INTEGRATION OF MATHEMATICAL COURSES AND COURSES IN CIVIL ENGINEERING: THE USE OF “MATHEMATICA†AND CASE STUDIES

Abstract

Two real-world problems are suggested in thepresent paper in order to integrate mathematical coursesand courses in civil engineering. One problem is related toleak detection in pipelines by transient damping method.Introducing a small transient in a pipeline, using time seriesfor pressure measurements and performing the discreteFourier transform one can obtain a relatively simpleformula for the location of the leak which includes the ratiosof two leak-induced damping rates. The problem can besolved (at least partially) during “Mathematica†lab session(lab sessions are integrated components of calculus coursegiven at the Riga Technical University). The second problemis based on bacteria regrowth model in water distributionnetworks. A simplified model is described by a system ofordinary differential equations which is solved numericallyby “Mathematica†built-in module NDSolve.

 

 

Index Terms - Leak detection, “Mathematicaâ€, bacteriaregrowth, Newton’s method.