714-0868 – Mathematics 3 (Math 3)

Goals and competence Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyse problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyse correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics. It is necessary to complete Mathematics 1 and Mathematics 2 courses or their equivalents.

Mathematics 3 is connected with Mathematics 1,2. We have to stress that student can enrol in this course only if he passed the course Mathematics 1 and 2 or an equivalent course. - Integral calculus of functions of more than one variable - Double and volume integral. Fubini's Theorem: integrating over regular regions. - Transformation of variables, polar, cylindrical and spherical coordinates. - Practical applications of double and volume integral. - Curves and their orientation, line integral of a scalar function and its geometrical applications. - Line integral of a vector function and its physical applications. - Path independence, Green's theorem.

http://mdg.vsb.cz/wiki/public/Double_Integral.pdf

Neustupa J., Kračmar S.: Mathematics II. ČVUT, Praha 1998. http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf (in czech language)