Linear Algebra (for Physics)

Faculteit Science and Engineering
Jaar 2021/22
Vakcode WBPH054-05
Vaknaam Linear Algebra (for Physics)
Niveau(s) bachelor
Voertaal Engels
Periode semester I b
ECTS 5
Rooster rooster.rug.nl

Uitgebreide vaknaam Linear Algebra (for Physics)
Leerdoelen At the end of this course, the student is able to:
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 rank-nullity 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 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), 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 ALL 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 mid-term exam and HW is the mark for the homework assignments, and G is the final grade. A student can only pass the course when all three computer lab assignments are completed.))
Vaksoort bachelor
Coördinator prof. dr. R.M. Mendez
Docent(en) prof. dr. R.M. Mendez
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
Opgenomen in
Opleiding Jaar Periode Type
BSc Natuurkunde 1 semester I b verplicht
BSc Sterrenkunde 1 semester I b verplicht
BSc Technische Natuurkunde 1 semester I b verplicht