Mathematical Analysis 1

General data

Course ID:	WS-EKN-AM1
Erasmus code / ISCED:	(unknown) / (unknown)
Course title:	Mathematical Analysis 1
Name in Polish:	Analiza matematyczna 1
Organizational unit:	Institute Sociology
Course groups:
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Subject level:	elementary
Learning outcome code/codes:	enter learning outcome code/codes
Short description:	Level: Basic Objectives: After completing the course, students will be able to use basic analytical methods (sequences, series and derivatives) in economics and finance. Prerequisites: none
Full description:	1) Subsets of the set of real numbers. Mathematical induction. Sequences, limits 2) Theorems about sequences. Euler number e. Newton's binomial formula. The average (arithmetic, geometric and harmonic). Inequalities between them. Recurrence sequences. Linear recurrence equations of degree 1. 3) Series. The sum of the series. A geometric series. A necessary condition of convergence. Harmonic series. Absolutely convergent series and relatively convergent series. Convergence criteria (d'Alembert, Cauchy, and Leibniz). Examples. 4) Real functions of one real variable. Linear function, quadratic and polynomial functions. Exponential function. Trigonometric functions. Exponential and logarithmic function. The natural logarithm. The limit of a function, continuous functions. Limits at infinity. Basic limits. 5) Derivative of the function. Formulas for derivatives of the functions discussed in the previous lecture. Derivatives of sum, difference, product and quotient of functions. Derivative of composite functions. Leibniz formula. Examples of calculations. Derivatives of higher orders. 6) Applications of derivatives. Extremes of function. Fermat's principle. Rolle's and Lagrange's theorems. Monotonicity intervals. Convexity intervals. Asymptotes. Testing of a function. Applications in economics (elasticity of a function, price elasticity of demand, the Economic Order Quantity). Taylor's formula. Passing conditions: test during the workshop,
Bibliography:	M. Skwarczyński, Istota struktury formalnej, Wyd SGGW A. Chiang, Podstawy ekonomii matematycznej, PWN Warszawa

This course is not currently offered.

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