Abstract
Many practical scientific and engineering problems are functions of multiple variables, which are systematically organized into a system of linear equations. The objective is then to solve the equations simultaneously. If the system is nonlinear, however, it may be always approximated to the first-order equations; therefore, the methods of linear algebra are almost universally applicable across scientific disciplines. Exercises given in this chapter illustrate some of the most typical definitions, forms, and techniques assumed to be in the repertoire of engineering and scientific students. Obviously, the scope of this single chapter is much too small to completely cover all details of this immense branch in mathematics; nevertheless, it serves as the solid introduction to basics of linear algebra.
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References
W. Appel, Mathématiques pour la physique et les physiciens, Number 978–2–35141–339–5, 5 edn. (H&K Éditions, Harrow, 2017)
MIT Open Courseware, Multivariable Calculus. https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/. Online July 2020
MIT Open Courseware. Signals and Systems. https://ocw.mit.edu/resources/res-6-007-signals-and-systems-spring-2011. Online July 2020
MIT Open Courseware. Single Variable Calculus. https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/. Online July 2020
B.P. Demidovič, Collection of Problems and Exercises for Mathematical Analysis (in Russian), Number 517.2 D30, National Printing House for Literature in Mathematics and Physics, 5th edn. (National Printing House ,Athinaion, 1963)
Y. Leroyer, P. Tessen, Mathématique pour l’ingénieur: exercises et problèmes, Number 978–2–10–052186–9, 1st edn. (Dunod, Paris, 2009)
D.S. Mitrinović, Matematika I: u obliku metodičke zbirke zadataka sa rešenjima, Number 2043, 3rd edn. (Gradjevinska Knjiga, Belgrade, 1967)
D.S. Mitrinovič, Kompleksna analiza, 4th edn. (Gradjevinska Knjiga, Belgrade, 1977)
D.S. Mitrinovič, Matematika I: u obliku metodičke zbirke zadataka sa rešenjima, Number 06–1785/1, 5rh edn. (Gradjevinska Knjiga, Belgrade, 1978)
D.S. Mitrinovič, Kompleksna analiza: zbornik zadataka i problema, vol. 3, Number 06–1431/1, 2 edn. (Naučna Knjiga, Belgrade, 1979)
P.S. Modenov, Collection of Problems in Special Program (in Russian). National Printing House for Literature in Mathematics and Physics (National Printing House, Athinaion, 1964)
D. Müller, Mathématiques. http://www.apprendre-en-ligne.net/MADIMU2/INDEX.HTM. Online July 2020
R. Sobot, Private Collection of Course Notes in Mathematics (2020)
R. Sobot, Engineering Mathematics by Example, Number 978–3–030–79544–3, 1 edn. (Springer, Berlin, 2021)
M.R. Spiegel, Analyse de Fourier et Application aux Problémes de Valeurs aux Limites, Number France 2–7042–1019–5 , 1 edn. (McGraw–Hill, New York City, 1980)
Stewart, Analyse concepts et contextes, Vol.1: Fonctions d’une variable, Number 978–2–8041–6306–8, 3 edn. (De Boeck Supérieur, Louvain-la-neuve, 2011)
Stewart, Analyse concepts et contextes, Vol.2: Fonctions de plusieurs variables, Number 978–2–8041–6327–3, 3 edn. (De Boeck Supérieur, Louvain-la-neuve, 2011)
Symbolab, Online calculator. https://www.symbolab.com/. Online July 2020
TikZ, Graphs generated by TikZ. https://en.wikipedia.org/wiki/PGF/TikZ. Online July 2020
T.B. Vene, Zbirka rešenih zadataka iz matematike, vol. 2, Number 86–17–09617–9, 22 edn. (Zavod za Udžbenike i Nastavna Sredstva, Podgorica, 1996)
T.B. Vene, Zbirka rešenih zadataka iz matematike, vol. 1, Number 86–17–09031–6, 28 edn. (Zavod za Udžbenike i Nastavna Sredstva, Podgorica, 2001)
T.B. Vene, Zbirka rešenih zadataka iz matematike, vol. 3, Number 86–17–10786–3, 27 edn. (Zavod za Udžbenike i Nastavna Sredstva, Podgorica, 2003)
T.B. Vene, Zbirka rešenih zadataka iz matematike, vol. 4, Number 86–17–11156–9, 36 edn. (Zavod za Udžbenike i Nastavna Sredstva, Podgorica, 2004)
Wikipedia, Fourier transform. https://en.wikipedia.org/wiki/Fourier_transform. Online July 2020
Wikipedia, Linear algebra. https://en.wikipedia.org/wiki/Linear_algebra. Online July 2020
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Sobot, R. (2023). Linear Algebra. In: Engineering Mathematics by Example. Springer, Cham. https://doi.org/10.1007/978-3-031-41200-4_8
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DOI: https://doi.org/10.1007/978-3-031-41200-4_8
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