Differential Equations, Modeling and SimulationLaajuus (3 ECTS)

Objective

The student can explain what is meant by a solution of a differential equation.

The student recognizes in what kinds of problems differential equations are needed, and can interpret results obtained using mathematical modeling and simulation using differential equations.

The student can list different ways of solving differential equations, and recognizes the most common applications of differential equations in environmental engineering.

The student is able to classify and solve systems of equations in environmental engineering applications using numerical mathematical software.

The student can solve analytically separable and linear differential equations.

Content

1. Solution of a differential equation.

2. Classification of differential equations.

3. Solving separable differential equations.

4. Solving linear differential equations.

5. Solving systems of differential equations numerically (Excel and Matlab/FreeMat).

6. Applications of systems of differential equations in environmental engineering.

7. Graphical visualization of solutions of differential equations.

8. Estimating parameters of systems of non-linear differential equations.

9. Computer aided mathematics.

Qualifications

Equations and matrices
Vectors and Analytical Geometry
Differential and Integral Calculus

Assessment criteria, satisfactory (1)

1. The student is can explain what is meant by a solution of an ordinary differential equation.

2. The student is able to distinguish between linear and nonlinear differential equations.

3. The student is able solve the simplest separable differential equations.

4. The student can solve linear homogenous differential equations.

5. The student can apply Euler’s method in solving differential equations.

6. The can list some typical environmental applications of differential equations.

7. The student can graph solutions of differential equations.

9. The student attends the mandatory computer labs.

Assessment criteria, good (3)

2. The student can classify differential equations.

3. The student is able solve separable differential equations.

4. The student can solve linear differential equations.

5. The student can apply Euler’s method in solving systems of differential equations.

6. The student can model simple environmental or chemical problems using differential equations.

8. The student is able to explain the idea of estimating parameters of differential equation by the least squares method.

9. The student shows his or her ability of applying mathematical software in solving differential equations.

Assessment criteria, excellent (5)

5. The student can apply numerical ODE solvers.

6. The student interpret published results obtained using modeling and simulation.

8. The student is able estimate parameters of differential equation by the least squares method.