Z-EKO-476. Analiza matematyczna. Economics 1st degree (1st degree / 2nd degree) General (general / practical)

Transkrypt

1 Projekt współfinansowany ze środków Unii Europejskiej w ramah Europejskiego Funduszu Społeznego MODULE DESCRIPTION Module ode Z-EKO-476 Module name Analiza matematyzna Module name in English Mathematial Analysis 1 Valid from aademi year 2012/13 MODULE PLACEMENT IN THE SYLLABUS Subjet Level of eduation Studies profile Form and method of onduting lasses Speialisation Unit onduting the module Module o-ordinator Eonomis 1st degree (1st degree / 2nd degree) General (general / pratial) Full-time (full-time / part-time) All The Department of Mathematis Mateusz Masternak, PhD Approved by: MODULE OVERVIEW Type of subjet/group of subjets Module status Language of onduting lasses Module plaement in the syllabus - semester Subjet realisation in the aademi year Initial requirements Examination Number of ECTS redit points 6 Method of onduting lasses Basi (basi / major / speialist subjet / onjoint / other HES) Compulsory (ompulsory / non-ompulsory) Polish 1st semester Winter semester (winter / summer) No requirements (module odes / module names) Yes (yes / no) Per semester Leture Classes Laboratory Projet Other TEACHING RESULTS AND THE METHODS OF ASSESSING TEACHING RESULTS

2 Projekt współfinansowany ze środków Unii Europejskiej w ramah Europejskiego Funduszu Społeznego Module target The aim of the module is to familiarise students with basi notions and theorems onerning differential and integral aluli of one real variable funtion as well as to develop the skills of applying the learnt mathematial apparatus to desribe and solve simple issues as regards eonomy being part of simple mathematial modelling. Effet symbol Teahing results Teahing methods (l//l/p/other) Referene to subjet effets Referene to effets of a field of study A student knows basi notions of differential and integral aluli (one-variable funtions) and appropriate mathematial symbols. A student knows standard proedures onerning suh issues as funtion analysis, determining primitive funtion using definite integrals, the issues of approximation, and marginal analysis. A student understands abstrat mathematial analysis (e.g. rossing limits and infinitesimal alulus). A student has suffiient alulation effiieny as regards typial tasks of mathematial analysis (alulating the limit, differentiation, funtion analysis, integration, et.) A student an also failitate operation with a omputer alulation program. A student an apply the learnt mathematial tools to solve simple issues referring to the dynamis of eonomi phenomena and interpret the obtained results. A student an use the mathematial language and orretly write the performed mathematial operations using appropriate symbols. A student is able to present his/her viewpoint (his/her manner of thinking) and defend it using fatual arguments in the disussion. A student an notie the neessity of improving his/her knowledge as regards the methods of applied mathematis depending on the needs of his/her professional work. l l/ l/ K_U02 K_U04 K_U04 K_K08 K_K01 K_K05 S1A_U02 S1A_U02 S1A_U04 S1A_U05 S1A_K06 S1A_K06 Teahing ontents: Teahing ontents as regards letures Leture number Teahing ontents The set of real numbers (operations and inequalities). Bounded sets. Powers with integral exponents. Newton s binomial. Absolute value. The notion of a funtion. Numeri funtions of a real variable. Periodi, even, odd, bounded, and monotone funtions. Composite funtions. One-to-one mapping. Inverse funtions. A review of elementary funtions (polynomials, rational funtions, exponential and logarithmi funtions, information on hyperboli funtions, trigonometri and ylometri funtions). The limit and funtion ontinuity. Calulus theorems on funtion limits. Asymptotes of a funtion. Theorems on ontinuous funtions: the Weierstrass Referene to teahing results for a module

