151-0444/02 – Differential and Difference Equation (DifDif)
Gurantor department | Department of Mathematical Methods in Economics | Credits | 5 |
Subject guarantor | prof. RNDr. Dana Šalounová, Ph.D. | Subject version guarantor | RNDr. Alena Poloučková |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 1 | Semester | winter |
| | Study language | Czech |
Year of introduction | 2006/2007 | Year of cancellation | 2009/2010 |
Intended for the faculties | EKF | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
Differential and Difference Equation
Knowledge
• collect the basics of differential and difference equations theory
• recognize individual types of differential equations covered in this course
Comprehension
• identify these equations according to their level and grade
• solve linear differential and difference equations with a special right side
Application
• demonstrate interdependencies of certain economical quantities (or systems) at time
• develop tools for further studies of differential and difference equations
Analysis
• calculate difference sequences at a point
• separate equations according to their grade and type
Synthesis
• assemble discrete cobweb models
• formulate conditions for economic equilibrium
Evaluation
• interpret general and particular solutions of basic types of differential and difference equations
• explain discrete and continues dynamical models
• argue difference sequences
Teaching methods
Lectures
Individual consultations
Summary
The aim of this course is to acquaint students with the basic types of differential and difference equations which are a means and tools for analysis of changes of economic variables over time. Attention is also given to some applications in geometry and economics.
Compulsory literature:
Study materials created for this course are available through the Moodle system.
Recommended literature:
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Osnova předmětu:
Úvodem
I. část - Diferenciální rovnice
1. Základy teorie obyčejných diferenciálních rovnic
2. Diferenciální rovnice se separovanými a separovatelnými proměnnými
3. Homogenní diferenciální rovnice
4. Lineární diferenciální rovnice 1. řádu
5. Bernoulliova diferenciální rovnice
6. Exaktní diferenciální rovnice
7. Některé aplikace v geometrii a ekonomii
8. Lineární diferenciální rovnice 2. řádu s konstantními koeficienty
9. Lineární diferenciální rovnice n - tého řádu
II. část - Diferenční rovnice
1. Základní pojmy teorie diferenčních rovnic
2. Lineární diferenční rovnice s konstantními koeficienty a speciální
pravou stranou
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.