Mathematics 3

1. Linear diferential equations of the n-th order, the initial value problem. Homogeneous equations with constant coefficients. Reductions of the order.
2. Nonhomogeneous equations, variations of parameters, the method of undetermined coefficients for special quasi-polynomial right-hand side.
3. Inner product vector spaces, examples. Norm and metric induced by inner product, Cauchy-Schwarz inequality. Boundary value problems for ordinary differential equations. The corresponding eigenvalue problems.
4. Symmetric, positive and positive definite linear operators, examples. Eigenvalues and eigenvectors of a linear operator. The solvability of the problem A(u)-l u =f.
5. The equation A(u)=f, quadratic functional corresponding to A. The variational principle.
6. Double and triple Riemann integral, Fubini theorem, substitution (polar, spherical and cylindrical coordinates), applications of double and triple integral.
7. Line integral of a function and its applications.
8. Line integral of a vector field and its applications, independence on the path, Green’s theorem.

Seminars are obligatory. During the 6^th week the students write the test (40 min.) with a total amount of points 15. 1/3 of these points is tranfserable to exam.
There is no possibility to repeat the test.

Test (90 min.) with a total amount of points 50 (+ at most 5 points transfered from seminars).

F. Bubeník: Mathematics for Engineers, Prague 2007

F. Bubeník: Problems to Mathematics for Engineers, Prague 2007