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Calculus for the second year of Bc. study (3. semester).
Topics :
power series,
complex functions,
Calculus of variation.
Last update: T_KMA (22.05.2003)
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K. Rektorys a j.: Přehled užité matematiky
J. Kopáček: Matematika pro fyziky III, V
S. Fučík, J. Milota: Matematická analýza II
B. Novák: Funkce komplexní proměnné Last update: T_KMA (14.05.2003)
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Power series.
Power series, radius of convergence, complex functions, holomorphic functions, Taylor polynom, elementary complex functions. Complex functions Holomophic functions, Cauchy-Riemann conditions, exponential a logarithmic functions, sin z, sinh z, sqrt, linear and rational functions, curve integral, winding number, Cauchy theorem, Liouville theorem, using power series, derivatives, uniqueness theorem. Primitive functions, Laurent series, rezidua, Integral(R(sin t, cos t))dt Integral(R(x))dx Integral(R(x).sin x)dx Calculus of variations. Extremal valuesof L(y)=Integral( f(x,y(x),y'(x)) , dx) and Euler equations, isoperimetrical problems. Last update: T_KMA (14.05.2003)
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