After completing the course, the student is familiar with and can utilize several methods of applied mathematics in solving practical problems. The student can form mathematical models from practical problems, solve them using Matlab software, and interpret the results. The methods of applied mathematics in the course focus on the needs of different engineering fields.
The student can utilize vectors and matrices in mathematical modeling. They are familiar with various methods of matrix computation and, for example, know the LU decomposition of a matrix and can utilize it. The student understands the basics of optimization, knows the gradient, and can use software to find local extremes.
In addition, the student has studied two of the following topics:
After completing the Operations Research topic, the student
- Can form a linear optimization model with variables, constraints, and an objective function.
- Can represent a linear optimization model in code form and solve it with software.
- Can graphically solve the solution of a linear optimization problem with two continuous variables.
- Can form constraints from logical conditions using binary variables.
- Can recognize what is a multi-objective task and what is a Pareto solution.
- Recognizes some typical integer tasks, for example: knapsack problem, assignment problem, facility location problem, single-processor scheduling problem, shortest path task, and traveling salesman problem.
After completing the Least Squares Method topic, the student
- Knows the mathematical theory behind the least squares method and can justify the optimality of the method using the gradient and Hessian matrix.
- Can utilize the least squares method in various situations.
- Can solve the least squares method with software and can analyze the results obtained also in situations where the initial values are modeled as random variables.
- Knows the connection between the least squares method and regression analysis.
After completing the Differential Equation Groups topic, the student
- Can form a group of differential equations and can solve it using software.
- Knows under what conditions a group of differential equations has a unique solution and can utilize the given initial values.
- Is familiar with numerical methods used to solve differential equations and can utilize them.
