MRES.A.02 Scientific Computing and Mathematical Modeling (MRES.A.02)
Ioannis Th. FAMELIS
This course module offers advanced knowledge and skills in the ‘horizontal’ or across-areas subject of scientific computing and mathematical modeling. Such methods and tools are expected to be of value and immediate usefulness to all students, regardless of the specific specialization area selected by each student.
LessThis course module offers advanced knowledge and skills in the ‘horizontal’ or across-areas subject of scientific computing and mathematical modeling. Such methods and tools are expected to be of value and immediate usefulness to all students, regardless of the specific specialization area selected by each student.
This course module offers advanced knowledge and skills in the ‘horizontal’ or across-areas subject of scientific computing and mathematical modeling. Such methods and tools are expected to be of value and immediate usefulness to all students, regardless of the specific specialization area selected by each student.
Course Description
Course Syllabus
- Mathematical Modeling
- Introduction to Scientific Programming (S.P.), Modern S.P. Environments. Computer Errors
- Numerical Linear Algebra in S.P. environments
- Methodologies of approximation of functions and scientific data in S.P. environments.
- Optimization Methodologies in S.P. Environments
- Differentiation, Integration, Differential Equations
- Introduction of parallel computation in modern S.P. Environments
Course Objectives/Goals
Students who successfully complete the Scientific Computing and Mathematical Modeling course
- will understand basic scientific programming methodologies for solving mathematical problems.
- will be able to implement solutions using the capabilities provided by modern scientific programming environments rather than programming them from scratch.
- after understanding the mathematical nature of the problem that he/she will be asked to solve, will be able to determine its parameters and address the solution using tools provided by modern scientific programming environments.
Prerequisites/Prior Knowledge
Undergraduate courses on Mathematical Analysis
- A course on Introduction to Linear Algebra
- A course on programming (Matlab, Python, Julia, R, …)
- A course on Numerical Analysis (optional).
Bibliography
- Numerical Analysis, Burden R., Faires J. D, Brooks\Cole.
- A First Course in Numerical Analysis, A. Ralston, Ph. Rabinowitz, Mc Graw Hill.
- Numerical Methods using Matlab, J. Mathews, K. Fink, Pearson Prentice Hall.
- Applied Numerical Analysism C. Gerald, P. O. Wheatley, Addison Wesley.
- Applied Numerical Analysis Using Matlab, L. Fausett, Pearson Prentice Hall.
- Numerical Methods for Engineers, With Software and Programming Applications Fourth Edition, S.C. Chapra, R.P. Canale , MC Geaw Hill, 2002
- Numerical Python, Scientific Programming and Data Science Applications with Numpy, Scipy and Matplotlib, R. Johansson, Apress
- Practical Numerical and Scientific Computing with MATLAB and Python”, 1st edition, Eihab B. M. Bashie , CRC Press “
- Learning Scientific Programming with Python, Christias Hill
Assessment Methods
Student evaluation comes from
- Class participation and contribution in the discussions held in class and online x 20%
- Average Grade of Homework Assignments (best 4 out of the total of 5 grades obtained) x 40%
- Final written exam on computer x 40%
Additional info
Relative Scientific Journals:
- SIAM Journal on Numerical Analysis
- International Journal for Numerical Methods in Engineering
- Applied Numerical Mathematics
- Journal of Computational and Applied Mathematics
- Numerical Algorithms
- Numerische Mathematik
- Scientific Programming
TOOLS
- Matlab: https://www.mathworks.com/products/matlab.html
- Mathematica: https://www.wolfram.com/
- Wolfram Alpha: https://www.wolframalpha.com/
- Python: https://www.python.org/
- scipy: https://scipy.org/
- Julia : https://julialang.org/
- R: https://www.r-project.org/
WEBSITES
- Mathematical Modeling
- Introduction to Scientific Programming (S.P.), Modern S.P. Environments. Computer Errors
- Numerical Linear Algebra in S.P. environments
- Methodologies of approximation of functions and scientific data in S.P. environments.
- Optimization Methodologies in S.P. Environments
- Differentiation, Integration, Differential Equations
- Introduction of parallel computation in modern S.P. Environments
Students who successfully complete the Scientific Computing and Mathematical Modeling course
- will understand basic scientific programming methodologies for solving mathematical problems.
- will be able to implement solutions using the capabilities provided by modern scientific programming environments rather than programming them from scratch.
- after understanding the mathematical nature of the problem that he/she will be asked to solve, will be able to determine its parameters and address the solution using tools provided by modern scientific programming environments.
Undergraduate courses on Mathematical Analysis
- A course on Introduction to Linear Algebra
- A course on programming (Matlab, Python, Julia, R, …)
- A course on Numerical Analysis (optional).
- Numerical Analysis, Burden R., Faires J. D, Brooks\Cole.
- A First Course in Numerical Analysis, A. Ralston, Ph. Rabinowitz, Mc Graw Hill.
- Numerical Methods using Matlab, J. Mathews, K. Fink, Pearson Prentice Hall.
- Applied Numerical Analysism C. Gerald, P. O. Wheatley, Addison Wesley.
- Applied Numerical Analysis Using Matlab, L. Fausett, Pearson Prentice Hall.
- Numerical Methods for Engineers, With Software and Programming Applications Fourth Edition, S.C. Chapra, R.P. Canale , MC Geaw Hill, 2002
- Numerical Python, Scientific Programming and Data Science Applications with Numpy, Scipy and Matplotlib, R. Johansson, Apress
- Practical Numerical and Scientific Computing with MATLAB and Python”, 1st edition, Eihab B. M. Bashie , CRC Press “
- Learning Scientific Programming with Python, Christias Hill
Student evaluation comes from
- Class participation and contribution in the discussions held in class and online x 20%
- Average Grade of Homework Assignments (best 4 out of the total of 5 grades obtained) x 40%
- Final written exam on computer x 40%
Relative Scientific Journals:
- SIAM Journal on Numerical Analysis
- International Journal for Numerical Methods in Engineering
- Applied Numerical Mathematics
- Journal of Computational and Applied Mathematics
- Numerical Algorithms
- Numerische Mathematik
- Scientific Programming
TOOLS
- Matlab: https://www.mathworks.com/products/matlab.html
- Mathematica: https://www.wolfram.com/
- Wolfram Alpha: https://www.wolframalpha.com/
- Python: https://www.python.org/
- scipy: https://scipy.org/
- Julia : https://julialang.org/
- R: https://www.r-project.org/
WEBSITES
- Deterministic and stochastic mathematical models.
- Mathematical modeling with dynamic systems and differential equations.
- Solving mathematical problems in scientific programming environments (Matlab, Mathematica, Python, Fortran). Numerical and symbolic calculations on a computer. Double, quadruple and higher precision calculations.
- Numerical calculation errors on the computer.
- Numerical Linear Algebra Methodologies in an S.P. environment. (solving linear systems, factorizations of matrices, calculation of eigenvalues, SVD).
- Interpolation and Approximation of functions and data.
- Interpolatory Procedures.
- Least Squares Approximation.
- Statistical processing and data analysis methodologies.
- Optimization Methodologies with or without conditions.
- Finding minimum of cost functions with classical or differential-evolutionary algorithms.
- Solving equations of non-linear systems.
- Numerical Integration and Differentiation.
- Numerical Solution of Ordinary Differential Equations
- Methodologies of solving Partial Differential Equations.
- Matlab parallel computing.
Calendar
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