This 12-minute video lesson looks at what happens when the characteristic equation only has one repeated root. [Differential Equations playlist: Lesson 20 of 45]

This 12-minute video lesson introduces separable differential equations. [Differential Equations playlist: Lesson 2 of 45]

This 14-minute video lesson explains how the product of the transforms of two functions relates to their convolution. [Differential Equations playlist: Lesson 44 of 45]

This 10-minute video lesson looks at using the method of undetermined coefficients to solve nonhomogeneous linear differential equations. [Differential Equations playlist: Lesson 22 of 45]

This 11-minute video lesson gives another example using undetermined coefficients. [Differential Equations playlist: Lesson 23 of 45]

This 8-minute video lesson gives another example where the nonhomogeneous part is a polynomial. [Differential Equations playlist: Lesson 24 of 45]

This 6-minute video lesson concludes the series on undetermined coefficients by putting it all together. [Differential Equations playlist: Lesson 25 of 45]

This 12-minute video lesson shows how to use the convolution Theorem to solve an initial value problem. [Differential Equations playlist: Lesson 45 of 45]

This 19-minute video lesson shows how to solve a non-homogeneous differential equation using the Laplace Transform. [Differential Equations playlist: Lesson 35 of 45]

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

This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations.

This subject provides an introduction to fluid mechanics. Students are introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of fluids and learn how to solve a variety of problems of interest to civil and environmental engineers. While there is a chance to put skills from calculus and differential equations to use in this subject, the emphasis is on physical understanding of why a fluid behaves the way it does. The aim is to make the students think as a fluid. In addition to relating a working knowledge of fluid mechanics, the subject prepares students for higher-level subjects in fluid dynamics.

This half-semester course introduces computational methods for solving physical problems, especially in nuclear applications. The course covers ordinary and partial differential equations for particle orbit, and fluid, field, and particle conservation problems; their representation and solution by finite difference numerical approximations; iterative matrix inversion methods; stability, convergence, accuracy and statistics; and particle representations of Boltzmann’s equation and methods of solution such as Monte-Carlo and particle-in-cell techniques.

This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable.

It is written in an informal, conversational style with a large number of interesting examples and exercises, so that a student learns to write proofs while working on engaging problems.

Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The series is divided into three sections:
Introduction

Why Professor Strang created these videos
How to use the materials

Highlights of Calculus

Five videos reviewing the key topics and ideas of calculus
Applications to real-life situations and problems
Additional summary slides and practice problems

Derivatives

Twelve videos focused on differential calculus
More applications to real-life situations and problems
Additional summary slides and practice problems

About the Instructor
Professor Gilbert Strang is a renowned mathematics professor who has taught at MIT since 1962. Read more about Prof. Strang.
Acknowledgements
Special thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.
The video editing was funded by the Lord Foundation of Massachusetts.

This workbook is primarily for students taking a first-year single variable integral calculus course. Topics covered include integration, techniques of integration, differential equations, and infinite series. The book is divided into two parts, with the first part featuring a diverse set of problems with some practical applications. The second part includes the solutions (each problem has a very detailed solution). Summaries of concepts are also included to make the workbook self-contained. OER Description: This problem bank was developed to support undergraduate lower-division students in integral calculus. Using practice problems with detailed solutions, solution prompts, examples, and concept summaries, this open educational resource supports students in building the problem-solving skills needed to master calculus.

This course introduces students to methods and background needed for the conceptual design of continuously operating chemical plants. Particular attention is paid to the use of process modeling tools such as Aspen that are used in industry and to problems of current interest. Each student team is assigned to evaluate and design a different technology and prepare a final design report.
For spring 2006, the theme of the course is to design technologies for lowering the emissions of climatically active gases from processes that use coal as the primary fuel.

The laws of physics are generally written down as differential equations. Therefore, all of science and engineering use differential equations to some degree. Understanding differential equations is essential to understanding almost anything you will study in your science and engineering classes. You can think of mathematics as the language of science, and differential equations are one of the most important parts of this language as far as science and engineering are concerned. As an analogy, suppose all your classes from now on were given in Swahili. It would be important to first learn Swahili, or you would have a very tough time getting a good grade in your classes.

This course introduces quantitative approaches to understanding brain and cognitive functions. Topics include mathematical description of neurons, the response of neurons to sensory stimuli, simple neuronal networks, statistical inference and decision making. It also covers foundational quantitative tools of data analysis in neuroscience: correlation, convolution, spectral analysis, principal components analysis, and mathematical concepts including simple differential equations and linear algebra.

This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations and direct and iterative methods in linear algebra.