Body and Soul is a mathematics education reform project combining analytical and computational mathematics into a foundation of modern information/industrial society.
The Industrial Society and the Information Society
The mathematics of integrals and differential equations referred to as Calculus was developed by Leibniz and Newton in the second half of the 17th century, which initiated the age of enlightenment and the scientific revolution and industrial revolution leading to the industrial society with the assembly line:
Manual assembly line of the industrial society.
Mathematics Education of Modern Society
- Modern Mathematics Education
- Why/What Mathematics for Engineers?
- Simulation Technology
- How to (Not) Organize a University.
The Essence of Calculus
(IVP) du/dt = f(u(t),t) for t > 0 with u(0) = g
- If f(u,t) = f(t) does not depend on t, then u(t) is a primitive function or integral of f(t).
- If f(u,t) = f(u) is a simple function of u, then u(t) is an elementary function, such as the exponential function exp(t) if f(u) = u.
The Essence of Computational Calculus
The fundamental study of Computational Calculus concerns computational methods for computing solutions of initial value problems of the form (IVP) with general vector-valued functions f(u,t) depending on derivatives of u with respect to space variables, such as
- Navier-Stokes equations of fluid mechanics
- Navier’s equations of solid mechanics
- Maxwell’s equations of electromagnetics
- Schrödinger’s equations of quantum mechanics