Mathematical Analysis 1 WS-EKN-AM1
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,
Subject level
Learning outcome code/codes
Bibliography
M. Skwarczyński, Istota struktury formalnej, Wyd SGGW
A. Chiang, Podstawy ekonomii matematycznej, PWN Warszawa
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