# 714-0399/01 – Partial Differential Equations (PDR)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 2 Subject guarantor doc. RNDr. Jarmila Doležalová, CSc. Subject version guarantor doc. RNDr. Jarmila Doležalová, CSc. Study level undergraduate or graduate Requirement Optional Year 2 Semester summer Study language Czech Year of introduction 2003/2004 Year of cancellation 2011/2012 Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
DOL30 doc. RNDr. Jarmila Doležalová, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### Subject aims expressed by acquired skills and competences

Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.

### Teaching methods

Lectures
Individual consultations
Tutorials
Project work

### Summary

Fourier series Partial differential equations of the first and the second order. Laplace equation: separated solutions, boundary conditions.Solution of the one- dimensional wave equation: d’Alembert solution, method of the separation of variables, solution of a boundary problem. Solution of the heat-conduction: one dimensional heat conduction equation, separation method.

### Compulsory literature:

James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

### Way of continuous check of knowledge in the course of semester

zápočet Účast ve cvičení je povinná, 20 % neúčasti lze omluvit - hodnocení 5 bodů. Odevzdání programů zadaných vedoucím cvičení v předepsané úpravě: 1. Fourierovy řady - hodnocení 0-15 bodů 2. PDR - hodnocení 0-20 bodů Student, který získá zápočet, bude hodnocen 5 – 40 body. zkouška Kombinovanou zkoušku tvoří praktická část (60 minut, příklady) a teoretická část (20 minut, teoretické otázky). Praktická část je hodnocena 0 - 50 body, teoretická část 0 - 10 body. Aby student u zkoušky uspěl musí získat v praktické části nejméně 25 bodů. klasifikace získané body známka 86 - 100 výborně 66 - 85 velmi dobře 51 - 65 dobře 0 - 50 nevyhověl Otázky k teoretické části zkoušky: 1. Fourierovy řady v reálném oboru - ortogonální systém funkcí, Fourierovy koeficienty 2. Řada sinová a kosinová, konvergence Fourierových řad 3. Parciální diferenciální rovnice - definice, řešení obecné, počátečního a okrajového problému 4. Některé typy PDR I. řádu - rovnice obsahující derivace pouze podle 1 proměnné, 5. PDR lineární a kvazilineární 6. PDR II. řádu - rovnice obsahující derivace pouze podle 1 proměnné, 7. Rovnice, u nichž lze snížit řád 8. Fourierova metoda separace proměnných 9. Lineární PDR II. řádu - klasifikace, charakteristiky 10. Kanonické tvary lineárních PDR II. řádu 11. Laplaceova rovnice - princip maxima a minima, Dirichletova úloha, vlastní čísla a funkce 12. Vlnová rovnice - počáteční problém kmitů struny, fázový tvar řešení 13. Okrajový problém kmitů struny 14. Rovnice vedení tepla - princip maxima a minima, počáteční a okrajová úloha

### Prerequisities

Subject codeAbbreviationTitleRequirement
714-0367 MII Mathematics II Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Syllabus of lecture 1. Fourier series: periodic functions, Fourier coefficients, functions of the period 2, function of the period T, even and odd functions 2. Even and odd functions, half - range cosine and sine series, convergence of Fourier series 3. Solution of 2nd order linear differential equations with constant coefficients by Fourier series 4. Partial differential equations: general discussion 5. Methods of solutions of partial differential equations of the first order 6. Methods of solutions of partial differential equations of the second order 7. Fourier´s method of separation 8. 2nd order partial linear differential equations 9. Canonical form of 2nd order partial linear differential equations 10. Laplace equation: separated solutions, boundary conditions 11. Solution of the one-dimensional wave equation: d’Alembert solution, method of the separation of variables, 12. Solution of a boundary problem 13. Solution of the heat-conduction: one dimensional heat conduction equation, separation method. 14. Reserve

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2009/2010 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 40 (40) 0
Project Project 35  0
Examination Examination 60 (60) 0
Written examination Written examination 50  0
Oral Oral examination 10  0
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2010/2011 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 2 Optional study plan
2010/2011 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 2 Optional study plan
2010/2011 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering P Czech Šumperk 2 Optional study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment (10) Transport Equipment and Technology P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering P Czech Šumperk 2 Optional study plan
2009/2010 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 2 Optional study plan
2009/2010 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 2 Optional study plan
2009/2010 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering P Czech Ostrava 2 Optional study plan
2008/2009 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 2 Optional study plan
2008/2009 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan
2007/2008 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 2 Optional study plan
2007/2008 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan
2006/2007 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 2 Optional study plan
2006/2007 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan
2005/2006 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 2 Optional study plan
2005/2006 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan
2004/2005 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan
2003/2004 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner