After successfully completing the course the students will be able do computations with complex numbers, completely characterise real functions with one real variable (maxima, minima, asymptotes, intervals of increasing, decreasing function values)- compute limits of functions using theorems for limits and limits of indefinable forms- compute derivatives of complicated functions, do implicit differentiation of algebraic forms and of functions expressed in parametric form- express and characterise functions in non-cartesian (polar) coordinates - solve problems that require applications of differentiation/extrema-finding in practical problems- expand functions in Taylor series and use them to conduct approximations- compute indefinite and definite integrals using theorems of integrations- compute improper integrals using theorems for integrations and for computing limits of functions- use integrals for solving practical problems (e.g. volumes of solids or rotation)
Course Content (Syllabus)
Differential Calculus – Complex numbers, Functions of one variable (Real Functions of a real variable, the derivative and the differential of the function, applications of a derivative, study of the real functions using derivatives), functions expressed and studied in parametric forms - Sequences, and convergence criteria, Series, with special application in Taylor and MacLaurin Series. Integral Calculus - Functions of one variable (Indefinite integrals, the definite integral, improper integrals, approximate methods, applications of integrals).
Course Bibliography (Eudoxus)
Απειροστικός Λογισμός, Briggs William, Cochran Lyle, and Gillett Bernard, Εκδόσεις ΚΡΙΤΙΚΗ
Μωυσιάδης, Εκδόσεις: ΧΡΙΣΤΟΔΟΥΛΙΔΗ