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Differential equations occupy a central role in mathematics, as it enables us to describe a variety of real-world systems. The module aims to emphasize the importance of theory and applications of differential equations.
The module starts with the resumption of a part of the material from the first year module on differential equations, which draw attention to limiting value problems and also to equations with a source period. See you then how to express a general periodic function with regard to the Fourier series of sinus and cosine functions.
The second section of the module introduces some of the basic concepts of partial differential equations (PDES). It is shown how PDEs can be used to model situations in a variety of situations, including biology, finance and applied mathematics. The three important classes of the second order PDE suitable for modeling various types of phenomena are introduced, and the corresponding boundary conditions for each of these are taken into account. The technique of separation of variables is used to reduce the problem to solve the type of ordinary differential equations seen at the beginning of the module, and the general solution with Fourier series writes. During the entire module, it is a strong focus on problem solving and examples.
Requirements (math1056 or math1059 and math1060) and math2039 or (math1006 and math1007)
After successfully completing this module, you can demonstrate knowledge and understanding of:
.
After successfully completing this module, you can:
After successfully completing this module, you can:
Material Revision of material from the variation of parameters, green functions, limit issues,
Eigenvalues ??and ienfunctions,
Orthogonality of own functions
odd and even functions, half-range series,
Introduction to PDE's
PDE type of PDE: Hyperbolic, parabolic and elliptical and appropriate boundary conditions
Examples: Shaft Equations, Diffusion in Physical and Biological Systems, Black-Scholes Equation, Finance Applications, Potential Theory Applications in Biology and Physics.
Separation of variables
Separation of variables
Applications on diffusion problems in finance and biology
2-dim: harmonious functions
3-dim: basic solution
Definition and basic theory
Examples of transformations
transformations of derivatives
Applications to Ode and Systems
Applications to PDE's
Lectures, Operations, Private Study
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For example, we assess them if they do not meet the criteria to pass this module.
Tags: service, essay, course, work, excellent, equations, differential
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