Course title
B00105003
Applied Analysis

 hosoya naoki Click to show questionnaire result at 2018
Course description
To lead ordinary differential equations and partial differential equations, applied analysis covers mathematical modelling in biology, economics, physics, and chemistry as an introduction against undergraduate students.
Purpose of class
Students should study a mathematical modelling which lead to ordinary differential equations and partial differential equations through practicing experimentations and observations. In addition, students should learn a theoretical method and numerical analytical approach for solving these differential equations.
Goals and objectives
  1. To understand the mathematical modelling in various fields
  2. To understand the derivation and solution of ordinary differential equations
  3. To understand the derivation and solution of partial differential equations
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Introduction To investigate the mathematical modelling 190minutes
2. Population models
Verhulst model (logistic equation) 		To investigate population models
To investigate Verhulst model (logistic equation) 		190minutes
3. Numerical simulation using Euler method for Verhulst model (logistic equation) To investigate Euler method 190minutes
4. Lotka-Volterra equations To investigate Lotka-Volterra equations 190minutes
5. Simple pendulum To investigate a method for obtaining analytically-predicted natural period 190minutes
6. Rocket flight (Tsiolkovsky rocket equation) To investigate a rocket flight 190minutes
7. Newton’s law of cooling To investigate Newton’s law of cooling 190minutes
8. Torricelli’s law for water flow To investigate Torricelli’s law for water flow 190minutes
9. Catenary line To investigate a catenary line 190minutes
10. Coriolis acceleration To investigate Coriolis acceleration 190minutes
11. Electric circuits To investigate electric circuits 190minutes
12. Fourier series-1
> 2 pi periodic function 		To investigate Fourier series 190minutes
13. Fourier series-2
> a periodic function f (t) with arbitrary period 		To investigate Fourier series 190minutes
14. Wave equation (vibrating-string problem) To investigate a wave equation 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Homework and quiz Total.
1. 33% 33%
2. 33% 33%
3. 34% 34%
Total. 100% -
Evaluation method and criteria
The grading for this class was broken down as follows:
Homework and quiz (100%)
Textbooks and reference materials
D.N. Burghes and M.S. Borrie, Modelling with differential equations
S.J. Farlow, Partial differential equations for scientists and engineers
Prerequisites
Mechanical engineering and differential equations should be reviewed in advance.
Office hours and How to contact professors for questions
  • Friday lunch break (You should make an appointment via e-mail in advance.)
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates a basic problem-solving skills
Active-learning course
About half of the classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Sun Mar 21 14:56:07 JST 2021