Objectives and competences
Objectives:
To know thoroughly the basics of functions of several variables, vector and scalar fields, double integrals and ordinary differential equations.
Competences:
The ability to use the acquired knowledge for solving of mathematical problems containing functions of several variables and differential equations.
The ability to use the acquired knowledge for computing some quantities in engineering and technics which appear in different basic and applied sciences, for example Physics, Thermodynamics, Electrical engineering.
Content (Syllabus outline)
1. Differential equations (basic notion, DE of 1st order, DE of 2nd order with the constant coefficients, Laplace transformation, applications in physics and engineering).
2. Functions of two or more variables (definition, partial derivatives, total diferential, local extrems of the function of two variables, constrained extremes).
3. Vector analysis (scalar and vector fields, gradient, rotor, divergence, operator nabla, directional derivative).
4. Integrals of functions of two variables (definition of double integral, introduction of new variables, polar coordinates, applications – surface, volume, moment of inertia, center of gravity).
Learning and teaching methods
Lectures, tutorial, coursework assignments.
Intended learning outcomes - knowledge and understanding
Knowledge and understanding:
At the end of the course students are going to:
1. Recognize and solve separable, 1st order, homogeneous, linear and Bernoulli DE, and 2nd order linear ODEs with constant coefficients including initial and boundary conditions.
2. Use Laplace transform for solving simple DE with initial conditions.
3. Find partial derivatives of the function of two or three variables and determine the extremes of the function of two variables.
4. Solve the problem with constrained extremes of function of two variables.
5. Distinguish between scalar and vector fields and calculate the gradient, divergence, directional derivative and rotor of a given scalar or vector field.
6. Compute double integral using Cartesian coordinates and use the computation techniques for double integral to evaluate areas, moments and center of gravity of shapes, and volumes of solids.
7. Use the polar coordinates for simple round areas.
Intended learning outcomes - transferable/key skills and other attributes
Transferable/key competences and other abilities:
1. Communication skills: unequivocal and precise expression.
2. Computational skills: performing a variety of computational operations.
3. Problem solving: identifying and solving mathematical problems that occur in energy and that are described by the theory of differential equations and scalar functions of several variables.
Readings
Osnovna/Basic:
- M. Mencinger, Zbirka rešenih nalog iz matematične analize in algebre, FG UM, Maribor, 2006.
- M. Žulj, Zbirka nalog iz Matematičnih metod II z rešitvami, Maribor: Univerzitetna založba Univerze v Mariboru, 2017.
- R. Jamnik, Matematika, DMFA Slovenije, Ljubljana, 2008.
Dodatna/Additional:
- E. Kreyszig: Advanced Engineering Mathematics, J. Willey and Sons, New York, 2011.
Additional information on implementation and assessment Method (written or oral exam, coursework, project):
• Written exam
• Oral exam
• coursework
Notes:The student must finish each part of the exam (written exam, oral exam, coursework) with at least 50%. In the case that a student is offered the opportunity to take a written exam in the form of two midterm exams, each must be graded with at least 30% and both with an average of at least 50% to pass the written part of the exam.
