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Differential equations Course work - Affordable Essay Services - Affordable Essay (Dissertation) Writing Services

Advanced Methods: Differential Equations (MAST90064)

Graduate course work Points: 12.5 Dual Delivery (Parkville)

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This topic develops the mathematical methods of applied mathematics and mathematical physics with a focus on ordinary differential equations. Both analytical and approximate techniques are used to determine solutions of ordinary differential equations. Accurate solutions by localized series expansion techniques of linear ordinary differential equations of second order and storm Liouville limit issues are explored. Special functions are introduced here. Regular and singular fault expansion techniques, asymptotic series solutions, dominant equilibrium and WKB theory are used to determine approximate solutions of linear and non-linear differential equations. Throughout the case, the theory is set in the context of examples of mathematics and mathematical physics used such as nonlinear oscillators, boundary layers and dispersive phenomena.

intended learning results

After completing this topic, students should be able to be:

  • describe how normal differential equation models and associated limit value problems occur in a variety of areas of applied mathematics and mathematical physics;
  • differentiate the role of serial solution methods for differential equations and can construct and use such solutions;
  • Apply the basic concepts of asymptotic analyzes and fault methods, implement these techniques and differentiate their value and restrictions;
  • recognize the basic features of special functions of applied mathematics and mathematical physics and their applications; and
  • develop important basic knowledge to pursue further studies in this discipline and related areas.

Generic Skills

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  • Troubleshooting capabilities: The ability to involve unknown problems and identify relevant solution strategies;
  • Analytical Skills: The ability to create and express logical arguments and to work in abstract or general conditions to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • Time management capabilities: The ability to meet regular deadlines while compelling competing commitments.

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