Advanced Mathematics for Economists

This book contains a compact, accessible treatment of the main
mathematical topics encountered in economics at an advanced level,
moving from basic material into the twin areas of static and
dynamic optimization.

Nearly half of the book is devoted to a survey of univariate
calculus, matrix algebra and multuvariate calculus. This
fundamental material is made vigorous by the inclusion of a variety
of applications. The later chapters focus on the Lagrange
multiplier technique: when it will work, why it works and what
economic insights it yields. The properties of maximum value
functions and duality are explored, as are the Hamiltonian
conditions for dynamic problems in the optimal control format.
Dynamic programming and the calculus of variations are also
covered.

Much of the discussion proceeds at a heuristic level and by worked
example, but the theorems and proofs required by the most
analytical user are also to be found. The underlying message is
that the language of mathematics can be productive, giving
expression to the ideas and facilitating approaches from which
insights flow that may be hard to come by in other ways.

The book will be particularly useful for final year
undergraduates doing mathematics for economists courses, and
postgraduate students.