These self-contained books give the necessary mathematical background and physical principles to build models for technological and scientific purposes. They show how to formulate problems, justify the solutions, and interpret the results.
Complex Analysis with Applications to Flows and Fields presents the theory of functions of a complex variable, from the complex plane to the calculus of residues to power series to conformal mapping. It explores numerous physical and engineering applications concerning potential flows, the gravity field, electro- and magnetostatics and steady heat conduction.
Transcendental Representations with Applications to Solids and Fluids focuses on four infinite representations: series expansions, series of fractions for meromorphic functions, infinite products for functions with infinitely many zeros, and continued fractions as alternative representations. Contains applications to incompressible rotational flows, compressible irrotational flows, unsteady flows, deflection of membranes, torsion of rods, plane elasticity, and plane viscous flows.
Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders. Contains applications to differential geometry, tensor calculus, theory of potential fields, self-adjoint and non-self-adjoint problems, multipolar expansions and Green’s functions for elastic strings and bars, potential and rotational flow, electro- and magnetostatics.
- Campos, L.M.B.C. (2014) Generalized Calculus with Applications to Matter and Forces. CRC Press, Boca Raton, USA. ISBN:978-1-4200-7115-3
- Campos, L.M.B.C. (2012) Transcendental Representations with Applications to Solids and Fluids. CRC Press, Boca Raton, USA. ISBN:978-1-4398-3431-2
- Campos, L.M.B.C. (2010) Complex Analysis with Applications to Flows and Fields. CRC Press, Boca Raton, USA. ISBN:978-1-4200-7118-4
Luís M. B. C. Campos