Mathematical Modelling

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Mathematics

Course Contents

Phenomenological, empirical and black-box models. Differential time and control volume definitions. Modeling of systems with one independent and one dependent variable. Applications to thermal and electrical systems. Analytical and numerical solutions of the model equations. Systems with several dependent variables. Applications to thermal systems and fluid flow. Modeling of systems with simple partial differential equations. Fick’s diffusion and Fourier’s heat conduction laws. Numerical solutions. Sensitivity analysis. Graphical methods. Parameter uncertainty.

Weekly Schedule

1) Introduction to Computer and Package programs and the introduction and use of Mathematica
2) Learning basic commands in Mathematica.
3) Basic mathematical functions, taking derivatives, differential, integral, limits.
4) Equations and Solutions with "Solve, Reduce and FindRoot " Commands. Vectors, matrices, complex numbers;
5) Algebraic Calculations; Assigning and Replacing Variables
6) Variable Definition; Creating Lists or Tables; Use of Four Types of Brackets.
7) Transformation of Algebraic Expressions I: Simplify, Expand, Factor, Together, Apart, Cancel etc. commands
8) Getting a Part of Algebraic Expressions: Coefficient, Exponent, Part, Numerator, Denominator etc. commands
9) Transformation of Algebraic Expressions II: Collect, FactorTerms, TrigExpand, TrigFactor, ComplexExpand, etc.
10) Midterm exam
11) Taylor and Maclaurin Power Series Expansion with Series Command and applications.
12) Lists (Table, Array); Vectors; Matrices: Inverse, Det, Dimensions, Diagonal Matrix, Identity Matrix, Transpose, etc. Commands.
13) Lists (Table, Array); Vectors; Matrices: Inverse, Det, Dimensions, Diagonal Matrix, Identity Matrix, Transpose, etc. Commands.
14) Two-dimensional graphic drawings: AspectRatio, Axes, AxesLabel, AxesOrigin, Frame, FrameLabel, FrameTicks, GridLines, PlotRange, Ticks, ContourPlot and DensityPlot, etc. Modifying with Commands.
15) Three-dimensional graphics drawings.
16) FINAL EXAMINATION

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

1) Lecture
2) Lecture
3) Lecture
4) Question-Answer
5) Question-Answer
6) Drill and Practice
7) Drill and Practice
8) Drill and Practice
9) Demonstration
10) Demonstration
11) Demonstration
12) Modelling
13) Modelling
14) Modelling
15) Self Study
16) Self Study
17) Self Study

Assessment Methods and Criteria

Contribution of Midterm Examination to Course Grade	40%
Contribution of Final Examination to Course Grade	60%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required