Calculus of One Variable, Vectors and Matrices (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. Also an objective is that the student builds a foundation for later studies in mathematics and learns new concepts and methods which support learning physics and the foundations of professional subjects.

Content

The system of linear equations: The Gaus's method. Determinant. The existence and uniqueness of the solution. Applications.

Vectors and analytic geometry: Sum of vectors and multiplying a vector by a scalar. Coordinates. The scalar and the vector product. Orthogonal projection. The triple scalar product. The parametric representation of a line, a plane, a sphere, a cylinder and a cone. The parametric representation of a circle and an ellipse. Applications.

Real functions: The properties and the graphs of elementary functions. The inverse function, the composite function. The inverse functions of the trigonometric functions. Limit, continuity, derivative, differential. Maxima and minima. Numerical solution of an equation. The concept of integral. The integral function. The fundamental theorem of calculus. Applications.

Matrices: Matrix operations. The inverse of a matrix. The matrix representation of a system of linear equations. Applications.

Qualifications

Lukion matematikan oppimäärä.