Description:

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.
Non-spring vector field. Irrotational field.

Contents:

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.
Non-spring vector field. Irrotational field.

Recommended literature:

Neustupa J.: Matematics II (skriptum fakulty strojní). Vydavatelství ČVUT, Praha 2008.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar