics at MIT.

  • Lecture notes Lecture notes
  • Projects and examples Projects and examples
  • Image Galleries Image Galleries
  • Selected lecture notes Selected lecture notes
  • Projects (no examples) Projects (no examples)
  • Online textbooks Online textbooks
  • Assignments and solutions Assignments and solutions
  • Exams and solutions Exams and solutions
  • Multimedia content Multimedia content
  • Assignments (no solutions) Assignments (no solutions)
  • Exams (no solutions) Exams (no solutions)

Updated within the past 180 days

  Course # Course Title Term
 
Lecture notesAssignments and solutionsExams and solutions
18.01 Single Variable Calculus Fall 2005
 
Lecture notesExams and solutionsMultimedia contentAssignments (no solutions)
18.01 Single Variable Calculus Fall 2006
 
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18.013A Calculus with Applications Spring 2005
 
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18.014 Calculus with Theory I Fall 2002
 
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18.02 Multivariable Calculus Spring 2006
 
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18.02 Multivariable Calculus Fall 2007
 
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18.022 Calculus Fall 2005
 
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18.024 Calculus with Theory II Spring 2003
 
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18.03 Differential Equations Spring 2006
 
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18.034 Honors Differential Equations Spring 2004
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18.034 Honors Differential Equations Spring 2009
 
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18.04 Complex Variables with Applications Fall 1999
 
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18.04 Complex Variables with Applications Fall 2003
 
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18.05 Introduction to Probability and Statistics Spring 2005
 
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18.06 Linear Algebra Spring 2005
 
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18.062J Mathematics for Computer Science (SMA 5512) Fall 2002
 
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18.062J Mathematics for Computer Science Fall 2005
 
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18.062J Mathematics for Computer Science Spring 2005
 
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18.06CI Linear Algebra - Communications Intensive Spring 2004
 
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18.091 Mathematical Exposition Spring 2005
 
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18.098 Street-Fighting Mathematics January (IAP) 2008
    18.100A Analysis I Fall 2007
 
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18.100B Analysis I Fall 2006
 
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18.100C Analysis I Spring 2006
 
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18.101 Analysis II Fall 2005
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18.102 Introduction to Functional Analysis Spring 2009
 
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18.103 Fourier Analysis - Theory and Applications Spring 2004
    18.104 Seminar in Analysis: Applications to Number Theory Fall 2006
 
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18.112 Functions of a Complex Variable Fall 2008
 
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18.152 Introduction to Partial Differential Equations Fall 2004
 
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18.152 Introduction to Partial Differential Equations Fall 2005
 
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18.238 Geometry and Quantum Field Theory Fall 2002
 
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18.303 Linear Partial Differential Equations Fall 2006
 
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18.304 Undergraduate Seminar in Discrete Mathematics Spring 2006
 
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18.310C Principles of Applied Mathematics Fall 2007
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18.311 Principles of Applied Mathematics Spring 2009
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18.312 Algebraic Combinatorics Spring 2009
 
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18.314 Combinatorial Analysis Fall 2005
 
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18.330 Introduction to Numerical Analysis Spring 2004
 
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18.337J Applied Parallel Computing (SMA 5505) Spring 2005
 
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18.353J Nonlinear Dynamics I: Chaos Fall 2006
NEW
  18.361J Introduction to Modeling and Simulation Spring 2008
 
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18.400J Automata, Computability, and Complexity Spring 2005
 
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18.410J Introduction to Algorithms (SMA 5503) Fall 2005
 
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18.413 Error-Correcting Codes Laboratory Spring 2004
 
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18.433 Combinatorial Optimization Fall 2003
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18.440 Probability and Random Variables Spring 2009
 
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18.443 Statistics for Applications Fall 2003
 
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18.443 Statistics for Applications Fall 2006
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18.443 Statistics for Applications Spring 2009
 
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18.700 Linear Algebra Fall 2005
 
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18.701 Algebra I Fall 2007
 
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18.702 Algebra II Spring 2008
 
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18.704 Seminar in Algebra and Number Theory: Rational Points on Elliptic Curves Fall 2004
    18.704 Seminar in Algebra and Number Theory: Computational Commutative Algebra and Algebraic Geometry Fall 2008
 
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18.712 Introduction to Representation Theory Fall 2008
 
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18.781 Theory of Numbers Spring 2003
 
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18.901 Introduction to Topology Fall 2004
 
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18.904 Seminar in Topology Fall 2005
 
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18.950 Differential Geometry Fall 2008
 
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18.994 Seminar in Geometry Fall 2004
 
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18.S34 Problem Solving Seminar Fall 2007
    18.S66 The Art of Counting Spring 2003
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Updated within the past 180 days

