Advanced Mathematics for Economics

This book contains a compact, accessible treatment of the mainmathematical topics encountered in economics at an advanced level,moving from basic material into the twin areas of static anddynamic optimization.Nearly half of the book is devoted to a survey of univariatecalculus, matrix algebra and multuvariate calculus. Thisfundamental material is made vigorous by the inclusion of a varietyof applications. The later chapters focus on the Lagrangemultiplier technique: when it will work, why it works and whateconomic insights it yields. The properties of maximum valuefunctions and duality are explored, as are the Hamiltonianconditions for dynamic problems in the optimal control format.Dynamic programming and the calculus of variations are alsocovered.Much of the discussion proceeds at a heuristic level and by workedexample, but the theorems and proofs required by the mostanalytical user are also to be found. The underlying message isthat the language of mathematics can be productive, givingexpression to the ideas and facilitating approaches from whichinsights flow that may be hard to come by in other ways.The book will be particularly useful for final year undergraduatesdoing mathematics for economists courses, and postgraduatestudents.