3 Projekt współfinansowany ze środków Unii Europejskiej w ramah Europejskiego Funduszu Społeznego 5 6 extreme value theorem and Darboux s theorem on intermediate values. Derivative. Physial and geometri interpretation. The priniples of differentiation. The derivative of the inversible funtion. Derivatives of elementary funtions. Derivatives of a higher order. The Fermat lemma; Rolle s theorem; Langrange s and Cauhy s theorems on inrements and their appliation in funtion property researh (monotoniity, extremes, and onvexity). Determining extreme values of a ontinuous funtion in a losed interval as well as differential funtion within the losed interval. The appliations in eonomy onerning optimization issues. 7 L Hopital s rules. Investigating the ourse of funtion variability. 8 Taylor s formula. Appliations in approximate alulations Definite integral of a ontinuous funtion. The relation with the notion of the area. Basi properties. The examples of estimations for integrals. Primitive funtion. Indefinite integral. Fundamental theorems of differential and integral aluli. Determining primitive funtions. Basi formulas. The methods of integration by parts and by substitution. The distribution of a rational funtion into partial frations. Integration of rational funtions. 13 Integrating ertain types of funtions with irrational expressions. 14 Integrating trigonometri funtions. 15 Definite integral alulating. Appliations in geometry and eonomy. Teahing ontents as regards lasses Class number Teahing ontents Referene to teahing results for a module 1 Transforming algebrai expressions. Solving equations and inequalities in a real domain. 2. Preparing diagrams of elementary funtions and desribing the properties of these funtions on the basis of the diagram. 3. Calulating funtion limits. Determining asymptotes of a rational funtion. 4. Calulating funtion derivative, inluding a derivative of a omposite funtion derivative. 5. Investigating the ourse of funtion variability. 6. Approximate alulations by substituting differential for the inrement of a funtion; the assessment of result auray. 7. Simple optimisation issues resulting in searhing the funtion extreme. Boundary values and the elastiity of a funtion present in eonomi appliations. 8. Determining a primitive funtion based on integration formulas by parts and by substitution. 9. Calulating the integrals of rational funtions by distribution into partial

4 Projekt współfinansowany ze środków Unii Europejskiej w ramah Europejskiego Funduszu Społeznego frations. 10. Calulating definite integrals. Appliations of integral alulus to determine boundary values in eonomy. The methods of assessing teahing results Effet symbol Methods of assessing teahing results (assessment method, inluding skills referene to a partiular projet, laboratory assignments, et.) A final test and a written examination. Ative partiipation in the lasses; a redit test and a written examination. A student s initiative and ative partiipation in a disussion the lasses. A final test and a written examination; a projet assignment. A final test and a written examination. Ative partiipation in a disussion during the lasses and a written examination; a projet assignment. Ative partiipation in a disussion during the lasses. Ative partiipation in a disussion during the lasses. STUDENT S INPUT Type of student s ativity ECTS redit points Student s workload 1 Partiipation in letures 30 2 Partiipation in lasses 20 3 Partiipation in laboratories 4 Partiipation in tutorials (2-3 times per semester) 10 5 Partiipation in projet lasses 6 Projet tutorials 13 7 Partiipation in an examination Number of hours requiring a leturer s assistane 10 Number of ECTS redit points whih are alloated for assisted work 11 Unassisted study of leture subjets Unassisted preparation for lasses Unassisted preparation for tests Unassisted preparation for laboratories Preparing reports 16 Preparing for a final laboratory test 17 Preparing a projet or doumentation 18 Preparing for an examination Preparing a projet assignment (sum) 20 Number of hours of a student s unassisted work 75 (sum) 21 Number of ECTS redit points whih a student reeives for unassisted 3

5 Projekt współfinansowany ze środków Unii Europejskiej w ramah Europejskiego Funduszu Społeznego work 22 Total number of hours of a student s work ECTS redit points per module 1 ECTS point=25-30 hours 6 24 Work input onneted with pratial lasses Total number of hours onneted with pratial lasses Number of ECTS redit points whih a student reeives for pratial lasses 4.8