Code: mk3mat2a6rx17-en
ECTS Credit Points: 6
Evaluation: mid-semester grade
Year, Semester: 1st year, 2nd semester
Its prerequisite(s): Mathematics I
Further courses are built on it: Yes/No
Number of teaching hours/week (lecture + practice): 2+4
Topics:
Differentiation and integration of multivariable and vector-valued functions, differential equations.
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
- M. D. Greenberg, Fundamentals of engineering analysis, Cambridge University Press, Isbn 978-0-521-80526-1
| 1st week | 8th week |
|---|---|
| Registration week | 1st drawing week Test 1,2 |
| 2nd week | 9th week |
| Lecture: Metric, topology, sequences in Rn. Linear functions. Practice: Limits of vectorsequences. Limits and continuity of multivariable functions. Linear functions. Notions of differential equations, classification of differential equations, initial value problem. | Lecture: Local and global extrema. Practice: Local extremas of functions of type. R2-R,R3-R |
| 3rd week | 10th week |
| Lecture: Parametric curves I. Notions of differentiation, linear approximation. Frenet-Serret frame. Some examples in physics Practice: Differentiation, linear approximation, tangent line. Applications: velocity, acceleration. Problems leading to differential equations. (Newton’s second law, Rlc, examples in economics). | Lecture: Vector fields. Derivatives. Divergence and curl. Potential function. Practice: Determination of global extremas on boundary closed sets. Solution of linear homogeneous differential equations of order two having constant coefficients. |
| 4th week | 11th week |
| Lecture: Parametric curves II. Curvature, torsion. Evolute, evolvent, conic sections. Practice: Curvature, torsion. Determinations of conic sections in parametric form. Differential equations which can be integrated on direct way. Separable differential equations. | Lecture: The notion of double and triple integrals on 2 and 3 dimensional intervals. The extensions of the integrals. Practice: Vector fields. Derivatives. Divergence and curl. Potential function. Method of undetermined coefficients. |
| 5th week | 12th week |
| Lecture: Differentiable functions of type Rn-Rn. Practice: Derivatives of functions of type Rn-Rm. First order linear differential equations (homogeneous and inhomogeneous, method of variation). | Lecture: Integrals over general regions. Applications: second moment of area, mass, center of gravity Practice: Double and triple integrals on 2 and 3 dimensional intervals. Special second order differential equations. |
| 6th week | 13th week |
| Lecture: Parametric surfaces. Tangent plane, linear approximation. Surfaces of revolution, ruled surfaces. Practice: Surfaces of revolution: ellipsoid and paraboloid in parametric form. Derivatives of functions of type R2-R3.The equation of the tangent plane. Determination of solutions of inhomogeneous first order linear differential equations | Lecture: The arc length of curves, surface area. Line and surface integrals. The theorems of Gauss and Stokes, Green’s formulae. Applications in physics. Practice: Integrals over general regions. Applications: second moment of area, mass, center of gravity. The theorems of Gauss and Stokes, Green’s formulae. Applications in physics. The Laplace transform and its applications. |
| 7th week | 14th week |
| Lecture: Scalar field, gradient. Young's theorem. Directional derivative. Practice: The domains of functions of type R2-R. Directional derivative and gradient. Higher order linear differential equations, Wronski determinant. | Lecture: Mathematical softwares Practice: The arc length of curves, surface area. Line and surface integrals. Slope fields, numerical methods. (Euler, Runge-Kutta). |
| 15th week | |
| 2nd drawing week Test 3, 4 |
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