Course ID: Computational Methods for Differential Equations An introduction to numerical methods for ordinary and partial differential equations. Ordinary differential equations: multistep and Runge-Kutta methods; stability and convergence; systems and stiffness; boundary value problems. Partial differential equations: finite difference methods for elliptic, hyperbolic and parabolic equations; stability and convergence. The course focuses on introducing widely used methods and highlights applications in the natural sciences, the health sciences, engineering and finance.
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Three hundred and fifty years ago, Isaac Newton wrote "it is useful to solve differential equations. Can you imagine what his reaction would be to the present widespread use of differential equations, with applications ranging from the space shuttle guidance system to epidemic models and neural networks? The essential idea is that, for many physical systems, one can, subject to suitable idealizations, formulate a differential equation to describe how the system changes in time.
Understanding the solutions of the differential equation is then of paramount interest. The course AM will introduce you to this fascinating area in the Mathematical Sciences. Brief description: The course introduces the standard elementary methods for solving differential equations, including use of the Laplace transform, and gives a variety of applications in the sciences and in engineering.
The mathematics used is primarily single variable calculus, with some dependence on linear algebra. AM will benefit students who are interested in Scientific Computation e. CS , Numeric Computation for Dynamic Simulation , since differential equations form the basis for many mathematical models that have to be investigated using computers.
AM will benefit students who are interested in Actuarial Science or in the Mathematics of Finance e. AM counts as a credit for all programs in the Math Faculty, and is also open to students in other faculties. The course has been designed for students who want a one-course introduction to the world of differential equations in order to broaden their education in the mathematical sciences. From a mathematical point of view, the subject is primarily "Applied Calculus".
AM is thus the ideal course for students who wish to consolidate their understanding of single variable calculus while applying it to problems in the sciences and engineering.
AMATH 250 - Introduction to Differential Equations
AMATH 250: Introduction to Differential Equations