Calculus Ia/IIa
\( \displaystyle \frac{d}{dx}\int^x f(t)\,dt = f(x) \)
Rates of change, integration, vector analysis, and differential equations are taught as tools for physics and engineering.
Courses and Education
Education
From calculus and linear algebra to logic, relativity, quantum theory, continuum physics, and space science. The emphasis is on treating mathematics not as a list of formulas to memorize, but as a language for describing the world.
Teaching
Courses Taught
Each course is paired with an equation that opens a route into the subject.
Linear Algebra I and II
\( \displaystyle \mathbb{R}^n=\mathcal{N}(A)\oplus\mathcal{R}(A^{T}) \)
Matrices, linear maps, and eigenvalue problems are presented as a language for structured multivariable phenomena.
Mathematics
\( \displaystyle \frac{\sqrt{n}(\bar{X}_n-\mu)}{\sigma}\Rightarrow N(0,1) \)
First-year mathematics is positioned as a bridge toward specialized courses, balancing calculation with concepts.
Logic
\( \displaystyle \neg(P\land Q)\Leftrightarrow(\neg P\lor\neg Q) \)
Propositions, inference, negation, and contraposition support clear reading and writing of arguments.
Basics of Space Science
\( \displaystyle H^2=\frac{8\pi G}{3}\rho-\frac{k}{a^2}+\frac{\Lambda}{3} \)
Stars, galaxies, cosmic expansion, and gravity are introduced through both equations and observation.
Relativity and Advanced Gravity
\( \displaystyle G_{\mu\nu}+\Lambda g_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu} \)
Relativity and gravity are treated as geometry of spacetime, with a clear route into research topics.
Quantum Mechanics A
\( \displaystyle i\hbar\frac{\partial\psi}{\partial t}=H\psi \)
States, operators, and eigenvalue problems frame quantum mechanics in the language of linear algebra.
Mechanics B
\( \displaystyle \bm{F}=m\bm{a} \)
Particle motion is developed through the relation between force, conservation laws, and equations of motion.
Continuum Physics
\( \displaystyle \frac{\partial\bm{v}}{\partial t}+(\bm{v}\cdot\nabla)\bm{v}=-\frac{1}{\rho}\nabla p+\nu\nabla^2\bm{v} \)
Fluids and continua are described through conservation laws and field equations.
Textbook
Textbook
A textbook that carries first-year calculus toward vector analysis and differential equations.
Differential and Integral Calculus and Its Applications
Umpei Miyamoto, Kyoritsu Shuppan, released on Nov. 22, 2022. ISBN 9784320114807.
The book emphasizes not only calculation techniques, but also a view of calculus as a bridge toward vector analysis, differential equations, physics, and engineering.
Teaching Experience
Courses taught across mathematics and physics.
Sugaku-Butsuri Kakekomidera
Mathematics and physics education using a peer-tutor system at Akita Prefectural University.
High School/University Articulation
Physics education on differential equations and dimensional analysis.