Introduction to Mathematical Modeling

The student is trained to understand a wide range of mathematical models that are used in practical situations, to formulate and mathematically model problems from real life, to construct an appropriate differential equation with relevant parameters and conditions and their numerical solution, and to predict and perform conclusions from the mathematical model.

Introduction: Why we need mathematical modeling. What can be done with mathematical modeling. Problems in real life. Modeling cycle. Basic Concepts of Differential Equation Modeling. Population modeling, epidemic modeling, glider trajectory modeling, modeling in medicine… Defining and solving real-life problems. Numerical methods for solving ordinary differential equations. Euler’s method, Euler’s backward method, and trapezoidal rule. Application of Euler’s midpoint method to medical problems. Taylor’s methods. Runge-Kutta methods, explicit and implicit Runge-Kutta schemes. Multistep methods. Application of a software package for solving differential equations. Model improvement based on initial solutions. Deriving conclusions from the mathematical model and predictions for real problems.

Blended way of learning: lectures supported by presentations and visualization of concepts and independent project assignments.