Fractional Differential Equations

EBook Description: This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.

* Solution of First-order ODE`s by Analytical, Graphical and Numerical Methods;
* Linear ODE`s, Especially Second Order with Constant Coefficients;
* Undetermined Coefficients and Variation of Parameters;
* Sinusoidal and Exponential Signals: Oscillations, Damping, Resonance;
* Complex Numbers and Exponentials;
* Fourier Series, Periodic Solutions;
* Delta Functions, Convolution, and Laplace Transform Methods;
* Matrix and First-order Linear Systems: Eigenvalues and Eigenvectors; and
* Non-linear Autonomous Systems: Critical Point Analysis and Phase Plane Diagrams.

Differential Equations with Boundary � Value Problems

Differential Equations with Boundary-Value Problems (7th Edition) strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, �Remarks� boxes, definitions, and group projects. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.

The Differential Equations Tutor

Solving higher order differential equations is challenging for most students simply because the solution methods usually run several pages in length even for the easier problems. The student must identify the type of equation to solve and apply the appropriate solution method, which can lead to valuable lost time on an exam if the wrong solution method is chosen at the outset.

We begin by showing the student real life applications of second order and higher ODEs to provide motivation for the material. Next, we show how to solve elemenary second order ODEs, and show the student that all solutions have a similar form.

Next, we discuss linear independence of solutions and show the students how to use the wronskian test to determine of a set of functions describe the entire solution space of the ODE.

We then get into the core solution techniques which revolve around constant coefficient differential equations. We examine the case where the roots of the characteristic polynomial are real and complex separately, to give the student a good grounding in what to do in either case.

"Stochastic Differential Equations"

differential equations and applications.- D.W. Stroock, S.R.S. Varadhan: Theory of diffusion processes.- G.C. Papanicolaou: Wave propagation and heat conduction in a random medium.- C. Dewitt Morette: A stochastic problem in Physics.- G.S. Goodman: The embedding problem for stochastic matrices.

"Image Processing Based on Partial Differential Equations: Proceedings of the International Conference

This book publishes a collection of original scientific research articles that address the state-of-art in using partial differential equations for image and signal processing. Coverage includes: level set methods for image segmentation and construction, denoising techniques, digital image inpainting, image dejittering, image registration, and fast numerical algorithms for solving these problems.

The Differential Equations Tutor Volume 2 - Higher Order Equations

Solving higher order differential equations is challenging for most students simply because the solution methods usually run several pages in length even for the easier problems. The student must identify the type of equation to solve and apply the appropriate solution method, which can lead to valuable lost time on an exam if the wrong solution method is chosen at the outset.

We begin by showing the student real life applications of second order and higher ODEs to provide motivation for the material. Next, we show how to solve elemenary second order ODEs, and show the student that all solutions have a similar form.

Next, we discuss linear independence of solutions and show the students how to use the wronskian test to determine of a set of functions describe the entire solution space of the ODE.

Mastering Differential Equations The Visual Method

For centuries, differential equations have been the key to unlocking nature's deepest secrets. Over 300 years ago, Isaac Newton invented differential equations to understand the problem of motion, and he developed calculus in order to solve differential equations.
Since then, differential equations have been the essential tool for analyzing the process of change, whether in physics, engineering, biology, or any other field where it's important to predict how something behaves over time.
The pinnacle of a mathematics education, differential equations assume a basic knowledge of calculus, and they have traditionally required the rote memorization of a vast "cookbook" of formulas and specialized tricks needed to find explicit solutions. Even then, most problems involving differential equations had to be simplified, often in unrealistic ways; and a huge number of equations defied solution at all using these techniques.

MathTutor Differential Equations Vol. 1 First Order Equations

Differential equations is used in all branches of engineering and science. In essence, once a student begins to study more complex problems, nature usually obeys a differential equation which means that the equation involves one or more derivatives of the unknown variable.
In other words, a differential equation involves the rate of change of a variable rather than the variable itself. The simplest example of this is F=ma. The "a" is acceleration which is the second derivative of the position of the object. Although differential equations may look simple to solve by just integration, they frequently require complex solution methods with many steps.
This 10 hour DVD course teaches how to solve first order differential equations using fully worked example problems. All intermediate steps are shown along with graphing methods and applications of differential equations in science and engineering.

Mastering Differential Equations:The Visual Method

For centuries, differential equations have been the key to unlocking nature's deepest secrets. Over 300 years ago, Isaac Newton invented differential equations to understand the problem of motion, and he developed calculus in order to solve differential equations.
Since then, differential equations have been the essential tool for analyzing the process of change, whether in physics, engineering, biology, or any other field where it's important to predict how something behaves over time.

The pinnacle of a mathematics education, differential equations assume a basic knowledge of calculus, and they have traditionally required the rote memorization of a vast "cookbook" of formulas and specialized tricks needed to find explicit solutions. Even then, most problems involving differential equations had to be simplified, often in unrealistic ways; and a huge number of equations defied solution at all using these techniques.

But that was before computers revolutionized the field, extending the reach of differential equations into previously unexplored areas and allowing solutions to be approximated and displayed in easy-to-grasp computer graphics. For the first time, a method exists that can start a committed learner on the road to mastering this beautiful application of the ideas and techniques of calculus.

Mastering Differential Equations: The Visual Method takes you on this amazing mathematical journey in 24 intellectually stimulating and visually engaging half-hour lectures taught by a pioneer of the visual approach, Professor Robert L. Devaney of Boston University, coauthor of one of the most widely used textbooks on ordinary differential equations.

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