'Initial value problem' presentation slideshows

Lectures 8, 9 and 10

Lectures 8, 9 and 10. Finite Difference Discretization of Hyperbolic Equations: Linear Problems. First Order Wave Equation. INITION BOUNDARY VALUE PROBLEM (IBVP) Initial Condition: Boundary Conditions:. Solution. First Order Wave Equation. Characteristics. General solution.

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Series-Expansion Methods

Series-Expansion Methods . Agathe Untch e-mail: Agathe.Untch@ecmwf.int (office 011). Acknowledgement This lecture draws heavily on lectures by Mariano Hortal (former Head of the Numerical Aspects Section, ECMWF) and on the excellent textbook

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QCD Critical Points and Associated Soft Modes

QCD Critical Points and Associated Soft Modes. Teiji Kunihiro (Kyoto) . New Frontiers in QCD 2010 --- Exotic Hadron Systems and Dense Matter --- January 18 (Mon.)-March 19 (Fri.), 2010 .

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Spectrum Synthesis and Supernovae

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ENGG2013 Unit 24 Linear DE and Applications

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Laplace Transforms

Laplace Transforms. Math 2306 Dr. Dillon SPSU Mathematics Department. What Are Laplace Transforms?. A Laplace transform is a type of integral transform. Plug one function in. Get another function out. The new function is in a different domain. When. is the Laplace transform of. Write.

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Laplace Transforms

Laplace Transforms. Math 2306 Dr. Dillon SPSU Mathematics Department. What Are Laplace Transforms?. A Laplace transform is a type of integral transform. Plug one function in. Get another function out. The new function is in a different domain. When. is the Laplace transform of. Write.

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Math 104

Math 104. Notes Part 4. Differential Equations. Differential Equations. The most important application of integrals is to the solution of differential equations.

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Ch 9.7: Periodic Solutions and Limit Cycles

Ch 9.7: Periodic Solutions and Limit Cycles. In this section we discuss further the possible existence of periodic solutions of second order autonomous systems x ' = f ( x )

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ALA 20210 On the operational solution of the system of fractional differential equations

ALA 20210 On the operational solution of the system of fractional differential equations. ?ur?ica Taka?i Department of Mathematics and Informatics Faculty of Science, Univer sity of Novi Sad Novi Sad, Serbia djtak@dmi.uns.ac.rs. The Mikusinski operator field.

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Ch 6.4: Differential Equations with Discontinuous Forcing Functions

Ch 6.4: Differential Equations with Discontinuous Forcing Functions . In this section focus on examples of nonhomogeneous initial value problems in which the forcing function is discontinuous. Example 1: Initial Value Problem (1 of 12). Find the solution to the initial value problem

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Examples of Various Formulations of Optimization Problems

Examples of Various Formulations of Optimization Problems. Example 1 (bad formulation).

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Chapter 1: First-Order Differential Equations

Chapter 1: First-Order Differential Equations. 1. Sec 1.1: Differential Equations and Mathematical Models. Definition: Differential Equation.

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Exponential Growth and Decay

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Ch 6.4: Differential Equations with Discontinuous Forcing Functions

Ch 6.4: Differential Equations with Discontinuous Forcing Functions . In this section, we focus on examples of nonhomogeneous initial value problems in which the forcing function is discontinuous. Example 1: Initial Value Problem (1 of 12). Find the solution to the initial value problem

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6.4 Exponential Growth and Decay

6.4 Exponential Growth and Decay. Glacier National Park, Montana Photo by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington.

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Ch 5.3: Series Solutions Near an Ordinary Point, Part II

Ch 5.3: Series Solutions Near an Ordinary Point, Part II. A function p is analytic at x 0 if it has a Taylor series expansion that converges to p in some interval about x 0 The point x 0 is an ordinary point of the equation

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Ch 2.2: Separable Equations

http://bcs.wiley.com/he-bcs/Books?action=resource &bcsId=2026&itemId=047143339X&resourceId=4140. Ch 2.2: Separable Equations. In this section we examine a subclass of linear and nonlinear first order equations. Consider the first order equation We can rewrite this in the form

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Ch 1.2: Solutions of Some Differential Equations

Ch 1.2: Solutions of Some Differential Equations. Recall the free fall and owl/mice differential equations: These equations have the general form y ' = ay - b We can use methods of calculus to solve differential equations of this form. Example 1: Mice and Owls (1 of 3).

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More on Modeling 1.2: Separation of Variables

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