Automotive Engineering

Applied Engineering Mathematics 2

Integrated course, 3.00 ECTS

 

Course content

Applied Engineering Mathematics 2 continues with the discussion of Gilbert Strang's general framework in Applied Mathematics for the description of equilibrium as well as dynamic systems and the underlying minimum principles. The discussion of one-dimensional elastic systems and of three-dimensional potential fields will be extended to three-dimensional elastic systems. For this purpose, an introduction to tensor algebra and analysis for graduate engineering students will be given that ties directly to vector calculus in orthonormal coordinate systems. Thus, the students will be enabled to tackle many applications, such as the theory of elastic bodies, involving higher rank tensors in any coordinate system.

Learning outcomes

The graduate students shall be given an idea and an overview of how to build mathematical models of equilibrium systems as well as dynamical systems; with the focus on tensor algebra and calculus the students should then be well equipped to go into modern coordinate-free formulations of e.g. continuum mechanics.

Recommended or required reading and other learning resources / tools

Gilbert Strang, Introduction to Applied Mathematics, Wellesley-Cambridge Press (1986)
F. Battaglia and T. F. George, Tensors: A guide for undergraduate students, Am. J. Phys. 81 (7), July 2013
A. E. Green and W. Zerna, Theoretical Elasticity, Dover Pubn Inc, revised edition (May 1992)

Mode of delivery

Integrated course: lectures and self-guided homework assignments

Prerequisites and co-requisites

Applied Engineering Mathematics 1

Assessment methods and criteria

Written exam