Analysis I

Opublikowano: 13.12.2014 22:25

Subject name Analysis I
Type of subject               Basic
Summary ECTS 5
Form of course 30h lecture, 30h tutorial
Lecturer                           Piotr Figurny, M.Sc.
A brief outline:
Lecture
  • Limits of sequences and functions: definitions, properties, applications.
  • Derivatives: definition, properties, applications: differential, tangent line, Taylor formula, de l'Hospital Rule, investigation of monotonicity, local and global extrema, convexity, asymptote.
  • Indefinite Integral: definition, properties, integration by substitution,  by parts, applications
  • Riemann Integral: definition, properties, applications: evaluation of area, volume, length of curves.
  • Improper Integral: definition, properties, applications.
Tutorial
  • Evaluating limits of sequences and functions, understanding of indefinite symbol,
  • Derivatives: evaluation, chain rule, differential, tangent line, Taylor formula, de l'Hospital Rule, investigation of monotonicity, local and global extrema, convexity, asymptotes, plotting graphs of functions..
  • Indefinite Integral: evaluation, integration by substitution, by parts,  functions: rational, trygonometric, roots, exponential
  • Riemann Integral: evaluation of integral, evaluation of area, volume, length of curves.
  • Improper Integral: evaluation, checking of convergence.