Introduction to the linear algebra, analytical theory of partial differential equations and their most important applications in engineering.

Upon successful completion of this course, students should be able to: 1) apply learned methods of linear algebra to slove technical problems; 2) detrmine analitical solution of partial differential equation of first order; 3) detrmine analitical solution of basic problems of mathematical physics.

Distance, norm, inner product. Orthonormal sets of vectors. Gram-Schmidt method. Linear operators. Characteristic and minimal polynomial of a square matrix. Reduction of a square form to a canonical form. Matrix analysis. Applications of matrix calculus in graph theory Linear programming. Solving 2nd order ordinary differential equations using power series. Boundary-value problem for 2nd order ordinary differential equations. Symmetric form of systems 1st order differential equations. Pfaffs equation. 1st order partial differential equations. Differentailbility of complex functions. Systems of 1st order partial differential equations. 2nd order partal differential equations - classification of equations of mathematical physics. D'Alambert method for hyperbolic equations. Fourier method. Laplace transform. Conformal mappings. Dirichlet problem on plane.

Distance, norm, inner product. Orthonormal sets of vectors. Gram-Schmidt method. Linear operators. Characteristic and minimal polynomial of a square matrix. Reduction of a square form to a canonical form. Matrix analysis. Applications of matrix calculus in graph theory Linear programming. Solving 2nd order ordinary differential equations using power series. Boundary-value problem for 2nd order ordinary differential equations. Symmetric form of systems 1st order differential equations. Pfaffs equation. 1st order partial differential equations. Differentailbility of complex functions. Systems of 1st order partial differential equations. 2nd order partal differential equations - classification of equations of mathematical physics. D'Alambert method for hyperbolic equations. Fourier method. Laplace transform. Conformal mappings. Dirichlet problem on plane.

No prerequisites.

1. D. Georgijević, Partial differential equations, Faculty of Mechanical Engineering, Beograd 2002. 2. Z. Mamuzić, Selected topics from the theory of ordinary and partial differential equations, Faculty of Mechanical Engineering, Beograd 1981. 3. Lj. Ćirić, Special functions, Faculty of Mechanical Engineering, Beograd 1984. 4. S. Nešić, Matrices, Faculty of Mechanical Engineering, Beograd 1992. 5. B. Đerasimović, Functions of complex variable. Euler's integrals, Faculty of Mechanical Engineering, Beograd 1969.

Total assigned hours: 65

New material: 40
Elaboration and examples (recapitulation): 10

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 10
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 5

Activity during lectures: 5
Test/test: 0
Laboratory practice: 0
Calculation tasks: 45
Seminar paper: 0
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 20

J. Kečkić, Linear algebra, Naučna knjiga, Beograd, 1990.; S. Radenović, Linearna algebra, Methodological collection of problems and exercises collection of problems and exercises, Naša knjiga, Beograd, 2007.; D. S. Mitrinović, J. D. Kečkić, Equations of mathematical physics, Građevinska knjiga, Beograd, 1985.; M. Arsenović, Equations of mathematical physics, Zavod za udžbenike, Beograd 2011.; D. Cvetković, Graph theory and its applications, Naučna knjiga, Beograd, 1990.