Home / Linear Algebra And Matrix Analysis

Linear Algebra And Matrix Analysis

Course Code:

GEO1020

Semester:

1st Semester

Specialization Category:

G.B.

Course Hours:

4

ECTS:

5

Eclass Link:

https://eclass.uniwa.gr/courses/GEO235/


Course Tutors

Katsouleas Giorgos

LEARNING OUTCOMES

Upon successful completion of the course, students:
• Will have understood basic concepts of linear algebra and vector calculus,
• Will be able to use matrices and vector spaces in the mathematical modelling of engineering problems and draw related conclusions,
• Will be able to interrelate the geometric/mathematical principles taught within this course with the scope of surveying and geoinformatics engineering.
• Will be fully aware of how to apply the related methods in applications typically encountered by a Topography and Geoinformatics Engineer,
Will have a general comprehension of how to apply all of the above to other engineering fields.

 

General Competences

  • Criticism and self-criticism
  • Mathematical thinking and analysis
  • Mathematical and analytical presentation of geometric concepts
  • Search for, analysis and synthesis of data and information, with the use of the necessary technology
  • Decision-making
  • Working independently
  • Production of free, creative and inductive thinking

 

SYLLABUS

  1. Vector spaces, linear dependence/independence, basis and dimension,orthogonality,
  2. Vector calculus: the concept of free vector, collinear and coplanar vectors, coordinate systems, cartesian, polar, cylindrical and spherical coordinates. Unit vectors, inner, outer (cross) and mixed vector products. Geometric implications of vector products.
  3. Line in 3-d space: vector, analytic and parametric expressions. Distance of point from line.
  4. Plane in 3-d space: vector, analytic and parametric expressions. Distance of point from plane. Curves and surfaces.
  5. Linear algebra and matrices: Definition, categories, properties, and operations (addition, scalar multiplication, multiplication, transpose). Row-reduced echelon form. Gauss-Jordan algorithm.
  6. Determinants: Definition and properties. Solution of linear systems.
  7. Augmented matrix. Invertible matrix. Formula and Gauss-Jordan algorithm for inverse matrix computation. Cramer systems.
  8. Bilinear forms. Symmetric matrices and applications. Eigenvalues and eigenvectors. Diagonalization and applications.

 

STUDENT PERFORMANCE EVALUATION

Language of evaluation: Greek (English for ERASMUS students, if required) Methods of evaluation:

  • Written exam at the end of the semester (multiple choice questionnaires, short-answer questions, & problem-solving questions)
  • Projects during the semester (practical exercises on both theoretical and practical objectives related to the course)

Evaluation criteria are known to the students before the final examination and the grades allotted to each exam question are indicated under each one. Students can see their corrected answers, their individual grade on each question, and receive comments on their mistakes.

 

ATTACHED BIBLIOGRAPHY

Greek:
1. Donatos, G., & Adam, M. (2008). Linear algebra: Theory and applications, Gutenberg, Athens.
2. Chalidias, N. (2018). Infinitesimal calculus, linear algebra and applications. Broken Hill Publishers Ltd.
3. Mpratsos, Ath. (2015), Lectures in advanced mathematics, Hellenic Academic Ebooks “Kallipos”, URI: http://hdl.handle.net/11419/424
4. Mpratsos, Ath. (2003), Advanced mathematics, Stamoulis, Athens.
5. Rassias, Th. (2017), Mathematics I (2nd Edition), Tsotras Editions.
6. Xenos, Th. (2004), Linear Algebra, Ziti Editions.
7. Strang, G. (2006), Introducton to Linear Algebra, Editions of University of Patras.
8. Strang, G. (2005), Linear Algebra and apllications, University Publications of Crete, Herakleion.

International:
1. Kreyszig, E. (2005), Advanced Engineering Mathematics, 9th edition, Wiley.
1. Glyn, J. et al. (2010), Advanced Modern Engineering Mathematics, 4th edition, Addison-Wesley Pub. Co.
2. Wylie, C.R. & Barrett, L.C. (1995), Advanced Engineering Mathematics, 6th edition, McGraw-Hill.
3. Zill, D.G. & Cullen, M.R. (2006), Advanced Engineering Mathematics, 3rd edition, Jones & Bartlett Pub.
4. Lipshutz, S. & Lipson, M. (2000), Linear Algebra, Schaum’s Outline Series, 3rd edition.
5. Datta, B.N. (1995), Numerical Linear Algebra and Applications, Books/Cole Publishing Company.
6. Golub, G.H. (2002), Matrix Computations, John Hopkins University Press.
7. Meyer, C.D. (2000), Matrix Analysis and Applied Linear Algebra, SIAM. URL: http://www.matrixanalysis.com/DownloadChapters.html.
8. Shores, T.S. (2007), Applied Linear Algebra and Matrix Analysis, Springer Science. URL: http://www.math.unl.edu/~tshores1/linalgtext.html.