This lecture focuses on the calculation algorithm for the numerical analysis that has been used for research and development. Additionally, this lecture covers the computer programming techniques. Lecture contents are applicable to practical numerical analysis.
The aim of this lecture is to learn the calculation algorithm for the numerical analysis. The numerical analysis is an essential tool for such characterization, simulation, design and operation control, which are necessary to research and development of materials, devices, circuits and systems in electrical and electronic engineering and information communication engineering areas. Principles and features of the calculation algorithm about sorting method, least squares method, numerical differentiation and integration, simultaneous equations, nonlinear equations, and differential equations will be lectured. In addition, basic programming techniques of variables, arithmetic, array, function, branching and loop will be lectured for the implementation of the calculation algorithm. The programming language used in this lecture is MATLAB that is easy to programming the numerical calculation. The ability learned in this lecture will be applicable to use in other lectures, experiments and researches.
At the end of this course, students will be able to:
1) Explain the basic configuration and the mechanism of the computer, which is an execution system of the numerical analysis.
2) Explain basic functions of the program technique, such as variable, arithmetic, array, function, branching, and loop.
3) Programming, execution, and graph drawing using the MATLAB language.
4) Explain the necessity of considering the algorithm that determines the processing speed and functionality limitations even in the same process.
5) Explain the principle and the calculation algorithm of the least squares method, and analyze numerical data using this method.
6) Explain the principles and calculation algorithms of the numerical differentiation and integration, simultaneous equations, nonlinear equations, ordinary differential equations, and partial differential equations, and analyze numerically using these methods.
Corresponding educational goals are:
(1) Specialist skills Fundamental specialist skills
(6) Firm fundamental specialist skills on electrical and electronic engineering, including areas such as electromagnetism, circuits, linear systems, and applied mathematics
calculation algorithm, numerical analysis, numerical simulation, programming, MATALB
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Students must familiarize themselves with topics described in the required learning section before coming to class.
Students are given exercise problems related to what will be taught on that day.
Students are given exercise problems related to what was taught on that day.
|Course schedule||Required learning|
|Class 1||Introduction||Understand the basic configuration of the computer. List up of use cases of numerical analysis.|
|Class 2||Variables and arithmetic||Preparation of the MATLAB programming system (Not mandatory). Understand the number of digits and the numerical range of the binary number. Understand the boolean value (logical value).|
|Class 3||Array and function||Understand the difference between the variable and array variable. Understand the difference between the built-in functions and the user functions.|
|Class 4||Matrix||Understand the numerical assignment method to the matrix. Understand the handling method of string in programming.|
|Class 5||Branching and loop||Understand the relationship of boolean and relational operators. Understand the type of logic operation.|
|Class 6||Graph drawing||Investigation of the graph type in MATLAB. Investigation of cases of time-series signal.|
|Class 7||Sorting||Understand the sorting procedure, and list up its procedure steps.|
|Class 8||Exercise problems to assess the understanding level for classes 1-7.||Test level of understanding and self-evaluate achievement for classes 1–7.|
|Class 9||Least squares method||Investigation of the cases of numerical data analysis of experiments. Explain the causes of errors in the experimental data acquisition.|
|Class 10||Numerical differentiation and integration||Understand definition of the differentiation and integration in mathematics.|
|Class 11||Simultaneous equations||Understand the solving procedure of 3 yuan simultaneous equations using the hands, and list up its procedure steps.|
|Class 12||Nonlinear equations||Confirmation of the meaning of solving the equation. Explain the causes of errors in the computer calculation.|
|Class 13||Ordinary differential equation||Confirmation of the meaning of solving the differential equations. Investigation of the cases of ordinary differential equations in physics. Understand the Taylor expansion.|
|Class 14||Partial differential equation||Confirmation of the meaning of the partial differential. Investigation of the cases of partial differential equations in physics. Understand the Maxwell's equations.|
|Class 15||Advanced techniques of MATLAB||Investigation of the built-in functions in MATLAB. Investigation of the Toolbox prepared in MATLAB. Survey of research and development case using MATLAB.|
Lecture using materials that faculty has created.
All materials used in class can be found on OCW-i.
Students will be assessed on their level of understanding of both the calculation algorithms and programming technique.
Students’ course scores are based on evaluation of understanding level for classes 1–7 (40%), final exams (40%), and exercise problems for each classes (20%).
No prerequisites are necessary, but preparation of the MATLAB programming system is desirable.
Tomoyuki Miyamoto, miyamoto.t.ac[at]m.titech.ac.jp, 045-924-5059
Yuya Shoji，shoji.y.ad[at]m.titech.ac.jp, 03-5734-2578
Contact by e-mail in advance to schedule an appointment.