Mathematics 3

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Course Unit Code Number of ECTS Credits Allocated Type of Course Unit * 310-2303/01 5 ECTS credits Choice-compulsory First Cycle, Second Cycle Winter, Summer Semester Face-to-face English Course succeeds to compulsory courses of previous semester ZID76 Mgr. Arnošt Žídek, Ph.D. 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. - Theory of the field. Scalar and vector fields. - 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. 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. Course description (weekly lessons): 1. Double integral over rectangular region. 2. Double integral over regular region. Fubini's Theorem. 3. Transformation of variables. Mapping and its Jacobian. Polar coordinates. 4. Practical applications of double integral. 5. Volume integral over rectangular region. 6. Volume integral over regular region. 7. Transformation to the cylindrical coordinates. 8. Transformation to the spherical coordinates. 9. Practical applications of volume integral. 10. Curves in R^3. Their equations and orientation of closed curves. 11. Line integral of a scalar function. 12. Line integral of a vector function. 13. Path independence. Green's Theorem. 14. Practical applications of line integrals of both kinds. Lectures in English on school Moodle system - lms.vsb.cz Lectures in English on school Moodle system - lms.vsb.cz Neustupa J., Kračmar S.: Mathematics II. ČVUT, Praha 1998. http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf (in czech language) Neustupa J., Kračmar S.: Mathematics II. ČVUT, Praha 1998. http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf (in czech language) Lectures, Seminars, Individual consultations, Other activities Tasks are not Defined