To comprehend and consolidate the notion of a function, with which they dealt in some degree in the last years of Lyceum. To use the graphic representation for the recognition of behavior of functions and to learn how to draw the graphic representation of elementary functions. To recognize the sequences and series (numerical and power series) and to find, if exist, limits and infinite sums. To differentiate various forms of functions (explicit, implicit, parametric, bivariate) and apply the derivatives in the geometry and elsewhere. To integrate elementary and relatively complicated functions with one or two variables and express various quantities as areas, volumes, etc as integrals. Also, to solve some simple differential equations and find their general and partial solution.
Course Content (Syllabus)
Functions (algebraic, exponential, logarithmic, trigonometric, transcendental, implicit, parametric), Sequences (the notion of limit, convergence, criteria of convergence), Series (definition, convergence, criteria of convergence), Power Series, Derivative (Derivative Rules, logarithmic differentiation, derivative of implicit and parametric functions, power series, second and higher order derivative), Taylor Polynomial and Taylor series, Applications of derivatives (geometrical applications, Newton-Raphson method for finding the roots of an equation), Complete study of a function (extrema, curvature, asymptote, graphic representation), Integrals (integration of elementary functions, theorem of mean value, the Fundamental Theorem of Calculus), Area under or between curves, Geometric applications, Techniques of Integration (Substitution, Integration by Parts, integration of a rational function), Functions of many variables (domain and continuity, partial derivative, extrema, double integrals), Differential equations (Separable, homogenous, linear of first order)
variable, function, sequence, series, derivative, integral, area, improper integral, numerical integration, partial derivative, double integral