Search result: Catalogue data in Autumn Semester 2018
|Materials Science Bachelor|
|Basic Courses Part 2|
|Examination Block 2|
|401-0603-00L||Stochastics (Probability and Statistics)||O||4 credits||2V + 1U||M. H. Maathuis|
|Abstract||This class covers the following concepts: random variables, probability, discrete and continuous distributions, joint and conditional probabilities and distributions, the law of large numbers, the central limit theorem, descriptive statistics, statistical inference, inference for normally distributed data, point estimation, and two-sample tests.|
|Objective||Knowledge of the basic principles of probability and statistics.|
|Content||Introduction to probability theory, some basic principles from mathematical statistics and basic methods for applied statistics.|
|Lecture notes||Lecture notes|
|401-0363-10L||Analysis III||O||3 credits||2V + 1U||A. Iozzi|
|Abstract||Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics.|
|Objective||Mathematical treatment of problems in science and engineering. To understand the properties of the different types of partial differential equations.|
The first lecture is on Thursday, September 27 13-15 in HG F 7 and video transmitted into HG F 5.
The reference web-page for exercise sheets, solutions and further info is
The web-page to enroll for an exercise class is
The coordinator is Stefano D'Alesio
Study Center D-MAVT: 16-18 every Monday from the 3rd week of the semester (first appointment: October the 1st)
room HG E22 Link
Study Center D-MATL: 15-17 every Wednesday from the 5th week of the semester (first appointment: October the 17th)
room HCI J 574
Tuesday 15 January 2019, at 12:30-14:00, in room HG G 19.1.
Monday 21 January 2019, at 12:30-14:00, in room HG G 19.2.
Tuesday 26 February 2019, at 17:00-18:30, in room HG 19.1.
Monday 4 March 2019, at 18:15-19:45, in room HG 19.1.
- Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting
- Transforms of Derivatives and Integrals, ODEs
- Unit Step Function, t-Shifting
- Short Impulses, Dirac's Delta Function, Partial Fractions
- Convolution, Integral Equations
- Differentiation and Integration of Transforms
Fourier Series, Integrals and Transforms:
- Fourier Series
- Functions of Any Period p=2L
- Even and Odd Functions, Half-Range Expansions
- Forced Oscillations
- Approximation by Trigonometric Polynomials
- Fourier Integral
- Fourier Cosine and Sine Transform
Partial Differential Equations:
- Basic Concepts
- Modeling: Vibrating String, Wave Equation
- Solution by separation of variables; use of Fourier series
- D'Alembert Solution of Wave Equation, Characteristics
- Heat Equation: Solution by Fourier Series
- Heat Equation: Solutions by Fourier Integrals and Transforms
- Modeling Membrane: Two Dimensional Wave Equation
- Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series
- Solution of PDEs by Laplace Transform
|Lecture notes||Lecture notes by Prof. Dr. Alessandra Iozzi:|
|Literature||E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011|
C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed.
S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY.
G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003.
Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005
For reference/complement of the Analysis I/II courses:
Christian Blatter: Ingenieur-Analysis
|327-0308-00L||Programming Techniques in Materials Science||O||2 credits||2G||C. Ederer|
|Abstract||This course introduces the general computing and programming skills which are necessary to perform numerical computations and simulations in materials science. This is achieved using the numerical computing environment Matlab and through the use of many practical examples and exercises.|
|Objective||On passing this course, the students should be able to develop their own programs for performing numerical computations and simulations, and they should be able to analyse and amend existing code.|
|Content||Introduction to Matlab; input/output; structured programming using loops and conditional execution; modular Programming using functions; flow diagrams; numerical accuracy; example: random walk model.|
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