Lecture:

Wednesdays 16:15 - 18:45, Building R, Room R512; and (CHANGED!) Thursdays 18:00-18:45, Building R, Room R513

Practice:

(CHANGED!) Thursdays 16:15 - 17:45, Building R, Room R513

Materials: The lecture does not follow any (English) book, but different topics can be found in the following book:

Thomas' Calculus (edited by J. Hass, C. Heil, D. Weir), 14th Edition, Pearson, 2018.
I. Farago, A. Havasi, I. Mezei, P. Simon: Introductory Course In Analysis, can be downloaded from here . (Chapters 10-12 and 15)
Strang: Introduction to Linear Algebra, 5th Edition, 2016.

Requirements:

1. For the practice part:

During the semester, there are going to be two midterms, 20 points, 90 minutes and 5-5 exercises each.
You need to get 30% (6 points) on each to get a signature.
For the proposed times of the midterms, see the schedule below.

There is also going to be a retake, possibly on the last week (Week 14) and a re-retake on Week 15.
Note though that the points you get on the retake will erase the points of the previous midterm, even if the points are lower.
If your first try was succesful (so you got at least 6 points) but you did not get 6 points on the retake, you will get 6 points for the 2nd one.

2. For the lecture part:

The course ends with a 120-min long written exam.

It has two parts: the first part consists of a test of yes-no questions. The list of all possible questions.

In the second part you will have to solve 5 exercises that will be similar to midterm-exercises.

You can get 60 points on the exam.

Your final points are the sum of your points at the exam and the points of your two midterms.

Mock exam

Grades at the end of the semester: (the points are subjects to modification, but only downwards)

40-54: grade 2
55-69: grade 3
70-84: grade 4
above 85: grade 5

Points

Schedule for the semester:

Week 1	7 September 2022	Lecture	Motivation for matrices: systems of linear equations. Matrices, operations of matrices: sum, product. Determinant.
	8 September 2022	Practice	Matrix operations, determinant.
	8 September 2022	Lecture	Linear dependence of vectors. The rank of a matrix. The inverse of a matrix.
Week 2	14 September 2022	Lecture	University Sports Day (no lecture)
	15 September 2022	Practice	The inverse of a matrix, the rank of a matrix.
	15 September 2022	Lecture	Systems of linear equations: easily solvable cases, row operations and their meaning in case of matrices.
Week 3	21 September 2022	Lecture	Gauss elimination, echelon and reduced echelon form. The connection between Gauss elimination and solutions, rank, determinant. Calculation of the inverse using Gaussian elimination. Theorem about the existence and unicity of solutions. Homogeneous linear equations. Eigenvalues, eigenvectors.
	22 September 2022	Practice	Gauss elimination.
	22 September 2022	Lecture	Similar matrices, diagonalizable matrix. Linear space, examples of linear spaces.
Week 4	28 September 2022	Lecture	Examples of linear spaces, subspace, generated subspace, generating set/span, basis, orthogonal and orthonormal basis. Linear operator and transformation. Matrix of a geometric transformation. Limes, differentiation, and integration as linear operators. Kernel, image, a theorem about dimensions.
	29 September 2022	Practice	Eigenvalues and eigenvectors
	29 September 2022	Lecture	The connection between a linear transformation and an SLAE. Geometric meaning of determinant and its applications: Cramer's rule.
Week 5	5 October 2022	Lecture	Geometric meaning of the determinant and its applications: polinom interpolation, and Vandermonde-determinant. Infinite series: numerical series, convergence, divergence. Famous sequences: 1/n^c, geometric, alternating, positive. Criteria of convergence: Leibniz, ratio, root, integral.
	6 October 2022	Practice	Numerical series I.
	6 October 2022	Lecture	Criteria of convergence: majorant, minorant. Absolute and conditional convergence. Estimation of errors: Leibniz series.
Week 6	12 October 2022	Midterm 16:15-17:45	First midterm Topics: matrices (determinant, inverse, rank), Gauss elimination, eigenvalue and eigenvectors. Solutions, Mock Midterm
	12 October 2022	Lecture 18:00-18:45	No Lecture!
	13 October 2022	Practice	Numerical series II.
	13 October 2022	Lecture	Estimation of errors: positive series. Sequences of functions: pointwise and uniform convergence.
Week 7	19 October 2022	Lecture	Series of functions. Power series: interval of convergence. Taylor series, Taylor polynomial, Taylor series of elementary functions.
	20 October 2022	Practice	Series of functions, Power series. Taylor series.
	20 October 2022	Practice	Taylor series.
Week 8	26 October 2022	Lecture	Application of the Taylor series: calculation of a hard intergral. Fourier series: odd and even functions, rewriting functions into the series form.
	27 October 2022	Practice	Fourier series
	27 October 2022	Practice	Fourier series
Week 9	2 November 2022	Lecture	Application of the Fourier series: computation of famous numerical series. Multivariable functions: basic notions of topology, definition of multivariable functions. Graphical interpretation, continuity. Differentiation: definition of partial derivatives.
	3 November 2022	Practice	Multivariable functions: limit, continuity.
	3 November 2022	Practice	Multivariable functions: partial differentiation.
Week 10	9 November 2022	Lecture	Total derivative, level curve. the connection between the gradient and partial derivatives, geometric meaning. Chain rule, mean value theorem, Theorem of Young, linear approximation. Directional derivative: computation, connection with partial derivatives, geometric meaning. Differentiation of vector-valued functions. Jacobi matrix and determinant. Extrema: local extrema, saddle point.
	10 November 2022	Practice	Multivariable functions: directional derivative, equation of the tangent plane. Local extrema.
	10 November 2022	Practice	Local extrema and its applications.
Week 11	16 November 2022	Lecture	Break issued by the Dean (no lecture).
	17 November 2022	Lecture	Students' Scientific Conference (no lecture/practice)
	17 November 2022	Practice	Students' Scientific Conference (no lecture/practice)
Week 12	23 November 2022	Lecture	Conditional extrema. Multivariable integration: definition of double and triple integrals, properties.
	24 November 2022	Practice	Conditional extrema
	24 November 2022	Lecture	Multivariable integration: integrals above rectangles and normal domains
Week 13	30 November 2022	Practice and Lecture	Multivariable integration. Integral transformations: polar, cylindric and spherical coordinates.
	1 December 2022	Break (4-5 pm)	No Lecture or Practice
	1 December 2022	Midterm (5-7 pm)	Second midterm Topics: Numerical series, Taylor series, Fourier series. Multivariable functions (limit, continuity, differentiation). Tangent plane, local extrema. Solutions, Mock Midterm
Week 14	7 December 2022	Break	The last exercise sheet can be read at home, but it is not part of the exam: Application of multivariable integration.
Week 14	8 December 2022	Midterm (5-7pm)	Midterm retakes Topic: same as the previous midterms.

Mathematics G2

BMETE93BG02

Requirements:

Mock exam

Points

First midterm

Second midterm

Midterm retakes