Mathematics II.
Code  Completion  Credits  Range  Language 

E011092  Z,ZK  7  4P+4C+0L  English 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Technical Mathematics
 Synopsis:

Differential calculus of functions of several variables  domain, graph (quadratic areas)
Continuity, partial derivatives, gradient and its physical meaning, differential, approximate evaluation of function value.
Local extremes, global extremes. Implicit function, its derivative, tangent, resp. tangent plane.
Integral calculus of functions of several variables  Fubini's theorem, calculation of double and triple integrals.
Transformation into polar, cylindrical and spherical coordinates.
Smooth curve, closed curve. Curve integral of scalar and vector functions, Green's theorem.
Smooth surface, closed surface. Area integral of scalar and vector functions. Gauss theorem, Stokes theorem.
Geometric and physical applications of integrals  calculation of surface area and volume of a body, length of a curve.
Weight, center of gravity, moment of inertia.
Work done by force along a curve. Flow of vector field through a surface.
Potential both in E2, and in E3. Independence of the curve integral on the integration path.
Work done by force along a closed curve.
Nonspring vector field. Irrotational field.
 Requirements:
 Syllabus of lectures:

Differential calculus of functions of several variables  domain, graph (quadratic areas)
Continuity, partial derivatives, gradient and its physical meaning, differential, approximate evaluation of function value.
Local extremes, global extremes. Implicit function, its derivative, tangent, resp. tangent plane.
Integral calculus of functions of several variables  Fubini's theorem, calculation of double and triple integrals.
Transformation into polar, cylindrical and spherical coordinates.
Smooth curve, closed curve. Curve integral of scalar and vector functions, Green's theorem.
Smooth surface, closed surface. Area integral of scalar and vector functions. Gauss theorem, Stokes theorem.
Geometric and physical applications of integrals  calculation of surface area and volume of a body, length of a curve.
Weight, center of gravity, moment of inertia.
Work done by force along a curve. Flow of vector field through a surface.
Potential both in E2, and in E3. Independence of the curve integral on the integration path.
Work done by force along a closed curve.
Nonspring vector field. Irrotational field.
 Syllabus of tutorials:
 Study Objective:
 Study materials:

Neustupa J.: Matematics II (skriptum fakulty strojní). Vydavatelství ČVUT, Praha 2008.
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: