The spring semester 2021 will generally take place online. New presence elements as of April 26 will be communicated by the lecturers.

# 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.

### Catalogue data

 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

### Performance assessment

 Performance assessment information (valid until the course unit is held again) Performance assessment as a semester course ECTS credits 5 credits Examiners R. Käppeli, V. C. Gradinaru Type session examination Language of examination English Repetition The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. Mode of examination written 120 minutes Additional information on mode of examination Takes place as a written session examination simultaneously with the session examination for the course unit 401-0141-00L. Written aids 20 pages DIN A4 in your own handwriting, no printouts, no copies. No other material admitted. This information can be updated until the beginning of the semester; information on the examination timetable is binding.

### Learning materials

 No public learning materials available. Only public learning materials are listed.

### Courses

NumberTitleHoursLecturers
406-0141-AA RLinear Algebra and Numerical Analysis
Self-study course. No presence required.
150s hrsR. Käppeli, V. C. Gradinaru

### Groups

 No information on groups available.

### Restrictions

 There are no additional restrictions for the registration.

### Offered in

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