Curriculum

Lectures of The SGU course of mathematical and Physical Sciences


The Math-Phys Unit started a new course for doctoral students!

Master's students can take the Basic Lectures which are conditions for the admittion of this course!

Click on this image → for more details.




For details of these lectures please refer to Syllabus.

A) Basic Lectures
Field Course Title Instructor Term credit
MathFoundation of Mathematical Analysis 1 Hideo KozonoSpring semester2 credits
MathFoundation of Mathematical Analysis 2 Yoshihiro ShibataFall semester2 credits
MathFoundation of Geometry 1 Martin GuestSpring semester2 credits
MathComputer Assisted Proof of Nonlinear Equations Shinichi OishiSpring semester2 credits
A MechFoundation of Geometry 2 Hiroaki YoshimuraSpring semester2 credits
A MechHeat Transfer Amano Yoshiharu, Kiyoshi Saito, Niccolo Giannetti,
Yamaguchi Seiichi,
Hifni Mukhtar Ariyadi
Spring semester2 credits
M MechAdvanced Topics in Applied Mechanics of Fluid-Structure Interactions Kenji TakizawaFall semester2 credits
PhysMathematical Formulation of Quantum Mechanics Tohru OzawaSpring semester2 credits
PhysMathematical Formulation of Classical Field Theory Tohru OzawaFall semester2 credits
PhysAdvanced Theoretical Quantum Physics Kazuya YuasaSpring semester2 credits
PhysQuantum Information Theory Kazuya YuasaSpring semester2 creditsWe don't hold in AY2020
PhysPhysics of Non-Equilibrium System A Yoshihiro YamazakiFall semester2 credits
PhysPhysics of Non-Equilibrium System B Yoshihiro YamazakiFall semester2 creditsWe don't hold in AY2020
PhysComputational Biophysics Mitsunori TakanoFall semester2 creditsWe don't hold in AY2020
B) Special Lectures
Field Course Title Instructor Term credit
MathAdvanced Study of Nonlinear Mechanics Hiroaki Yoshimura, Guest Martin, Peng Linyuintensive4 credits
MathSpecial Lecture on Mathematical Fluid Mechanics Hideo Kozono, Yoshihiro Shibata, Mads Kyed,
Shuichi Kawashima
intensive4 credits
MathSpecial Lecture on SPDE Funaki Tadahisaintensive2 credits
M MechFluid Mechanics of Computing Kenji Takizawa, Tayfun E. Tezduyarintensive (Spring semester)2 credits
PhysSpecial Lecture on Quantum Physics Kazuya Yuasa, Hiromichi Nakazato, Ozawa Tohru,
Vladimir Simeonov Gueorguiev
intensive4 credits
*Special Lectures include Mini-courses and short terms lectures by visiting scholars in international workshops.
*Special lectures which you take in Master's program can be counted fot the course requirements up to 4 credits.
C) Independent Studies
Field Course Title Instructor Term credit
General StudiesInternship Takashi ArigaFull year2 credits

For details of these lectures please refer to Syllabus.

A) Basic Lectures
Field Course Title Instructor Term credit
MathFoundation of Mathematical Analysis 1 Hideo KozonoSpring semester2 credits
MathFoundation of Mathematical Analysis 2 Yoshihiro ShibataFall semester2 credits
MathFoundation of Geometry 1 Martin GuestSpring semester2 credits
MathComputer Assisted Proof of Nonlinear Equations Shinichi OishiSpring semester2 credits
A MechFoundation of Geometry 2 Hiroaki YoshimuraSpring semester2 credits
A MechHeat Transfer Amano Yoshiharu, Kiyoshi Saito, Niccolo Giannetti,
Yamaguchi Seiichi, Yoshida Akira
Spring semester2 credits
M MechAdvanced Topics in Applied Mechanics of Fluid-Structure Interactions Kenji TakizawaFall semester2 credits
PhysMathematical Formulation of Quantum Mechanics Tohru OzawaSpring semester2 credits
PhysMathematical Formulation of Classical Field Theory Tohru OzawaFall semester2 creditsWe don't hold in AY2019
PhysAdvanced Theoretical Quantum Physics Kazuya YuasaSpring semester2 creditsWe don't hold in AY2019
PhysQuantum Information Theory Kazuya YuasaSpring semester2 credits
PhysPhysics of Non-Equilibrium System A Yoshihiro YamazakiFall semester2 creditsWe don't hold in AY2019
PhysPhysics of Non-Equilibrium System B Yoshihiro YamazakiFall semester2 credits
PhysComputational Biophysics Mitsunori TakanoFall semester2 credits
B) Special Lectures
Field Course Title Instructor Term credit
MathAdvanced Study of Nonlinear Mechanics Hiroaki Yoshimura, Martin Guestintensive4 credits
MathSpecial Lecture on Mathematical Fluid Mechanics
(Advanced Study of Mathematical Fluid Dynamics)
Hideo Kozono, Yoshihiro Shibata, Masao Yamazakiintensive4 credits
M MechFluid Mechanics of Computing Kenji Takizawaintensive (Spring semester)2 credits
PhysSpecial Lecture on Quantum Physics Kazuya Yuasa, Hiromichi Nakazato, Ozawa Tohruintensive4 credits
*Special Lectures include Mini-courses and short terms lectures by visiting scholars in international workshops.
*Special lectures which you take in Master's program can be counted fot the course requirements up to 4 credits.
C) Independent Studies
Field Course Title Instructor Term credit
General StudiesInternship Takashi ArigaFull year2 credits

