Analyyttinen geometria ja vektoritLaajuus (3 op)

Osaamistavoitteet

The student understands to concept of a vector and is able to interpet vectors expressing state or change. The student knows how to apply 2D ja 3D vectors in chemical and physical problems. The student knows typical examples of higher dimensional vectors in analytical chemistry and in environmental engineering. The student is able express dependencies using tools of analytical geometry and linear (empirical) models. The student understands what is meant by a function and how it can be applied. The student can interpretgraphs of functions.

The student com form inverse and composite functions. The students is able to visualize elementary functions and typical functions arising in enviromental engineering. The student can differentiate functions numerically, analytically and by using mathematical software. The student can solve equations numerically. The student can apply functions and derivates in describing dependencies in physics, chemistry and environmental engineering

Sisältö

The concept of a vector and its geometrical and other interpretations. Elementary vector algebra and applications in physics and chemistry. Vectors in higher dimensions and their chemical and enviromental interpretations and applications. Vectors, straight lines and (hyper)planes in n-dimensional spaces and their applications in environmental engineering. The idea of empirical modeling and introduction to linear models. The concepts of a function, composite function and inverse function. Graphs of elementary functions.

Eigenvalue, eigenvectors and introduction to principal component analysis.