Rationale

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).

Objectives

  • 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 PDF PS
EMT1201 Engineering Mathematics II