|
|
Main menu for Browse IS/STAG
Course info
KMA / M2E
:
Course description
Department/Unit / Abbreviation
|
KMA
/
M2E
|
Academic Year
|
2023/2024
|
Academic Year
|
2023/2024
|
Title
|
Mathematics 2
|
Form of course completion
|
Exam
|
Form of course completion
|
Exam
|
Accredited / Credits
|
Yes,
4
Cred.
|
Type of completion
|
Combined
|
Type of completion
|
Combined
|
Time requirements
|
Lecture
2
[Hours/Week]
Tutorial
2
[Hours/Week]
|
Course credit prior to examination
|
Yes
|
Course credit prior to examination
|
Yes
|
Automatic acceptance of credit before examination
|
No
|
Included in study average
|
YES
|
Language of instruction
|
Czech, English
|
Occ/max
|
|
|
|
Automatic acceptance of credit before examination
|
No
|
Summer semester
|
232 / -
|
0 / -
|
0 / -
|
Included in study average
|
YES
|
Winter semester
|
0 / -
|
0 / -
|
0 / -
|
Repeated registration
|
NO
|
Repeated registration
|
NO
|
Timetable
|
Yes
|
Semester taught
|
Summer semester
|
Semester taught
|
Summer semester
|
Minimum (B + C) students
|
1
|
Optional course |
Yes
|
Optional course
|
Yes
|
Language of instruction
|
Czech, English
|
Internship duration
|
0
|
No. of hours of on-premise lessons |
|
Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
|
Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
|
Fundamental theoretical course |
No
|
Fundamental course |
No
|
Fundamental theoretical course |
No
|
Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
|
None
|
Preclusive courses
|
N/A
|
Prerequisite courses
|
N/A
|
Informally recommended courses
|
N/A
|
Courses depending on this Course
|
N/A
|
Histogram of students' grades over the years:
Graphic PNG
,
XLS
|
Course objectives:
|
The course goal is to acquaint the students with basic types of ordinary differential equations, with phenomena described by these equations, and with methods of solving these equations. We emphasize the fundamental methods of solving linear initial and boundary value problems, including the Laplace transform, and power and Fourier methods based on the theory of function series.
|
Requirements on student
|
Use rigorous arguments in calculus and be able to apply them in solving problems on the topics in the syllabus.
Credit: written tests during the term (required at least 60%)
Exam: witten and oral part.
|
Content
|
Week 1: ODEs of the 1st order, nonlinear, linear. Physical motivation (RC circuit). General and particular solutions, singular solutions. Formulation of the initial value problem.
Week 2: Methods of solving ODEs of the 1st order: direct integration, separation of variables, variation of parameters. First order linear ODEs. Physical motivation (RL circuit).
Week 3: Linear ODEs of higher orders - homogeneous, nonhomogeneous, with constant coefficients. Physical motivation (RLC circuit) Method of characteristic equation.
Week 4: Variation of parameters. Estimate of particular integral.
Week 5: Systems of ODEs of the 1st order. Physical motivation (inductively connected RL circuits). Vector functions of one real variable (limit, continuity, derivative, parametric curves).
Week 6: Systems of ODEs of the 1st order. Fundamental matrix. Variation of parameters.
Week 7: Boundary value problems. Eigenvalue problems.
Week 8: Direct Laplace transform with a real parameter and its proerties.
Week 9: Inverse Laplace transform.
Week 10: Application of Laplace transform to initial value problems for ODEs. Fourier transform.
Week 11: Taylor series.
Week 12: Fourier series.
Week 13: Recapitulation.
|
Activities
|
-
Link to: CourseWare:
KMA/M2E
-
Link to Google Classroom: :
Rozvrhová akce KMA/M2E (2023/24, LS) - Pá 08:25-10:05, EU-307
-
Link to Google Classroom: :
Rozvrhová akce KMA/M2E (2023/24, LS) - Pá 08:25-10:05, UC-235
-
Link to Google Classroom: :
Rozvrhová akce KMA/M2E (2023/24, LS) - Pá 12:05-13:45, EP-206, Týden: 6
-
Link to Google Classroom: :
Rozvrhová akce KMA/M2E (2023/24, LS) - Pá 12:05-13:45, EU-307
-
Link to Google Classroom: :
Rozvrhová akce KMA/M2E (2023/24, LS) - Pá 12:05-13:45, UC-237
-
Link to Google Classroom: :
Rozvrhová akce KMA/M2E (2023/24, LS) - Po 13:55-15:35, EU-109
|
Fields of study
|
Studentům je k dispozici kurz v Google Classroom se všemi podstatnými informacemi a materiály.
