Óbuda University, Donát Bánki Faculty of
Institute of Mechatronics and Autotechnique
Mechanical and Safety Engineering
Course name and code: Mathematics II. BGRMA2ENND
Credits: 6
Regular course 2014-2015, Semester II.
Course leaders:
Bércesné dr. Novák
Ágnes, dr. Hanka László
Prerequisits
Weekly contact
hours:
Evaluation type
Lecturer and
seminar teacher:
Bércesné dr. Novák
Ágnes
Mathematics I. BGRMA1ENND
Lectures: 3
Seminars: 2
Lab: 0
exam
Goals: : In this course students learn the most important topics of mathematics. Through the
learning proccess they develop their problem-solving skills and abstraction ability. In the
seminars they let solve problems in connection to the theory they learnt in the lectures.
After completing this course, students should have developed a clear understanding of the
fundamental concepts of single and multivariable variable calculus, linear algebra basics,
differenetial equations and probability theory. Students will have a range of skills allowing them
to work effectively with the concepts.
The basic concepts are:
-
partial and total derivatives
global and local extrema in case of multivariable functions
classical notion of probability
random variables and their distributions
basic statistics
notion of differential equations (De)
De solving methods
solving linear system of equations
notion and application of matrices and determinants
eigenvalues and eigenvectors
Weeks
1.
2015.02.11.-12
2.
2015.02.18-19.
3.
2015.02.25-26.
4.
Schedule and Syllabus
Topics
Linear algebra II: Inverse of a matrix. Solving system of linear equations by Gaussian , and
Jordan elimination.
Linear algebra III:
Eigenvalues, eigenvectors.
Determinants.
Introduction to Multivariable Functions I.
Notion of a multivariable function. Partial derivatives.
Introduction to Multivariable Functions II.
Differential of a function of several variables. Applications.
Numerical series
Sum of an infinite series. Convergent, divergent series. The harmonic series. Absolute
2015.03.03.
convergent series. Tests for convergence. The convergence of the series
1
n
p
Functional series I.
Notion of a functional series. Convergence interval. Differentiating and integrating power
series.
5.
Functional series II.
Power series: Taylor and MacLaurin expansion of a function. Remainder term.
2015.03.10.
Differential equations I.
Notion of a DE.Separable Des.
6.
2015.03.18.-19.
7.
2015.04. 1.-2.
Differential equations II.
First order homogenous Des. First order inhomogenous Des. Empirical method and constant
variation. Second order linear homogenous Des with constant coeffitiens.
MIDTERM TEST I
Differential equations III.
Homogeneous linear Des with constant coefficients. Second order inhomogeneous Des with
constant coefficients.
Laplace-transformation (in lack if time this part may be skipped)
Solving first order and second order Des with constant coefficient using Laplace tarnsformation.
8.
2015.04.8-9.
9.
2015.04.15-16.
10.
2015.04.22-23.
11.
2015.04.29-30.
12.
2015.05.6-7.
13.
2015.05.13-14.
Introduction to Probability theory I
Combinatorics.
Events algebra. Kolmogorov's Classical Probability Calculus.
Introduction to Probability theory II
Conditional probability, Bayes-theorem.
Introduction to Probability theory III
Discrete and contnupus random variables. Expected value and standard deviation.
Distribution function.
Introduction to Probability theory IV
Discrete distributions: Binomial, Hioergeometrical, Poisson.
Continuous distributions: Normal, Exponential.
Statistics
Sampling. Estimation, testing statistical hypothesis.
MIDTERM TEST 2
Consolidation.
Assignments
During the academic year:
For getting the signature:
2 Midterm tests (planned: week 7) each 20 points
10 quizzes up to 10 points
In the exam period: Final exam
Getting the signature:
Attendance is mandatory:
You supposed to visit each lecture and seminar. If you are ill, you supposed to get a medical
certificate by your GP. If you miss more than 30% of the lectures, or seminars, then you fail, and
have to take the course again.
Regarding to the assignments:
You must reach 50% of the points on each midterm exam and each topic. If you miss that criteria,
you may write the worst test from the 2 again (This one is not the reset test yet: just one more
chance for improving your knowledge and points. However, you may degrade your result as well).
Exact date and time will be advertised later in lectures.
Altogether you must reach 25 points from the possible 50 (20+20+10) on the exams.
If you have less points than 25, you need to write a reset exam! There will be only one date
for that!
MIDTERMS RESET: 12 MAY 2015
With a successful reset exam you will have exactly 25 points.
EXAMS
Students, who are not able to reach the 25 points even not with the reset, will have a
FORBIDDEN note in the system, and are not allowed to take the final exam. They may take
the course next spring.
Students with 25 points or more are going to write the final exam in the exam period. 50
points can be got on this final exam.
The grade is composed from 2 sources: sum of points achieved during the academic year and
the points on the final exam will be added.
Regarding to this sum, the grades are:
0- 39 % failed (1)
40 - 54 % satisfactory (2)
55 - 69 % average (3)
70 - 85 % good (4)
85 - 100 % excellent (5)
Lecture notes in English:
Web material will be posted regularly. Course web-page:
http://digitus.itk.ppke.hu/~b_novak/BANKI/
Erwin Kreiszig: Advanced engineering mathematics, 2012, 10th Edition,
Wileyplus.com
Stroud: Engineering Mathematics
in Hungarian:
1. Kovács J.-Takács G.-Takács M.: Analízis, NTK 1998
or
2. Rudas I.-Hosszú F.: Matematika I., BMF BDGFK L-544, Bp. 2000
3. Rudas I.-Lukács O.-Bércesné Novák Á.-Hosszú F.: Matematika II., BMF
BDGFK L-543, Bp. 2000
4. Sréterné Lukács Zs. szerk. : Matematika Feladatgyűjtemény, BMF KKVFK
1190, Bp. 2000
or
5. Scharnitzky V. szerk. : Matematikai feladatok, NTK 1996
Suggested readings in Hungarian:
Szász Gábor: Matematika I-II-III.: NTK 1995
Bárczy Barnabás: Differenciálszámítás Műszaki KK, 1995
Bárczy Barnabás: Integrálszámítás Műszaki KK 1995
Other sources:
http://digitus.itk.ppke.hu/~b_novak/BANKI/
Budapest, 10 of February 2015.
………………………………
Bércesné dr. Novák Ágnes
lecturer