  Course # Course Title Term
 
Lecture notesAssignments and solutions
18.075 Advanced Calculus for Engineers Fall 2004
 
Assignments and solutionsExams and solutionsMultimedia content
18.085 Computational Science and Engineering I Fall 2008
 
Projects and examplesMultimedia content
18.086 Mathematical Methods for Engineers II Spring 2006
 
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18.094J Teaching College-Level Science Spring 2006
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18.094J Teaching College-Level Science and Engineering Spring 2009
 
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18.117 Topics in Several Complex Variables Spring 2005
 
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18.125 Measure and Integration Fall 2003
 
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18.155 Differential Analysis Fall 2004
 
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18.156 Differential Analysis Spring 2004
 
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18.175 Theory of Probability Fall 2008
 
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18.305 Advanced Analytic Methods in Science and Engineering Fall 2004
NEW
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18.306 Advanced Partial Differential Equations with Applications Fall 2009
    18.307 Integral Equations Spring 2006
 
Lecture notes
18.315 Combinatorial Theory: Hyperplane Arrangements Fall 2004
    18.315 Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics Spring 2005
 
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18.318 Topics in Algebraic Combinatorics Spring 2006
    18.319 Geometric Combinatorics Fall 2005
 
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18.327 Wavelets, Filter Banks and Applications Spring 2003
 
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18.335J Introduction to Numerical Methods Fall 2004
 
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18.335J Introduction to Numerical Methods Fall 2006
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18.336 Numerical Methods for Partial Differential Equations Spring 2009
 
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18.338J Infinite Random Matrix Theory Fall 2004
 
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18.366 Random Walks and Diffusion Fall 2006
 
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18.369 Mathematical Methods in Nanophotonics Spring 2008
 
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18.376J Wave Propagation Fall 2006
 
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18.377J Nonlinear Dynamics and Waves Spring 2007
 
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18.385J Nonlinear Dynamics and Chaos Fall 2004
 
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18.404J Theory of Computation Fall 2006
 
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18.405J Advanced Complexity Theory Fall 2001
 
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18.409 Behavior of Algorithms Spring 2002
NEW
  18.409 Topics in Theoretical Computer Science: An Algorithmist's Toolkit Fall 2007
    18.415J Advanced Algorithms Fall 2005
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  18.415J Advanced Algorithms Fall 2008
 
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18.416J Randomized Algorithms Fall 2002
 
Projects and examplesSelected lecture notes
18.417 Introduction to Computational Molecular Biology Fall 2004
 
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18.426J Advanced Topics in Cryptography Spring 2003
 
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18.435J Quantum Computation Fall 2003
 
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18.437J Distributed Algorithms Fall 2005
 
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18.465 Topics in Statistics: Nonparametrics and Robustness Spring 2005
 
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18.465 Topics in Statistics: Statistical Learning Theory Spring 2007
 
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18.466 Mathematical Statistics Spring 2003
 
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18.705 Commutative Algebra Fall 2008
 
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18.725 Algebraic Geometry Fall 2003
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18.726 Algebraic Geometry Spring 2009
 
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18.727 Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces Spring 2006
 
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18.727 Topics in Algebraic Geometry: Algebraic Surfaces Spring 2008
 
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18.755 Introduction to Lie Groups Fall 2004
 
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18.785 Analytic Number Theory Spring 2007
 
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18.786 Topics in Algebraic Number Theory Spring 2006
 
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18.905 Algebraic Topology Fall 2006
 
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18.906 Algebraic Topology II Spring 2006
 
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18.917 Topics in Algebraic Topology: The Sullivan Conjecture Fall 2007
 
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18.965 Geometry of Manifolds Fall 2004
 
Lecture notesAssignments and solutions
18.966 Geometry of Manifolds Spring 2007
 
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18.969 Topics in Geometry: Dirac Geometry Fall 2006
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18.969 Topics in Geometry: Mirror Symmetry Spring 2009
 
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18.996 Topics in Theoretical Computer Science : Internet Research Problems Spring 2002
 
Projects and examplesSelected lecture notes
18.996 Random Matrix Theory and Its Applications Spring 2004
 
Lecture notes
18.996A Simplicity Theory Spring 2004
 
Lecture notes
18.997 Topics in Combinatorial Optimization Spring 2004
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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

 

 

© 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


  1. Linearity

       Also available in an Adobe Acrobat version


       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)


       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)


       Also available in an Adobe Acrobat version (without links)


       Also available in an Adobe Acrobat version (without links)


      A test at this stage.

       End of the red syllabus.

Link to


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.
You can also download the source, (the LaTeX and graphics files). There is a makefile for compiling the sources. Feel free to cut and paste the sources to make documents that suit your needs. I have a users guide that describes how to use the source of the text.

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.)

 

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


 



 

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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