Code: mk3mat1a8rx17-en
ECTS Credit Points: 8
Evaluation: mid-semester grade
Year, Semester: 1st year, 1st semester
Its prerequisite(s): -
Further courses are built on it: Yes/No
Number of teaching hours/week (lecture + practice): 4+4
Topics:
The basic notions of linear algebra, differentiation and integration for real functions; some applications in physics.
Literature:
Compulsory:
- Thomas’ Calculus, Addison Wesley (11th edition, 2005), Isbn : 0-321-24335-8
- S. Minton, Calculus Concept and Connections, McGraw Hill (2006), Isbn : 0-07111200-6
| 1st week | 8th week |
|---|---|
| Registration week | 1st drawing week Test 1 |
| 2nd week | 9th week |
| Lecture: Real numbers Axiom system.Boundary, inf, sup, min, max. Dedekind-complete, real line. Distance, neighbourhood, interior point, accumulation point. Intervals. The sets ℝ, ℝ2 , ℝ3 and their geometric interpretations. Natural numbers, integer numbers, rational numbers. Coordinate systems Polar coordinate system. Spherical- and Cylindrical coordinate systems. Practice: Operations of sets, Boole algebra. Logic values, logic operations, logic functions.Cartesian product, 2-tuple, n-tuple.Cardinality. Illustrations of sets on the plane and in the space. | Lecture: Matrices. The arithmetic of matrices, determinants and their properties: operations, the notions of symmetrical matrix, skew-symmetrical matrix, determinant, the inverse matrix. Practice: Matrices. Operations, determinants and inverses with adjoint matrices |
| 3rd week | 10th week |
| Lecture: Sequences of real numbers and their limit. The notion of real sequences. Limits and operations. Some important sequences and their properties. Monotone and bounded sequences. Practice: Vector geomety, vector algebra. The algebra of vectors in 2 and 3 dimensions: operations, coordinate systems. The algebraic definition of the cross product. Geometric interpretations of the scalar product and the cross product. The mixed product. | Lecture: Vector spaces. The notion of linear (or vector) space, linear combinations of vectors, linearly dependent and independent systems, basis, dimension, coordinates.Ranks of vector systems, ranks of matrices Practice: Vector spaces. Linearly independent and dependent systems, bases.Ranks of vector systems, ranks of matrices |
| 4th week | 11th week |
| Lecture: Series of real and complex numbers. Partial sums and convergence. Absolute convergence Geometric series, criteria of convergence. (Comparison test, ratio test, root test). Practice: Applications: Mechanical work, moment of a force with respect to a point, moment of a force with respect to an axis. | Lecture: Systems of linear equations: Gauss elimination (addition method) and Cramer’s rule. Applications: Calculations for direct current using Kirchhoff’s current and voltage laws. Practice: Systems of linear equations: Gauss elimination (addition method) and Cramer’s rule. |
| 5th week | 12th week |
| Lecture: Series of real functions. The notion of series of real functions, the convergence domain, the radius of the convergence.Power series. Power series of some elementary functions. Practice: Vector geomety, vector algebra. Unit vector in the direction of a vector, projections. Geometric applications: lines and planes in the space. The area of a triangle, the volume of a tetrahedron. The distance between a point and a line, or between a point and a plane. | Lecture: Systems of linear equations: by the inverse of the coefficient matrix Practice: Systems of linear equations: by the inverse of the coefficient matrix |
| 6th week | 13th week |
| Lecture: Approximations of real functions. Lagrange interpolation.Linear regression. Practice: The set of thee complex numbers. Complex plane, rectangular form, trigonometric form, exponential form, operations. Application: complex impedance | Lecture: Linear functions. The notion of the linear function, the matrices of linear functions.Eigenvalues, eigenvectors. Practice: Linear functions. Determinations of matrices of linear transformations.Determinations of eigenvalues, eigenvectors. |
| 7th week | 14th week |
| Lecture: Summary, sample test Practice: Sequences of real numbers. Limits and operations. Monotone and bounded sequences, convergence and relations among them. | Lecture: Linear functions. Bases transformations Practice: Linear functions. Bases transformations |
| 15th week | |
| 2nd drawing week Test |
Requirements
A, for a signature:
Participation at practice, according to Rules and Regulations of University of Debrecen. The correct solution of homework and submission before deadline. Solving assorted tasks.
B, for a grade:
All the tests must be written during the semester. Evaluation is according to the Rules and Regulations of University of Debrecen.
Last update:
2023. 10. 16. 15:11