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ME-AEM1

1.0

## Offered by

Mechanical Engineering

## ECTS

5

### Prerequisites

ME-MAT1 and ME-MAT2 or similar

### Main purpose

The purpose of this course is to give students a mathematical foundation for studying mechanical engineer-ing beyond the Bachelor level. The focus is on a comprehensive introduction to partial differential equations and methods for their solution.

### Knowledge

After completing this course the student must know:
* How differential equations are used in the modelling of physical phenomena including: mixing problems; the forced harmonic oscillator; the elastic beam; 1D and 2D wave equations; the heat equation
* The key concepts in the theory of ordinary differential equations (ODEs) and their solution including: direc-tional fields; linear, separable, exact ODEs; linear ODEs and systems of linear ODEs w. constant coefficients; phase plane methods, linearization
* The key concepts in vector calculus including: gradient, divergence, curl; line, surface and volume integrals; Gauss divergence theorem; Stoke’s theorem
* The key concepts in the theory of partial differential equations (PDEs) including: principle of superposition; boundary conditions; separation of variables; Fourier solutions
* The key concepts in the theory of Fourier analysis including: Fourier series and integrals; expansion of even/odd functions

### Skills

After completing this course, the student must be able to:
* Recognize and solve different types of ODEs
* Apply the most important differential operators
* Evaluate multi-dimensional integrals of vector functions also using integral transformation theorems
* Calculate Fourier series and integrals
* Recognize different types of PDEs and boundary conditions
* Solve PDEs using Fourier analysis

### Competences

After completing this course, the student must be able to:
* Recognize physical phenomena and engineering problems where ODEs and/or PDEs are needed for mathe-matical modelling.
* Perform such mathematical modelling in simple cases and solve the resulting equations.
* Use sources of information that apply the language of ODEs, vector analysis, and PDEs in either a job situa-tion or in the context of further studies.

### Teaching methods and study activities

The teaching will consist of summaries of key points and problem solving in class. Students are expected to read assigned parts of the textbook, do assigned problems and discuss the subjects outside of class.
Student Activity Model:
According to the Study Activity Model, the workload is divided as follows:

Category 1, Initiated by the lecturer with the participation of lecturer and students: 36 hours – 26%

Category 2: Initiated by lecturer with participation of students: 50 hours – 36 %

Category 3: Initiated by students with participation of students: 48 hours – 35 %

Category 4: Initiated by students with the participation of lecturer and students: 4 hours – 3%

### Resources

Erwin Kreyszig, Advanced Engineering Mathematics (Wiley) – latest edition

### Examination

​Requirements for attending examination
No requirements

Type of examination:
Written 4 hours.
Censor: Internal

Allowed tools:
All

Re-examination:
Please note that the school can decide that the re-examination can be oral.

### Responsible

Uffe Vestergaard Poulsen

### Valid from

8/1/2019 12:00:00 AM

### Course type

6. semester
Elective for Mechanical Engineering

### Keywords

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