Course
MA2 - Mathematics 2
PDF Course Catalog Deutsche Version: MA2
Version: 1 | Last Change: 24.09.2019 16:56 | Draft: 0 | Status: vom verantwortlichen Dozent freigegeben
| Long name | Mathematics 2 |
|---|---|
| Approving CModule | MA2_BaET |
| Responsible |
Prof. Dr. Christoph Bold
Professor Fakultät IME |
| Level | Bachelor |
| Semester in the year | summer semester |
| Duration | Semester |
| Hours in self-study | 120 |
| ECTS | 10 |
| Professors |
Prof. Dr. Christoph Bold
Professor Fakultät IME |
| Requirements | Knowledge of school mathematics to achieve university entrance as well as logical thinking. Modul MA1 |
| Language | German |
| Separate final exam | Yes |
Literature
L. Papula, Mathematik für Ingenieure und Naturwissenschaftler, Band 1 und 2, Vieweg+Teubner Verlag
Final exam
Details
The exam sets tasks from the area of the analysis of one and several variables, including ordinary differential equations, which shall be solved without tools (or if necessary with a given collection of formulas). On the one hand, the correctness of the approach, respectively the solution, is evaluated. It also assesses the extent to which symbolic and formal mathematical language is used correctly.In order to take part in the summary examination at the end (written exam), students must first prove that they have satisfactorily completed the exercises, which are usually held on a weekly basis.
Minimum standard
Students- Show that they understand simple mathematical statements and can comprehend simple given proofs
- Can explain and apply the most important concepts of analysis
- Can solve simple tasks of known type from the field of analysis without electronic aids. The written representation of the solution and the way to solve it is done in the formal language of mathematics and uses the correct mathematical symbols.
Exam Type
The exam sets tasks from the area of the analysis of one and several variables, including ordinary differential equations, which shall be solved without tools (or if necessary with a given collection of formulas). On the one hand, the correctness of the approach, respectively the solution, is evaluated. It also assesses the extent to which symbolic and formal mathematical language is used correctly.In order to take part in the summary examination at the end (written exam), students must first prove that they have satisfactorily completed the exercises, which are usually held on a weekly basis.
Learning goals
Knowledge
Differential calculus: definition of the derivative, tangent, derivatives of elementary functions, derivation rules, monotony, higher derivatives, Taylor polynomial, elements of the curve discussion, rule of de l'Hospital, Taylor series and power series
Higher complex functions and complex equations
Integral calculus: Definition of the Riemann integral, main theorem of differential and integral calculus, basic integrals, partial integration, substitution rule, partial fraction decomposition, improper integrals, multidimensional integration in Cartesian coordinates and in polar coordinates.
Ordinary Differential Equations: Differential equations of first order, linear differential equations of second order with constant coefficients.
Functions of several variables: limit and continuity, partial derivatives, extreme values, total differential, error propagation.
Higher complex functions and complex equations
Integral calculus: Definition of the Riemann integral, main theorem of differential and integral calculus, basic integrals, partial integration, substitution rule, partial fraction decomposition, improper integrals, multidimensional integration in Cartesian coordinates and in polar coordinates.
Ordinary Differential Equations: Differential equations of first order, linear differential equations of second order with constant coefficients.
Functions of several variables: limit and continuity, partial derivatives, extreme values, total differential, error propagation.
Skills
The students master the handling of complex functions.
They master the Riemann integral and can estimate integral values. They use the law of differential and integral calculus and the most important integration rules for calculating integrals.
They are able to solve linear differential equations of first order and second order with constant coefficients.
You can calculate partial derivatives for functions of several variables and determine their extremes.
They master the Riemann integral and can estimate integral values. They use the law of differential and integral calculus and the most important integration rules for calculating integrals.
They are able to solve linear differential equations of first order and second order with constant coefficients.
You can calculate partial derivatives for functions of several variables and determine their extremes.
Expenditure classroom teaching
| Type | Attendance (h/Wk.) |
|---|---|
| Lecture | 5 |
| Exercises (whole course) | 3 |
| Exercises (shared course) | 2 |
| Tutorial (voluntary) | 2 |
Special literature
keine/none
Special requirements
none
Accompanying material
Lecture notes printed and electronic
Exercises with solutions only electronic
Exercises with solutions only electronic
Separate exam
Exam Type
solving exercises within limited functional / methodical scopeDetails
Presence exercises and self-learning exercises, see also exam concept of summary final examMinimum standard
50% of the maximum achievable credit points
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