Basics of Mathematics (Winter-Term 2024)
| Lecturer: Prof. Dr. Thomas Stiehl |
| Tutor: Chenxu Zhu |
Dates:
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| Start: 7.10.2024 |
| Lecture Notes: Lecture notes are updated after the lectures. |
| Exercise sheets to be completed as homework: The written solutions have to be handed to the tutor before the tutorium starts. |
| Exercise sheets to be considered in the tutorium: These exercise sheets do not have to be handed in! |
| Summary: The course recapitulates relevant topics of engineering mathematics. It begins with a summary of fundamental concepts such as mathematical proofs, sets and numbers. Relevant topics of linear algebra including vector spaces, linear transformations, matrix calculus, determinants and eigenvalues are covered. Important foundations of calculus such as limits, sequences and series are summarized in a compressed form. A major part of the course deals with multidimensional differential and integral calculus including extreme values, fundamental theorem of calculus, Fourier analysis, Divergence Theorem, Stokes’ Theorem and Green’s Theorem. A primer on ordinary differential equations covering linear systems, fixed points and linearized stability analysis is also given. The course is designed as a refresher with a focus on applications and practical calculations. It does not provide a comprehensive derivation of the underlying mathematical theories. Topics:
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