This 10-minute video lesson shows the Laplace Transform of t^n: L{t^n}. [Differential Equations playlist: Lesson 37 of 45]

This 11-minute video lesson shows how to use the Laplace Transform to solve an equation we already knew how to solve. [Differential Equations playlist: Lesson 32 of 45]

This 11-minute video lesson provides a grab bag of things to know about the Laplace Transform. [Differential Equations playlist: Lesson 34 of 45]

This 9-minute video lesson gives an example of using initial conditions to solve a repeated-roots differential equation .[Differential Equations playlist: Lesson 21 of 45]

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]

This text is an introductory treatment on the junior level for a two-semester electrical engineering course starting from the Coulomb-Lorentz force law on a point charge. The theory is extended by the continuous superposition of solutions from previously developed simpler problems leading to the general integral and differential field laws. Often the same problem is solved by different methods so that the advantages and limitations of each approach becomes clear. Sample problems and their solutions are presented for each new concept with great emphasis placed on classical models of physical phenomena such as polarization, conduction, and magnetization. A large variety of related problems that reinforce the text material are included at the end of each chapter for exercise and homework.

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 course introduces finite element methods for the analysis of solid, structural, fluid, field, and heat transfer problems. Steady-state, transient, and dynamic conditions are considered. Finite element methods and solution procedures for linear and nonlinear analyses are presented using largely physical arguments. The homework and a term project (for graduate students) involve use of the general purpose finite element analysis program ADINA. Applications include finite element analyses, modeling of problems, and interpretation of numerical results.

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.