Applied Mathematics: Body & Soul is a mathematics education reform
project developed at Chalmers University of Technology and includes a
series of volumes and software. The program is motivated by the computer
revolution opening new possibilitites of computational mathematical
modeling in mathematics, science and engineering. It consists of a
synthesis of Mathematical Analysis (Soul), Numerical Computation (Body)
and Application. Volumes I-III present a modern version of Calculus and
Linear Algebra, including constructive/numerical techniques and
applications intended for undergraduate programs in engineering and
science. Further volumes present topics such as Dynamical Systems, Fluid
Dynamics, Solid Mechanics and Electro-Magnetics on an advanced
undergraduate/graduate level.
Volume I (Derivatives and Geometry in R3) presents basics of Calculus
starting with the construction of the natural, rational, real and
complex numbers, and proceeding to analytic geometry in two and three
space dimensions, Lipschitz continuous functions and derivatives,
together with a variety of applications.
Volume II (Integrals and Geomtery in Rn) develops the Riemann integral
as the solution to the problem of determining a function given its
derivative, and proceeds to generalizations in the form of initial value
problems for general systems of ordinary differential equations,
including a variety of applications. Linear algebra including numerics
is also presented.
Volume III (Calculus in Several Dimensions) presents Calculus in several
variables including partial derivatives, multi-dimensional integrals,
partial differential equations and finite element methods, together with
a variety of applications modeled as systems of partial differential
equations.
The authors are leading researchers in Computational Mathematics who
have written various successful books.
Further information on Applied Mathematics: Body and Soul can be found
at http: //www.phi.chalmers.se/bodysoul/.
