Mathematics for Engineers 3 (ETF EEO IM3 4765)

General information

Module title

Mathematics for Engineers 3

Module code

ETF EEO IM3 4765

Study

ETF-B

Department

Electric Power Engineering

Year

1

Semester

1

Module type

Mandatory

ECTS

6

Hours

65

Lectures

42

Exercises

0

Tutorials

23

Module goal - Knowledge and skill to be achieved by students
  It is clear that knowledge and skills acquired through previous courses of mathematics for engineers are insufficient for describing and modeling engineering problems that are presented to the students during their senior years (years 4 and 5). The goal of this course is to fill this gap.

Syllabus
  1. Integral transformations: Fourier's series, Fourier's transformation, Laplace's transformation, Z-transformation, connection between the Fourier's and Laplace's transformation.
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2. Signal Processing: linear systems, continuous and discrete systems in time, frequency response, convolution and impulse response; differential and difference equations and frequency response in state variables.
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3. Numerical integration and differentiation: Simpson's rule, Gaussian quadrature, Monte-Carlo integration, multidimensional integration; numerical differentiation. numerical solving of ordinary differential equations.
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4. Interpolation and extrapolation: polynomial interpolation; usage of rationalized functions; application of Fourier's transformation; inverse extrapolation and interpolation; cubic spline.
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5. Linear programming: Basic theory; Simplex method and practical techniques.
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6. Non-linear programming: Lagrange multipliers, Karush-Kuhn-Tucker optimal conditions; convex, duality of approximative method of non-linear programming.
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7. Calculus of variations: Euler–Lagrange equation; boundary conditions, limitations; introduction to dynamic programming; basics of numerical approximation.
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Literature
Recommended
Additional

Didactic methods
  Course lessons are taught by the professor in lecture halls, and followed by demonstration and solving of practical examples and mathematical equations/graphs. Additionally, students spend time on tutorials and lab-exercises. They resolve specific problems pertaining to their theses, using available or student-developed software. Goal of these activities is to enable students to get hands-on, practical experience in this area, as well as to gauge students' knowledge through assigned papers and exams (mid-term, as well as final).

Exams
  During the course students earn points according to the following system:
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- Attending classes and tutorials: 10 points; a student with more than three absences from lectures and/or tutorials will not be eligible to get these points.
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- Home assignments, laboratory reports and/or final thesis: maximum of 10 points.
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- Mid-term and final exams: a student can score up to 20 points on each exam (passing grade is 10 points).
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During each of the two exams (time assigned is 90 minutes) students will solve simple questions - designed to examine whether students acquired basic theoretical knowledge –multiple choice problems, as well as one open-answer problem. Students who gain less than 20 points during one semester must re-take that course.
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Students who earn 40 or more points during the semester are eligible for taking a final exam; the exam asks the student to discuss mathematical problems from the mid-term exam and home assignments, as well as to answer to simple questions related to general course topics.
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A student can score a maximum of 40 points on the final oral exam (passing threshold is 20 points). A student who gets less than this minimum, must take a makeup oral exam.
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A student who earns 20 points or more, and less than 40 points during the whole semester will have to take a makeup exam. The makeup exam is organized in the following manner:
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- Written part is structured similarly to mid-term written exam, during which students will have to solve problems in which they failed on their mid-term exams (got less than 10 points).
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- Oral part of the exam is structured in the same way as the oral part of the final exam.
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Aditional notes