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Differential Equations Vol. 1 First Order Equations
n 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
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.
Modern Aspects of the Theory of Partial Differential Equations
The book provides a quick overview of a wide range of active research areas in partial differential equations. The book can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions from authors from a large variety of countries on different aspects of partial differential equations, such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches.
Partial Differential Equations II
The book contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.
Partial Differential Equations II: Elements of the Modern Theory, Equations With Constant Coefficients (Encyclopaedia of Mathematical Sciences)
The book contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.
Fractional Differential Equations
This book is a landmark title in the continuous move from integer to noninteger in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integerorder 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 fractionalorder 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.
MIT Open Courseware Differential Equations
* Solution of Firstorder 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 Firstorder Linear Systems: Eigenvalues and Eigenvectors; and * Nonlinear Autonomous Systems: Critical Point Analysis and Phase Plane Diagrams.
Differential Equations with Boundary – Value Problems
Differential Equations with BoundaryValue 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 boundaryvalue 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.
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