Elektronická skripta P. Tomiczek - http://home.zcu.cz/~tomiczek/Data/MA2.pdf
|
Guarantors and lecturers
|
-
Guarantors:
Doc. Ing. Josef Daněk, Ph.D. (100%),
-
Lecturer:
Doc. Ing. Josef Daněk, Ph.D. (100%),
RNDr. Petr Tomiczek, CSc. (100%),
-
Tutorial lecturer:
Doc. Ing. Josef Daněk, Ph.D. (100%),
Ing. Hana Kopincová, Ph.D. (100%),
RNDr. Milena Šebková (100%),
RNDr. Mgr. Jakub Teska, Ph.D. (100%),
RNDr. Petr Tomiczek, CSc. (100%),
|
Literature
|
-
Extending:
almamather.zcu.cz/m2e
-
Recommended:
Coddington, Earl; Carlson, Robert. Linear ordinary differential equations. Philadelphia, 1997. ISBN 0-89871-388-9.
-
Recommended:
Matematická analýza II
(Tomiczek, Petr)
-
Recommended:
Kufner, Alois. Obyčejné diferenciální rovnice. 1. vyd. Plzeň : Západočeská univerzita, 1993. ISBN 80-7082-106-X.
-
Recommended:
Míka, Stanislav; Kufner, Alois. Okrajové úlohy pro obyčejné diferenciální rovnice. 2. upr. vyd. Praha : SNTL - Nakladatelství technické literatury, 1983.
-
Recommended:
Nagy, Jozef. Soustavy obyčejných diferenciálních rovnic : Vysokošk. příručka pro vys. školy techn. směru. 2., nezm. vyd. Praha : SNTL, 1983.
-
On-line library catalogues
|
Time requirements
|
All forms of study
|
Activities
|
Time requirements for activity [h]
|
Preparation for an examination (30-60)
|
32
|
Contact hours
|
52
|
Preparation for formative assessments (2-20)
|
20
|
Total
|
104
|
|
Prerequisites
|
Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
state the Taylor's theorem |
describe the derivative and the integral of a real-valued function of one real variable |
describe a sequence and a series of real numbers |
describe a continuous function and the inverse function |
use actively vectors and matrices |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
calculate derivatives and integrals of basic functions of one real variable |
draw the graphs of inverse functions; algebraic functions; goniometric functions; exponential and hyperbolic functions |
establish convergence and divergence of a sequence, a series, and an integral |
calculate the determinant of a matrix |
find eigenvalues and eigenvectors of a matrix |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
|
Learning outcomes
|
Knowledge - knowledge resulting from the course: |
formulate the basic initial and boundary value problems for ODEs |
define Laplace transform and describe its properties |
define Fourier transform |
define Taylor and Fourier series of a function |
describe a vektor-valued function of one real variable and a parametric curve |
Skills - skills resulting from the course: |
solve ODEs of the first order |
solve linear ODEs of higher orders with constant coefficients |
solve systems of linear ODEs of the first order with constant coefficients
|
apply the Laplace transform to solve the initial value problems. |
apply ordinary differential equations and their solutions to real problems |
solve the boundary value problems |
find the Taylor and Fourier expansion of basic functions |
Competences - competences resulting from the course: |
N/A |
N/A |
|
Assessment methods
|
Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Test |
Skills demonstration during practicum |
Skills - skills achieved by taking this course are verified by the following means: |
Oral exam |
Written exam |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Oral exam |
|
Teaching methods
|
Knowledge - the following training methods are used to achieve the required knowledge: |
Interactive lecture |
Practicum |
Skills - the following training methods are used to achieve the required skills: |
Practicum |
Task-based study method |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
|
|
|
|