LECTURES ON FUNCTIONAL EQUATIONS AND THEIR APPLICATIONS

Numerous detailed proofs highlight this systematic treatment, which offers upper-level undergraduates and graduate students an elementary approach to functional equations. Starting with equations that can be solved by simple substitutions, the firstpart examines the determination of the values of the unknown function on a dense set. It also surveys equations with several unknown functions and methods of reduction to differential and integral equations. The second part begins with simple equations and advances to composite equations, equations with several unknown functions of several variables, and reduction to partial differential equations, concluding with explorations of vector and matrix equations.