Numerical methods
Summary
This course introduces students to modern computational and mathematical techniques for solving problems in chemistry and chemical engineering. The use of introduced numerical methods will be demonstrated using the MATLAB programming language.
Content
- Numerical differentiation (Euler forward, backward, Richardson extrapolation, error analysis)
- Numerical integration (Trapezoid rule, Simpson rule, composite rules, Romberg integration)
- Methods for solving nonlinear equations (bisection, Regula-Falsi, Newton-Raphson, error analysis)
- Methods for solving ordinary differential equations (notion of stability of solutions, stiffness, Euler methods, Runge-Kutta methods, Adams-Bashfort-Moulton, adaptive methods)
- Boundary value problems (finite difference method, FTCS scheme, Crank-Nicolson method, Finite difference methods in 2 and 3 spatial dimensions, Transient Boundary value problems)
- Basic notions of data analysis/processing
Keywords
Numerical differentiation and integration, nonlinear equations, ordinary differential equations, partial differential equations
Assessment methods
The final grade will be the combination of exercises (30%) and written exams (70%)
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Numerical methods
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Numerical methods
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Numerical methods
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 1 Hour(s) per week x 14 weeks