Linear Algebra 1
Faculteit  Science and Engineering 
Jaar  2017/18 
Vakcode  WILA106 
Vaknaam  Linear Algebra 1 
Niveau(s)  propedeuse 
Voertaal  Engels 
Periode  semester I b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Linear Algebra 1  
Leerdoelen  After this course: 1. compute solutions of linear equations, determinant, matrix inverses, eigenvalues, eigenvectors etc. 2. prove basic statements of standard linear algebra in a mathematically precise manner. 3. know 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. 4. apply major theorems (like ranknullity theorem) to given instances. 5. transfer the theory developed in the lectures to basic applications and solve problems using Matlab. 

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 threedimensional 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 threedimensional "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), Practisch werk (PRC), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Practisch werk (PR), Schriftelijk tentamen (WE), Tussentoets (IT)
(Only those students who had a passing grade from BOTH computer lab sessions are entitled to take the final exam. 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 midterm exam and HW is the mark for the homework assignments, and G is the final grade. A student can only pass the course when both computer lab sessions are passed.) 

Vaksoort  propedeuse  
Coördinator  prof. dr. M.K. Camlibel  
Docent(en)  prof. dr. M.K. Camlibel  
Verplichte literatuur 


Entreevoorwaarden  
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