For details of these lectures please refer to Syllabus.

A) Basic Lectures
Field Course Title Instructor Term credit
MathFoundation of Mathematical Analysis 1 Hideo KozonoSpring semester2 credits
MathFoundation of Mathematical Analysis 2 Yoshihiro ShibataFall semester2 credits
MathFoundation of Geometry 1 Yasushi HommaSpring semester2 credits
MathComputer Assisted Proof of Nonlinear Equations Shinichi OishiSpring semester2 credits
A MechFoundation of Geometry 2 Hiroaki YoshimuraSpring semester2 credits
A MechHeat Transfer Kiyoshi SaitoSpring semester2 credits
M MechAdvanced Topics in Applied Mechanics of Fluid-Structure Interactions Kenji TakizawaFall semester2 credits
PhysMathematical Formulation of Quantum Mechanics Tohru OzawaSpring semester2 credits
PhysMathematical Formulation of Classical Field Theory Tohru OzawaFall semester2 credits
PhysAdvanced Theoretical Quantum Physics Kazuya YuasaSpring semester2 credits
PhysQuantum Information Theory Kazuya YuasaFall semester2 creditsWe don't hold in AY2018
PhysPhysics of Non-Equilibrium System A Yoshihiro YamazakiFall semester2 credits
PhysPhysics of Non-Equilibrium System B Yoshihiro YamazakiFall semester2 creditsWe don't hold in AY2018
PhysComputational Biophysics Mitsunori TakanoFall semester2 creditsWe don't hold in AY2018
B) Special Lectures
Field Course Title Instructor Term credit
MathAdvanced Study of Nonlinear Mechanics Hiroaki Yoshimura, Guest Martinintensive4 credits
MathSpecial Lecture on Mathematical Fluid Mechanics
(Advanced Study of Mathematical Fluid Dynamics)
Hideo Kozono, Yoshihiro Shibataintensive4 credits
M MechFluid Mechanics of Computing Kenji Takizawaintensive (Spring semester)2 credits
PhysSpecial Lecture on Quantum Physics Hiromichi Nakazato, Kazuya Yuasaintensive4 credits
*Special Lectures include Mini-courses and short terms lectures by visiting scholars in international workshops.
*Special lectures which you take in Master's program can be counted fot the course requirements up to 4 credits.
C) Independent Studies
Field Course Title Instructor Term credit
General StudiesInternship Takashi ArigaFull year2 credits

For details of these lectures please refer to Syllabus.

A) Basic Lectures
Field Course Title Instructor Term credit
MathFoundation of Mathematical Analysis 1 Hideo KozonoSpring semester2 credits
MathFoundation of Mathematical Analysis 2 Yoshihiro ShibataFall semester2 credits
MathFoundation of Geometry 1 Guest MartinSpring semester2 credits
MathComputer Assisted Proof of Nonlinear Equations Shinichi OishiSpring semester2 credits
A MechFoundation of Geometry 2 Hiroaki YoshimuraSpring semester2 credits
M MechAdvanced Topics in Applied Mechanics of Fluid-Structure Interactions Kenji TakizawaFall semester2 credits
PhysMathematical Formulation of Quantum Mechanics Tohru OzawaSpring semester2 credits
PhysQuantum Information Theory Kazuya YuasaFall semester2 credits
PhysPhysics of Non-Equilibrium System B Yoshihiro YamazakiFall semester2 credits
PhysComputational Biophysics Mitsunori TakanoFall semester2 credits
*We don't hold "Mathematical Formulation of Classical Field Theory" (Tohru Ozawa/Fall semester/2 credits), "Advanced Theoretical Quantum Physics"(Kazuya Yuasa/Spring semester/2 credits) and "Physics of Non-Equilibrium System A"(Yoshihiro Yamazak/Spring semester/2 credits) in AY2017.
*A Mech: the Department of Applied Mechanics and Aerospace Engineering
*M Mech: the Department of Modern Mechanical Engineering
B) Special Lectures
Field Course Title Instructor Term credit
MathAdvanced Study of Nonlinear Mechanics Hiroaki Yoshimura, Guest Martinintensive4 credits
MathSpecial Lecture on Mathematical Fluid Mechanics
(Advanced Study of Mathematical Fluid Dynamics)
Hideo Kozono, Yoshihiro Shibataintensive4 credits
M MechFluid Mechanics of Computing Kenji Takizawaintensive (Spring semester)2 credits
PhysSpecial Lecture on Quantum Physics Hiromichi Nakazato, Kazuya Yuasaintensive4 credits
*Special Lectures include Mini-courses and short terms lectures by visiting scholars in international workshops.
*Special lectures which you take in Master's program can be counted fot the course requirements up to 4 credits.
C) Independent Studies
Field Course Title Instructor Term credit
General StudiesInternship Takashi ArigaFull year2 credits

