1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2019/2020
4. Computer science and econometrics - pierwszego stopnia z tyt. licencjata
5. Analiza matematyczna 1

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Analiza matematyczna 1 - opis przedmiotu

Cel przedmiotu

The purpose of the course is to provide the students with the fundamentals and basic notions of mathematical analysis.

Wymagania wstępne

Zapisz zmiany

High shool course in mathematics.

Zakres tematyczny

Lecture

Elements of logic and review of sets (3 hours)

Real and complex numbers, elementary functions (5 hours)

• The rational numbers, the irrational numbers, the field of real numbers. Complex numbers. Elementary functions. 

Sequences (5 hours)

• Sequences of real numbers. Convergence of sequences. Theorems concerning the limits of sequences. The number "e". Subsequences and their limits. 

Limit of a function, continuity of a function (5 hours)

• The limit of a function and some of its properties. One-sided limits. Theorems on continuity of a function. Properties of continuous functions. Monotonic and convex functions.

Differentiability (12 hours)

• Definition of the derivative. Interpretation of the derivative. Basic properties of differentiable functions. Differentiability versus continuity. de L'Hospital rule. Rules of differentiation. The mean value theorem. Higher order derivatives. Taylor's theorem. Extrema of functions. Polynomial approximation.

Class

Elements of logic and review of sets (2 hours)

Real and complex numbers, elementary functions (6 hours)

• Proving simple equalities and inequalities by means of mathematical induction. Solving some equations with absolute values. Examples of functions applied in econometrics.

Sequences (4 hours)

• Calculation of limits using various methods. Exercises with sequences related to "e" number. Discussion of cases when a sequence has no limit.

Limit of a function, continuity of a function (6 hours)

• Calculation of limits of functions. Left- and right-hand limits of functions. Continuity of a function at a given point and on an interval. Continuous and discontinuous functions.

Differentiability

• Calculation of derivatives of functions at a point from the definition and elementary rules. Study of monotonicity of some functions. Application of de L'Hospital rule in calculations of some limits. Search of local and global extrema of functions.

Metody kształcenia

Traditional lecture - the teacher conducts a lecture, provides theory and examples.

Class: Students, led by the teacher, solve exercises and discuss problems.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Class.

The final grade for the class is issued on the basis of the points obtained from three written tests (with tasks of various difficulty levels, allowing to check whether the student achieved the learning outcomes to a minimum degree) and for active participation in classes.

Lecture.

The condition for taking the exam is a positive grade from the class. The exam verifies the learning outcomes in terms of knowledge and skills. The exam consists of two parts: written and oral. The condition for joining the oral part is to obtain 30% of the points in the written part. Obtaining 50% of the points in the written part guarantees a positive assessment.

The grade for the subject consists of an class grade (50%) and an exam grade (50%).

The condition for passing the course is a positive exam grade.

Literatura podstawowa

1. S.Ponnusamy, Foundatins of Mathematical Analysis, Birkhauser, 2012.
2. J. Stewart, Single variable calculus, Brooks/Cole, 2012.

 

Literatura uzupełniająca

1. W. Krysicki, L. Włodarski, Analiza matematyczna w zadaniach, PWN, W-wa, 2008.
2. R. Rudnicki, Wykłady z analizy matematycznej, PWN, W-wa, 2006.

Uwagi

Zmodyfikowane przez dr Alina Szelecka (ostatnia modyfikacja: 21-11-2020 06:10)