Analysis and Differential Equations (SEFI)Laajuus (9 ECTS)

Objective

One of the objectives is that the student ensures and deepens what he or she has learned in the high school and also learns new concepts and methods which support learning physics and professional subjects. Also an objective is that the student builds a foundation for later studies in mathematics and professional subjects and learns to see mathematics as a natural part of his or her professional skills and is ready to use mathematical concepts and methods.

Content

Integral calculus: Integration by differentiation rules, by substitution and by parts. Partial fractions. The method of small differentials. Improper integral. Hyperbolic functions and their inverse functions. Applications.

Complex numbers: The real and imaginary part of a complex number. The exponential form of a complex number. The complex plane. The exponential function on the complex plane. Applications.

Ordinary differential equations: Separable DE. Linear DE. A pair of linear DE. Numerical solution of a DE. Applications.

Vector calculus: A vector of one real variable, a curve. Skalar and vector field. Partial derivative, differential, gradient. Maxima and minima, the method of least squares. Double and triple integrals, the line integral in space. The potential of a vector field. The theorems of Green, Stokes and Gauss. Applications.

Qualifications

Reaalifunktioiden differentiaalilaskentaan ja vektoreihin liittyvien käsitteiden ymmärtäminen ja soveltamisen taito. Integraalin ja integraalifunktion käsitteiden sekä analyysin peruslauseen ymmärtäminen.