A key aim of the course is building practical skills that can be applied in a wide range of scientific, business and research settings. A range of important biological problems, from areas such as resource management, population dynamics, and public health, drives the study of analytical and numerical techniques for systems of nonlinear ODEs. This course focuses on ordinary differential equations (ODEs) and develops students' skills in the formulation, solution, understanding and interpretation of coupled ODE models. Construct and solve partial differential equations in a variety of real-world modeling contexts including heat diffusion, waves, and vibrating strings.Differential equation models describe a wide range of complex problems in biology, engineering, physical sciences, economics and finance.Use perturbation theory to find approximate solutions to differential equations starting from exact solutions in simpler cases.Employ numerical techniques including Euler’s method and the Runge-Kutta method to estimate solutions to initial value problems.Find the recurrence relation that generates a power series solution for a given differential equation.Compute Laplace transforms and use them to solve differential equations.Construct and solve systems of differential equations in a variety of real-world modeling contexts including predator-prey populations and the motion of a mass on a spring.Extend qualitative techniques and variation of parameters to systems of linear differential equations. ![]() Express higher-order differential equations as first-order systems.Solve homogeneous systems of linear differential equations by computing eigenvalues and eigenvectors.Extend second-order solution techniques to Nth-order linear differential equations.Construct and solve second-order differential equation models in a variety of real-world modeling contexts including oscillators and vibrating systems.Solve instances of the Cauchy-Euler equation.Use variation of parameters as a general technique for finding a particular solution to an inhomogeneous second-order differential equation.Interpret the right-hand side of an inhomogeneous differential equation as a forcing function, and use the method of undetermined coefficients to find particular solutions for various types of forcing functions.Use the characteristic equation in conjunction with the superposition principle to solve homogeneous linear second-order differential equations.Use reduction of order to reduce second-order differential equations to first-order differential equations for which solution techniques are known.Construct and solve first-order differential equation models in a variety of real-world modeling contexts including population growth, temperature cooling, mechanics, and more. ![]()
0 Comments
Leave a Reply. |