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Delft University of Technology
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Courseware
The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, KahaneKhintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γRadonifying operators, γboundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Stochastic partial differential equations Evolution equations
 Resource Type:
 Courseware

Courseware
How do populations grow? How do viruses spread? What is the trajectory of a glider? Many reallife problems can be described and solved by mathematical models. In this course, you will form a team with another student and work in a project to solve a reallife problem. You will learn to analyze your chosen problem, formulate it as a mathematical model (containing ordinary differential equations), solve the equations in the model, and validate your results. You will learn how to implement Euler’s method in a Python program. If needed, you can refine or improve your model, based on your first results. Finally, you will learn how to report your findings in a scientific way. This course is mainly aimed at Bachelor students from Mathematics, Engineering and Science disciplines. However it will suit anyone who would like to learn how mathematical modeling can solve realworld problems.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematical models
 Resource Type:
 Courseware