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ebook
"Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student's place, and have chosen to err on the side of too much detail rather than not enough. An elementary text can't be better than its exercises. This text includes 2041 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and defonitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 299 completely worked out examples. Where appropriate, concepts and results are depicted in 188 figures."BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations Textbooks
 Resource Type:
 ebook

Video
This video playlist covers the topic of: 1. PDE 1  Introduction 2.PDE 2  Three fundamental examples 3.PDE 3  Transport equation: derivation 4.PDE 4  Transport equation: general solution 5. PDE 5  Method of characteristics 6. PDE 6  Transport with decay and nonlinear transport 7.PDE 7  Wave equation: intuition 8.PDE 8  Wave equation: derivation 9.PDE 9  Wave equation: general solution 10.PDE 10  Wave equation: d'Alembert's formula 11.PDE 11  Wave equation: d'Alembert examples 12.PDE 12  Wave equation: characteristics 13.PDE 13  Wave equation: separation of variables 14.FA 1  Fourier series introduction 15.FA 2  Computing Fourier series 16.PDE  Heat equation: intuition 17.PDE  Finite differences: introduction
 Course related:
 AMA3723 Further Mathematical Methods for Finance
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations Partial
 Resource Type:
 Video

ebook
This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take. This book consists of 10 chapters, and the course is 12 weeks long. Each chapter is covered in a week, and in the remaining two weeks I summarize the entire course, answer lots of questions, and prepare the students for the exam. I do not cover the material in the appendices in the lectures. Some of it is basic material that the students have already seen that I include for completeness and other topics are "tasters" for more advanced material that students will encounter in later courses or in their project work. Students are very curious about the notion of chaos, and I have included some material in an appendix on that concept. The focus in that appendix is only to connect it with ideas that have been developed in this course related to ODEs and to prepare them for more advanced courses in dynamical systems and ergodic theory that are available in their third and fourth years.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations Textbooks Differential equations Partial
 Resource Type:
 ebook

ebook
A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. This free online book (ebook in webspeak) should be usable as a standalone textbook or as a companion to a course using another book such as Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling or Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (section correspondence to these two is given). I developed and used these notes to teach Math 286/285 at the University of Illinois at UrbanaChampaign Sample Dirichlet problem solution (one is a 4dayaweek, the other a 3dayaweek semesterlong course). I have also taught Math 20D at University of California, San Diego with these notes (a 3dayaweek quarterlong course). There is enough material to run a 2quarter course, and even perhaps a two semester course depending on lecturer speed.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations Textbooks Boundary value problems
 Resource Type:
 ebook

ebook
Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student's place, and have chosen to err on the side of too much detail rather than not enough. An elementary text can't be better than its exercises. This text includes 1695 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and definitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 250 completely worked out examples. Where appropriate, concepts and results are depicted in 144 figures. Although I believe that the computer is an immensely valuable tool for learning, doing, and writing mathematics, the selection and treatment of topics in this text reflects my pedagogical orientation along traditional lines. However, I have incorporated what I believe to be the best use of modern technology, so you can select the level of technology that you want to include in your course. The text includes 336 exercises – identified by the symbols C and C/G – that call for graphics or computation and graphics. There are also 73 laboratory exercises – identified by L – that require extensive use of technology. In addition, several sections include informal advice on the use of technology. If you prefer not to emphasize technology, simply ignore these exercises and the advice.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Textbooks Differential equations Partial Boundary value problems
 Resource Type:
 ebook

Courseware
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations
 Resource Type:
 Courseware