For details of these lectures please refer to Syllabus.

A) Basic Lectures
Field Course Title Instructor Term credit
MathFoundation of Mathematical Analysis 1 Yoshihiro ShibataSpring semester2 credits
MathFoundation of Mathematical Analysis 2 Hideo KozonoFall semester2 credits
MathFoundation of Geometry 1 Guest MartinFall semester2 credits
MathComputer Assisted Proof of Nonlinear Equations Shinichi OishiSpring semester2 credits
MechFoundation of Geometry 2 Hiroaki YoshimuraSpring semester2 credits
PhysMathematical Formulation of Quantum Mechanics Tohru OzawaSpring semester2 credits
PhysMathematical Formulation of Classical Field Theory Tohru OzawaFall semester2 credits
PhysAdvanced Theoretical Quantum Physics Kazuya YuasaSpring semester2 credits
PhysPhysics of Non-Equilibrium System A Yoshihiro YamazakiSpring semester2 credits
* We don't open "Advanced Theoretical Quantum Physics" (Kazuya Yuasa/Spring semester/2 credits) and "Physics of Non-Equilibrium System B" (Yoshihiro Yamazak/Fall semester/2 credits) in 2016.
B) Special Lectures
Field Course Title Instructor Term credit
MathAdvanced Study of Nonlinear Mechanics Hiroaki Yoshimura, Guest Martinintensive4 credits
MathSpecial Lecture on Mathematical Fluid Mechanics
(Advanced Study of Mathematical Fluid Dynamics)
Hideo Kozono, Yoshihiro Shibataintensive4 credits
PhysSpecial Lecture on Quantum Physics Hiromichi Nakazato, Kazuya Yuasaintensive4 credits
*Special Lectures include Mini-courses and short terms lectures by visiting scholars in international workshops.
C) Independent Studies
Field Course Title Instructor Term credit
General StudiesInternship Nozomu TogawaFull year2 credits

Course Title Tnstructor Course Description Goals and objectives of the lesson

Special Lecture on Mathematical Fluid Mechanics
Intensive course (Fall semester)

Hideo KOZONO

Yoshihiro SHIBATA

Maria SCHONBEK

Yukihito SUZUKI

Masao YAMAZAKI

1. Prof. Kozono's Lecture
Critical Sobolev inequality in Besov spaces andits application to the Beale-Kato-Majda blow-up criterion
Abstract: It is known that the space H1,n(Rn)is continuously embedded in Lp(Rn) for all p < ∞, but not in L(Rn). More precisely, H1,n(Rn) is embedded into BMO space. In the lecture, we give alogarithmic L bound of functions in terms on BMO and H1,p(Rn)(n < p < ∞). Furthermore, the generalization to the Besov space in B0∞,∞(Rn)is established.
As an application, we show such a blow-upcriterion as Beale-Kato-Majda type for local strong solutions to the Euler andthe Navier-Stokes equations.

2. Prof. Shibata's Lecture
The Free Boundary Problem for the Navier-Stokes Equations Abstract: In this lecture, we prove the local and global well-posedness of the free boundary problem for the Navier-Stokes equations. The key issues are to prove the maximal regularity and the stability of the semi-group for the linearized problem. The maximalo regularity is proved with the help of the R boundedness of the Stokes operators with free boundary condition. The stability of the semi-gorup is proved by some sharp analysis of the spectrum near the origin.

Topics in Numerical Analysis B
(Spring semester)

Shinichi OISHI

Segfried M. RUMP

We introduce so-called "Verification methods" in this lecture. These are numerical methodscomputing correct error bound for the true result including a proof ofsolvability and possibly uniqueness. The proof of correctness is withmathematical rigor including in particular discretization and rounding errors.The methods are introduced with INTLAB, the Matlab/Octave toolbox for ReliableComputing.

To understand possible weaknesses of numerical methods, to understand principle of verification methods, and to be able to devise and write new verification methods.