Essential Mathematics for Global LeadersⅡto begin on October 5, 2017

 Class List of Fall Semester 2017

“Essential Mathematics for Global LeadersⅡ” will begin on October 5. This is a class for students in “Minor Course of Science and Technology for Global Leaders”. But all master’s & doctoral students can take it if you have interest. The class will be conducted in English.

Theme & Objective

Prof. DahanTheme: Differential Equations (in the broader sense of dynamical systems) are the core topics in mathematical modeling.

Objective: Through examples in Mathematica to understand

  • what are Ordinary, Partial Differential Equations (ODE, PDE)

  • some methods of resolution: closed forms, Series Solutions, Fourier & Laplace Transforms…

  • how to use Mathematica to solve and visualize solutions.

Message to Students

As part of the Essential course series, Essential Maths I (Statistics) and II (modeling ODE and PDE) are supposed to endow/increase capability to model concrete problems with mathematical equations. Essential Math II focuses on the use of a math software, and through its visualization functionality to learn/put into practice basic methods of resolution. Mathematical notions will be introduced formally, but main theorems will be stated in a concrete way. Most proofs will be omitted, in particular only basic notions of Calculus and of Linear Algebra are expected for this course.

Lecture Outline

Essential Mathematics for Global LeadersⅡ [17S1007]
Number of Credits
Dahan, Xavier (Project Associate Professor of Ochanomizu University)
Target Audience
Graduate Students
Graduate School of Humanities & Sciences Building R408
Date & Time
Thursday, Period 3-4 (10:40-12:10)
Year 2017
  October 5, 12, 19, 26
  November 2, 9, 16, 30
  December 7, 14, 21
Year 2018
  January 4, 18, 25
  February 1
Lecture Types
Lecture, computer practice.
Lecture Plan

Content: Introduction to mathematical modeling with Mathematica

The following topics will be introduced, (maybe not exactly in this order !). All topics are illustrated with Examples and some small projects in Mathematica.

0. Introduction to Mathematica. Mathematica

1. Continuous differential systems.
1.1 Planar linear systems: phase portrait. Linear systems.
1.2 Planar non-linear system: Stability, Linearization (Hartman theorem).
1.3 Planar non-linear systems II. Limit Cycles. Poincare theorem. 
1.4 Three-dimensional non-linear systems: Notion of Chaos. Lorentz’s strange attractor.

2. Discrete differential systems (finite-difference systems).
2.1 Linear recurrence relations. Leslie Model.
2.2 Non-linear examples: logistic model. Logistic and Henon map.

3. Partial Differential Equations.
3.1 Introduction & classification. Boundary conditions.
3.2 Hyperbolic PDE: Wave equations, vibrating string.
3.3. Parabolic PDE: Heat equation, diffusion problem.
3.4 Elliptic PDE: Laplace equations.

a) Dynamical Systems with applications using Mathematica (S. Lynch, Birkhauser 2007)
b) Introduction to Partial Differential Equations for Scientists and Engineers Using Mathematica (Kuzman Adzievski, Abul Hasan Siddiqi. Taylor & Francis, 2013)


Registration Period: Mon., October 2 through Sat., October 14
If you cannot register during above period, please contact Academic Affairs Office in Student Affairs Building.


Ochanomizu University Leading Graduate School Promotion Center
Tel: 03-5978-5775