Divu argumentu funkciju diferenciālrēķini pretpiemēros
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Latvijas Universitāte
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Bakalaura darbs ir veltīts divu argumentu funkciju diferenciālrēķiniem, īpašu uzmanību pievēršot speciāla veida piemēriem (pretpiemēriem), kas parāda, ka divu argumentu funkciju īpašības, kas izpildās attiecībā pret katru argumentu atsevišķi, ne vienmēr izpildās attiecībā pret diviem argumentiem kopumā. Darbā ir aprakstīti divu argumentu funkciju robežu un atkārtotu robežu piemēri, pirmās kārtas parciālo atvasinājumu un otrās kārtas jaukto parciālo atvasinājumu piemēri, kā arī ir izanalizēta sakarība starp parciālo atvasinājumu eksistenci, diferencējamību un nepārtrauktību.
This bachelor's work is devoted to twovariable differential calculus. Counterexamples considered in the work refer to three topics of differential calculus: limits, continuity and differentiation. By examples we show the distinction of properties of twovariable functions, executed with respect to both variables, and properties, executed with respect to each variable independently. Double limits and iterated limits for functions of two variables are described. The relation between partial derivatives, differentiability and continuity is discussed. Some examples on mixed partials of multivariable functions are also considered.
This bachelor's work is devoted to twovariable differential calculus. Counterexamples considered in the work refer to three topics of differential calculus: limits, continuity and differentiation. By examples we show the distinction of properties of twovariable functions, executed with respect to both variables, and properties, executed with respect to each variable independently. Double limits and iterated limits for functions of two variables are described. The relation between partial derivatives, differentiability and continuity is discussed. Some examples on mixed partials of multivariable functions are also considered.