Differentiaaliyhtälöt, mallinnus ja simulointiLaajuus (3 op)

Osaamistavoitteet

The student can solve equations and system of numerically using derivative (gradient) based methods. The student understands what is meant by a solution of a differential equation. The student understands in what kind of problems differential equations are needed. The student understands the idea of mathematical modeling and simulation using differential equations. The student knows different ways of solving differential equations. The student knows the most common applications of differential equations in environmental engineering.

The student knows how to solve systems of equations in environmental engineering applications using numerical math software. The student is able to classify differential equations. The student can solve separable and linear differential equations. The student is able to solve numerically differential equations and systems of differential equations. The student can apply differential equations in the most common problems of environmental engineering. The student is able to use Excel and mathematical software in solving differential equations numerically.

Sisältö

Derivative based numerical methods for solving nonlinear equations and system of equations. Hyperbolic functions and their derivatives. The gradient of a function and its applications.Solution of a differential equation. Classification of differential equations. Applications of differential equations environmental engineering: the idea of mathematical modeling and simulation. Solving separable differential equations. Linear differential equations. Solving systems of differential equations numerically. Applications of systems of differential equations in environmental engineering. Using Excel in solving differential equations and systems of differential equations. Graphical visualization of solutions of differential equations. Using mathematical software in solving differential equations and systems of differential equations.

Estimating parameters of systems of non-linear differential equations.

Esitietovaatimukset

Differential and integral calculus