Differential EquationsLaajuus (3 ECTS)

Objective

The student is able to classify differential equations. The student can solve linear differential equations with constant coefficients. Given the direction field of the differential equation, the student is able to sketch solutions. The student can use mathematical programs when solving differential equations. The student is able to linearize a differential equation and estimate the effect of linearization to the solution. The student is able to choose a suitable step for discretization and convert a differential equation into the corresponding difference equation. The student is able to solve the difference equation and estimate the difference between the solutions of the original differential equation and the corresponding difference equation.

Content

The concepts of the differential equation and of its solution. Techniques to solve simple differential equations; the main emphasis is on linear differential equations with constant coefficients. Initial value problems. Mathematical programs and numerical solutions of differential equations. Linearization of a single differential equation and a pair of differential equations. Discretization of a differential equation. Matrix exponential function. The system of differential equations in state-space representation and the form of the solution.

The student is aware of different types of differential equations and different methods, characteristic to each type, to solve these equations. The student understands the connection of basic numerical methods and the information he or she sees in the direction field of a differential equation. The student knows that linearization and discretization change the values of the solution of a differential equation.

Qualifications

Expressions and equations, Systems of equations and matrices, Functions with an introduction to differentiation, Differential and integral calculus and Laplace Transforms