**Mathematics
A2 (BMETE90AX02). Course Requirements. Spring 2019.**

Lecturer:
*Dr.
Marianna Bolla *(__marib@math.bme.hu__
, +3614631111/5902),*
Dr. Peter Moson*
(__moson@math.bme.hu__
, +3614632690, +36309329626).

*Prerequisites:*
Mathematics A1.

*Detailed
program *(see
e.g. Bulletin – BME).

Mathematics A2a -Vector Functions

Solving systems of linear equations: elementary row operations, Gauss- Jordan- and Gaussian elimination. Homogeneous systems of linear equations. Arithmetic and rank of matrices. Determinant: geometric interpretation, expansion of determinants. Cramer’s rule, Vandermonde determinant. Linear space, subspace, generating system, basis, orthogonal and orthonormal basis, Gram-Schmidt orthogonalization. Linear maps, linear transformations and their matrices. Kernel, image, dimension theorem. Linear transformations and systems of linear equations. Eigenvalues, eigenvectors, similarity, diagonalizability.

Infinite series: convergence, divergence, absolute convergence. Sequences and series of functions, convergence criteria, power series, Taylor series.

Fourier series: expansion, odd and even functions.

Functions in several variables: continuity, differential and integral calculus, partial derivatives, Young’s theorem. Local and global maxima/minima. Vector-vector functions, their derivatives, Jacobi matrix. Integrals: area and volume integral.

6 hours/6 credits.

*Literature:*

THOMAS’CALCULUS by Thomas, G.B. et al. Addison-Wesley, 2005. (ISBN0321185587)

K.F.RILEY,M.P.HOBSON,S.J.BENCE. Mathematical methods for physics and engineering. Cambridge University Press 1998 (reprinted 2000). (ISBN 0 521 55529 9 paperback)

ANTON, H., Elementary Linear Algebra, Wiley, 1987.

*Lectures, practical
lectures.*

On Mondays Dr. Bolla will teach the part “Linear algebra” of the course.

On Wednesdays, Thursdays Dr. Moson will teach the parts “Function of several variables” and “Functional sequences, series”.

*Attendance:***
**

Being absent for more than 30% of the classes will result in denial of the final grade.

*Grading system.*

*Midterm tests. 40%. *

Ms. Bolla’s
part: March 11, 2019. *7%*.,
May
6,
2019. *7%.*

Mr. Moson’s
parts: March 14, 2019. *13%,
*May
2, 2019. *13%*.
The sum of the results of the 4 tests must be at least 12% for the
signature.

*Make up
tests*
(for students whose sum of the midterm tests is less than *12%*):
14-th week (May 13-17, 2019). One
test can be repeated /improved in the week right after the semester
(for extra fee): May 23, 2019.

*Written
exam. 60%. *Only
for students having signature. Dates: May 23, 28, June 4, 12, 2019.

Marks:*
*0-39
fail (1), 40-54 pass (2), 55-69 satisfactory (3), 70-… good (4).

If the sum
of midterm tests and written exam is more than 78% then the student
can take part at an *oral
exam*
for the mark excellent (5).

Home pages of the professors: Google: Bolla Marianna, Moson Péter.

**Good
Luck, Have a Nice Semester!**