URL study guide
https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=2MBC10&collegejaar=2025&taal=enOmschrijving
Largely due to the rapid progress in both hardware and numerical algorithms, computer simulations of mathematical models have inarguably become indispensable in engineering, the physical sciences, as well as in life sciences, social sciences, medicine, business, and even the arts. Furthermore, there is evidence that our present ability to solve complex problems depends not only on faster hardware, but even more so on efficient algorithms.This course introduces the student to the basic concepts of numerical analysis --- the study of the numerical methods and algorithms that are at the core of computer simulations, and which use numerical approximations to solve problems in mathematical analysis that cannot be solved exactly. The numerical methods will be analysed with respect to their properties (such as accuracy) and effectiveness, and will be applied to simple, real-world problems using scientific computing software.
- Finite precision arithmetic, round off error, error propagation, condition number
- Interpolation
- Numerical differentiation
- Numerical integration
- Solution of nonlinear equations
- Solution of initial value and two-point boundary value problems
Doelstellingen
By the end of the course, the student should be able to- understand, explain, and recognize the effect of floating-point representation, machine precision, round-off errors, and condition number on the accuracy of numerical approximations
- use basic interpolation techniques to approximate functions
- approximate the integral of functions using basic numerical integration techniques
- approximate the derivatives of functions using difference formulas
- numerically solve for the solution of nonlinear algebraic equations
- analyse numerical methods with respect to accuracy (or error), stability, and convergence
- numerically solve (systems of) ordinary differential equations
- apply numerical methods to compute the solution to a realistic modeling problem using scientific computing software (e.g., Python), and evalute the error in the obtained approximation