Mathematical Analysis IIa - NMAI049
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Last update: T_KMA (17.05.2001)
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Last update: T_KMA (15.05.2003)
I. Metric spaces
Completeness, connectedness, Banach contraction theorem.
II. Differential equations.
Peano and Picard theorems on the existence, respectively uniqueness, of the solution. Linear equations and systems, theorem on global existence and uniqueness for linear equations.
Particular solutions and methods of their determination: variation of constants, special right-hand sides.
III. Lebesgue integral
Riemann integral in Rn and its properties. Extension of Riemann integral, Lebesgue integral and its basic properties.
Levi and Lebesgue theorems. Fubini theorem. Regular mapping, change of variables. Continuity and differentiability of the integral depending on a parameter. |