Code | DIM208 |

Name | Supplementary Mathematics (for mechanical engineering) |

Status | Compulsory/Courses of Limited Choice |

Level and type | Undergraduate Studies, Academic |

Field of study | Mathematics and Statistics |

Faculty | |

Academic staff | Ilona Dzenīte, Andrejs Koliškins, Sergejs Smirnovs, Tamāra Kabiša, Māra Birze, Inta Volodko, Evija Kopeika, Vera Gošteine, Jeļena Liģere |

Credit points | 2.0 (3.0 ECTS) |

Parts | 1 |

Annotation |
Fourier series. Line and surface integrals. Elements of complex variable theory: Complex variables and functions of complex variable. Cauchy’s theorem and Cauchy’s integral formula. Elements of field theory: Scalar and vector field. Directional derivatives, gradient, vector field flux, work, circulation, divergence, rotor, Gauss-Ostrogradsky and Stokes' formula. Operator calculus: Laplace transform, its properties and applications.. |

Goals and objectives of the course in terms of competences and skills |
To enable students to acquire basic knowledge of mathematical concepts necessary for the understanding of processes and algorithms in professional subjects. To develop students’ logical thinking and skills to be able to analyse more complicated problems related to study courses of professional specialization. |

Learning outcomes and assessment |
Based on the acquired knowledge of Fourier series, a student is able to analyse periodic processes that take place in engineering and physics, for instance, in signal theory. - Evaluation of students’ knowledge is based on the results of final examination and homework assignments. Able to find line integrals and solve related problems on vector field work and circulation, and weight of material line. - Evaluation of students’ knowledge is based on the results of final examination and assessment tests. Able to find surface integrals and solve related problems on vector field flux through different shape surfaces, and weight of material surface. - Evaluation of students’ knowledge is based on the results of final examination and assessment tests. Able to find basic characteristic values of scalar and vector field: directional derivatives, gradient, vector field flux, work, circulation, divergence, rotor, and able to check if the vector field is potential. - Evaluation of students’ knowledge is based on the results of final examination and assessment tests. Able to use the acquired knowledge of elements of complex variable theory to solve problems that arise in theoretical physics, hydromechanics, elasticity theory and radio engineering. - Evaluation of students’ knowledge is based on the results of final examination and assessment tests. Able to use Laplace transforms to solve differential equations and systems of differential equations in electrical engineering and automatic control theory. - Evaluation of students’ knowledge is based on the results of final examination and homework assignments. |

Course prerequisites | Single variable and multivariable differential calculus. Indefinite and definite integral. Double and triple integral. Numerical and functional series. |

[Extended course information PDF]