This lecture will prepare Engineering students with mathematical foundation with the following details: Solving LES with GA, Vector spaces, Matrix and linear maps, Linear system of equations, Gauss-algorithm and LU-decomposition, Eigenvalues and its properties, Properties of symmetric matrices, SVD, Generalised inverse problem, QR-decomposition, Norms, Numeric of eigenvalues, Errors, Best fit functions, ODE, Linear diff. eqn. with constant coeff., Linear diff. eqn. of higher order, Calculus with more variables, Inverse and implicit functions, Taylor expansions, Symm. matrix and quadratic forms, Extreme values, Stability of ODE.
A few literature, which can be found in Central library of TU Dortmund, are listed below.
1. Lang, Linear Algebra
2. Golub, Matrix Computation
3. Kreyszig, Advanced Engineering Mathematics
Handout of this lecture will be provided later on a Miniwebsite.