Linear Algebra 1

Uitgebreide vaknaam	Linear Algebra 1
Leerdoelen	At the end of thos course, the student is able to: 1. reproduce mathematical definitions of all notions studied during the course, such as consistent system, rank, nonsingular matrix, similarity, row/column equivalence, vector space, subspace, linear dependence, basis, dimension, linear map, similarity, matrix representation, row/column space, scalar product, eigenvalue, eigenvector etc. 2. prove basic statements of standard linear algebra in a mathematically precise manner. 3. apply major theorems (like rank-nullity theorem) to given instances 4. compute solutions of linear equations, determinant, matrix inverses, eigenvalues, eigenvectors etc. 5. verify if certain basic concepts are applicable (can a given matrix be diagonalized, etc.) to given instances.
Omschrijving	Many physical quantities, such as "force", "position", "velocity", and "acceleration", have not only a magnitude but also a direction. Such quantities are called "vectors". A vector is often represented by an arrow of which the length is the magnitude, and the direction is the direction of the vector. Vectors may be added and be multiplied by numbers. A collection of vectors (together with these two operations) that satisfies certain rules (axioms) is called a vector space. It turns out that collections of certain objects that are different from three-dimensional arrows also satisfy these axioms. For instance, the set of all polynomials is also a vector space; the set of continuous functions on the real numbers is a (yet another) vector space. Often a vector space generated by a finite number of its elements. Such a finite set of elements is called a "basis" of the vector space and the number of elements is called the "dimension" of the vector space. Within the context of vector spaces, (linear) operations that convert vectors into vectors play an important role. An example is the mirror of three-dimensional "arrows" at the origin. Another example is the operation of "differentiation", which converts functions into functions. In the case of vector spaces having a finite dimension, such an operation can be represented by a "matrix". The course provides a mathematical study of the aforementioned concepts of "vector", "matrix", "vector space", "linear operator", etc.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)
Toetsvorm	Opdracht (AST), Schriftelijk tentamen (WE), Tussentoets (IT) (The grade for this course is determined by the following rules: 1) if FE <4.5 then G=FE 2) if FE>=4.5 then G=max(FE, 0.2 HW + 0.2 ME + 0.6 FE) where FE is the mark for the final exam, ME is the mark for the mid-term exam and HW is the mark for the homework assignments, and G is the final grade.)
Vaksoort	propedeuse
Coördinator	Prof. Dr. M.K. Camlibel
Docent(en)	Prof. Dr. M.K. Camlibel
Verplichte literatuur	Titel Auteur ISBN Prijs Linear Algebra with Applications. 8th edition. (Pearson International Edition) Steven J. Leon 978-0135128671
Entreevoorwaarden	This course is the first Linear Algebra course of the curriculum and builds on high school knowledge of Mathematics.
Opmerkingen	This course was registered last year with course code WILA1-06
Opgenomen in	Opleiding Jaar Periode Type BSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester I b BSc Mathematics and Physics (double degree) 1 semester I b verplicht BSc Mathematics: General Mathematics  ( Major track General Mathematics) 1 semester I b verplicht BSc Mathematics: Probability and Statistics 1 semester I b verplicht BSc Technische Wiskunde 1 semester I b verplicht MSc Farmacie  (Keuzevakken) - semester I b keuze