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!