International Centre for Physical Land Resources
Mathematics or Physics
Dip.- Mathematics or Physics
Real functions of one variable are introduced in a concatenation of proofs and minimal definitions, with priority for the concrete and the applicable, in conjunction with a set of exercises orientated towards practical applications. The implementation is guided by the goal of reaching linear differential equations as soon as possible. The following choices have been made : introduction of the real number field through cuts (an axiomatic approach would demand a model), Riemann integration through partitions (typical of the geometrical background of the concept of an integral), elementary functions defined by integrals (the logarithm and arctangent are prototypes of integrals of rational functions) and their inverses (which provides a general method for generating periodic functions, such as elliptic functions).