## DIM205 Supplementary Mathematics (for electrical engineering)

 Code DIM205 Name Supplementary Mathematics (for electrical engineering) Status Compulsory/Courses of Limited Choice Level and type Undergraduate Studies, Academic Field of study Mathematics and Statistics Faculty Academic staff Marija Iltiņa, Vladislavs Kremeņeckis, Irina Eglīte, Vera Gošteine, Ilmārs Iltiņš, Jeļena Liģere, Marija Dobkeviča, Sergejs Smirnovs, Māra Birze, Vaira Buža, Evija Kopeika, Jeļena Mihailova Credit points 2.0 (3.0 ECTS) Parts 1 Annotation Line integrals and surface integrals. Scalar and vector fields. Derivative in the direction, gradient, flux, circulation, divergence, rotor, Gauss' and Stokes' theorems. Laplace operator in curvilinear coordinates. Function of complex variable. Cauchy's theorem and integral formula. Taylor and Laurent series. Residues. Laplace transform, its basic properties and applications. Bessel functions.. Goals and objectives of the course in terms of competences and skills To enable students to acquire basic knowledge of the theory of functions of complex variable, the theory of integral transforms and the field theory necessary for he successful acquisition of specialized courses. To develop student's argumentative reasoning and the ability to use the newly learned concepts in practice. Learning outcomes and assessment After successful completion of the study course a student is able to calculate line integrals of the first and second type, to apply the Green's formula. - Evaluation of students’ knowledge and skills is based on the results of homework assignments and final examination. Able to calculate the value of complex variable function, to check Cauchy-Riemann conditions, to find an analytical function by either its real or imaginary part. - Evaluation of students’ knowledge and skills is based on the results of homework assignments and final examination. Able to calculate an integral of complex variable function, to apply Cauchy's theorem, to expand a function in Taylor and Laurent series. - Evaluation of students’ knowledge and skills is based on the results of homework assignments and final examination. Able to calculate a residue and integrals with the aid of residues. - Evaluation of students’ knowledge and skills is based on the results of homework assignments and final examination. Able to find a Laplace transform of a function and an inverse transform, to solve differential equations using Laplace transform. - Evaluation of students’ knowledge and skills is based on the results of homework assignments and final examination. Able to calculate surface integrals of the first and second kind. - Evaluation of students’ knowledge and skills is based on the results of homework assignments and final examination. Able to calculate a directional derivative and a gradient of a scalar field, to calculate flux and divergence of a vector field, to apply the Gauss-Ostrogradsky formula. - Evaluation of students’ knowledge and skills is based on the results of homework assignments and final examination. Able to calculate the circulation and curl of a vector field, to apply Stokes' formula, to calculate the potential of a field. - Evaluation of students’ knowledge and skills is based on the results of homework assignments and final examination. Course prerequisites DIM101, Mathematics

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