Mathematical Modeling Design | MA | Course

Brief Information
  • Name : Mathematical Modeling Design 수학적모델설계
  • Lecturer : Lee Jongwoo 이종우
  • Semester : 2016 Spring
  • Major : BS, Mathematics
  • Textbook
    • Using lecture notes
  • Syllabus : Syllabus_2016-5-1__Mathematical Modeling Design.pdf
  • In short
    • Applied mathematics
    • Modeling from data: least squares
    • Modeling from theory: approximation theory
    • Logistic model: population model
    • Theory of conflicts
    • Temperature control model
    • Curve of pursuit
    • Control theory
    • Traffic flow

Assignments/Projects

Lectures

1. Introduction | 2016-03-04 Fri.
  • The professor read and explain the syllabus with the students.
  • Software: Microsoft Excel
  • Applied mathematics
  • The cycloid slope is the fastest road to arrive on the slopes of the same beginning position and end position.
  • Logistic curve. Logistic regression.
2. Mathematical Modeling and the Method of Least Squares | 2016-03-11 Fri.
Mathematical Modeling
  • What is the mathematical model?
  • Real world → observation → modeling → prediction
    • Observe the real world → modeling → predict the real world
  • Types of mathematical modeling
    • Empirical modeling: modeling based on data alone.
    • Theoretical modeling: modeling based more on theory than on data alone.
The Method of Least Squares
  • Types of models
    • Linear models
    • Nonlinear models
  • Linear models
    • y = w_0 x_0+w_1 x_1+...+w_n x_n
  • Nonlinear models
    • Convert the nonlinear models into
      f(y) = w'_0 g(x_0)+w'_1 g(x_1)+...+w'_n g(x_n)
    • For example,
      y=ae^x
      \Rightarrow ln(y)=ln(a) + x
    • Then, approach the converted equation as a linear model.
Project 1

Project 1 - Mathematical Modeling Design

 

 

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