Advanced Engineering Mathematics

Code

ME-AEM1

Version

2.0

Offered by

Mechanical Engineering

ECTS

Prerequisites

MA/ME-MAT1 and MA/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.

Topics

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.

Resources

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

Evaluation

Examination

Exam prerequisites:
No requirements

Type of exam:
Written 4 hours.
Censor: Internal

Allowed tools:
All, except for access to websites or AI-tools that can provide solution steps.

Re-examination:
Can be oral

Grading criteria

Additional information

Responsible

Uffe Vestergaard Poulsen

Valid from

01-02-2025 00:00