The Body and Soul Project

reform of mathematics education

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Abstract


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.

Computational Calculus is the modern version of Calculus based on digital computation by computers as the basis of our modern information society with automated production:

                                        Automated assembly line of the information society.

Mathematics Education of Modern Society

Body&Soul is an educational reform program presenting Computational Calculus as the foundation of modern science/engineering education. Body&Soul presents a synthesis of analytical and computational mathematics giving the student the capabilty to model and simulate complex phenomena in science and engineering. Body represents digital computation and Soul represents mathematical analysis. The role of mathematics today is described in the knols:

The relation between Body and Soul is explored in 

An interactive web-version of Body&Soul will be presented on Icarus

The Essence of Calculus

The fundamental study of of classical Analytical Calculus concerns initial value problems of the form 

(IVP)                                         du/dt = f(u(t),t) for t > 0 with u(0) = g

where du/dt is the derivative of the unknown function u(t), f(u,t) is a given function of u and t, and g is a given initial value:

  • 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

forming the theoretical basis of science and engineering.

Modernity = Automation

Modern society is based on automated production of material goods and automated digitial processing of information. Body&Soul gives a mathematical basis for automation and is supported by the open-source  software project FEniCS for automated computational solution of differential equations:

                                                           Modern Times of Automation