EMT1201 Engineering Mathematics II introduced Differential Equation and Solution Techniques for ODEs with Exact Solutions in terms of Elementary Functions (Algebraic, Trigonometric, Exponential, Logarithmic and Hyperbolic Functions) and EMT2101 Engineering Mathematics III Introduced the Power Series Solutions to ODEs, it was appreciated that the analysis of Engineering Systems containing lumped parameters often leads to ODEs in which time is the only independent variable. However, the assumption that all masses exit as conceptualized mass points; that all springs are weightless; or that elements of an electric circuit are concentrated in idea resistors, capacitors, and inductors, rather than continuously distributed, is frequently not sufficiently accurate. In such cases, a more realistic approach must take into account the fact that the independent variables depend not only on time but also on one or more space variables. With more than one independent variable manifested, the formulation of such problems leads to Partial, rather than Ordinary, Differential Equations. This course introduces the Course Participant to the Concept of Partial Differential Equations (PDEs).
- An important emphasis of the course is to develop problem solving skills and proof skills by working on specific problems in which it is natural to look at special or simpler cases in order to try to discover patterns. An integral part of the process of mathematical thinking is to wander into blind alleys, sometimes being frustrated, before ultimately obtaining a solution or proof. In this process mathematical scientists often work together with colleagues, and this group work and sharing of ideas often adds great value to a mathematical investigation.
- A major goal of the course is to give a balanced introductory treatment of the area of PDE so that a student appreciates the power of PDE modeling; and is aware of major techniques for their solution. The focus of the course is on analytical techniques for the classical linear PDE of physics and engineering (heat, wave and Laplace equations), and their frequent occurrence in applications.
|Attachment Name||Attachment Type|
|EMT3202 Partial Differential Equations||DOC||PS|