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

• [Assignment 1] Modeling with Data: Least Squares Method | Mathematical Modeling Design
• [Assignment 2] Estimate Scores From Rankings Using Least Square Method on the 3 Models | Mathematical Modeling Design
• [Assignment 3]?Theoretical Modeling:?Find the Minimum Surface of the Cake?When its Volume Is Constant
• [Assignment 4]?Numerical Integration: Deriving Boole’s Rule
• [Project 1] Finding Appropriate Data Models
• [Assignment 5]?Animal Longevity and Scale
• [Project 2]?Heating and Cooling, Newtonian Cooling Law

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