# 406-0141-AAL Linear Algebra and Numerical Analysis

Semester | Autumn Semester 2016 |

Lecturers | R. Käppeli, V. C. Gradinaru |

Periodicity | every semester recurring course |

Language of instruction | English |

Comment | Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. |

Abstract | Introduction to Linear Algebra and Numerical Analysis for Engineers. This reading course is based on chapters from the book "Introduction to Linear Algebra" by Gilbert Strang (SIAM 2009), and "A first Course in Numerical Methods" by U. Ascher and C. Greif (SIAM, 2011). |

Objective | To acquire basic knowledge of Linear Algebra and some aspects of related numerical metjhods and the ability to apply basic algorithms to simple problems. |

Content | * Linear systems of equations: Gaussian elimination, row echelon form, theory abiut existence and uniqueness of solutions (Strang Ch. 2 and 3.4) * Mathematical modelling by linear systems (e.g. networks, trusses) (Strang, parts of Ch. 8) * Column space, null space and rank of matrices (Strang 3.2, 3.3) * linear combinations, linear (in)dependence, bases, dimension theorem for matrices (Strang 3.5, 3.6) * inner product, orthogonality, length in Euclidean space (Strang 4.1, 4.2) * Least squares solutions and orthogonalization (Gram-Schmidt and QR) (Strang 4.3, 4.4) * Linear mappings, matrix representation and change of basis (Strang Ch. 7) * Determinants and diagonalization of matrices (eigenvalues and eigenvectors) (Strang 6.1, 6.2, 6.5, 6.6) * Diagonalization applied to linear differential and difference equations. (Strang 6.3) * Numerical methods for solving linear systems of equations (Ascher/Greif 5.1, MATLAB Documentation of \) * Interpolation with polynomials and splines (Ascher/Greif Ch. 10 and 11) |

Literature | Gilbert Strang, Introduction to Linear Algebra, 4th ed., SIAM & Wellesley-Cambridge Press, 2009. U. Ascher and C. Greif, A first Course in Numerical Methods", SIAM, 2011. |

Prerequisites / Notice | Knowledge of elementary calculus |