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Program

EN IT

Updated A.Y. 2021-2022

Detailed Program

You can find below a detailed program which will be update on a daily basis during the teaching period.

Sep 15, 2021 Natural numbers, Integers, rational numbers and the properies of operations. Decimal and fractional representations of rational numbers. The solution of the equation x^2=2 and the Real numbers. Decomal representation of real numbers

Sep 16, 2021 Axioms of real numbesr: Axioma of operations, Axioms of ordering and Axiom of completeness. The meaning of the exaiom of completeness (examples of separating points). The set of rational numbers does not satisfy the axiom of completeness (example). Set theory: quantifiers For all, Exists, Exists only one, Not Exist, Subsets. Union of sets, Intersection of sets, Subtraction of sets, the complementary of a set. Intervals as subsets of real numbers: open, closed, not open nor closed, bounded, unbounded. 

Sep 17, 2021 Implications: if-then, if and only if. Structure of a Theorem (Hypotheses-Thesis). Distance in R and the absolute value. Functions: general definition and examples. Real function of a real variable, domain of a function, range of a function, graph of a function, plot of a function, Examples.  

Sep 22, 2021

Sep 23, 2021

Sep 24, 2021

Sep 29, 2021

Sep 30, 2021

Oct 01, 2021

Oct 06, 2021

Oct 07, 2021

Oct 08, 2021

Oct 13, 2021

Oct 14, 2021

Oct 15, 2021

Oct 20, 2021

Oct 21, 2021

Oct 22, 2021

 

Syllabus in short

  • Real Numbers
  • Real Functions
  • Limits of Sequences
  • Numerical Series
  • Limits of Functions and Continuous Functions
  • Derivatives
  • Applications of Derivatives to the study of Functions
  • Taylor/McLaurin polynomials

 

Teaching Material

It is strongly recommended to take notes during lecttures.

Slides of Lectures and Exercises will be provided by the Professor. Slides do not substitute books; they only provide a rough indication of the material covered in classes.

Suggested books:

Knut Sydsaeter, Peter Hammond and Arne Strom, Essential Mathematics for Economic Analysis

Carl P. Simon, Lawrence Blume, Mathematics for Economists

Available on the webpage of the course and on Teams:

Slides of the course

Additional Exercises

Available on Moodle:

Self-check tests are uploaded on a weekly basis