Further mathematics for economic analysis
Financial Times/Prentice Hall, 2005 - Business & Economics - 595 pages
Further Mathematics for Economic Analysis By SydsÆter, Hammond, Seierstad and StrØm Further Mathematics for Economic Analysis is a companion volume to the highly regarded Essential Mathematics for Economic Analysis by Knut SydsÆter and Peter Hammond. The new book is intENDed for advanced undergraduate and graduate economics students whose requirements go beyond the material usually taught in undergraduate mathematics courses for economists. It presents most of the mathematical tools that are required for advanced courses in economic theory - both micro and macro. This second volume has the same qualities that made the previous volume so successful. These include mathematical reliability, an appropriate balance between mathematics and economic examples, an engaging writing style, and as much mathematical rigour as possible while avoiding unnecessary complications. Like the earlier book, each major section includes worked examples, as well as problems that range in difficulty from quite easy to more challenging. Suggested solutions to odd-numbered problems are provided. Key Features Systematic treatment of the calculus of variations, optimal control theory and dynamic programming. Several early chapters review and extEND material in the previous book on elementary matrix algebra, multivariable calculus, and static optimization. Later chapters present multiple integration, as well as ordinary differential and difference equations, including systems of such equations. Other chapters include material on elementary topology in Euclidean space, correspondences, and fixed point theorems. A website is available which will include solutions to even-numbered problems (available to instructors), as well as extra problems and proofs of some of the more technical results. Peter Hammond is Professor of Economics at Stanford University. He is a prominent theorist whose many research publications extEND over several different fields of economics. For many years he has taught courses in mathematics for economists and in mathematical economics at Stanford, as well as earlier at the University of Essex and the London School of Economics. Knut SydsÆter, Atle Seierstad, and Arne StrØm all have extensive experience in teaching mathematics for economists in the Department of Economics at the University of Oslo. With Peter Berck at Berkeley, Knut SydsÆter and Arne StrØm have written a widely used formula book, Economists' Mathematical Manual (Springer, 2000). The 1987 North-Holland book Optimal Control Theory for Economists by Atle Seierstad and Knut SydsÆter is still a standard reference in the field.
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arbitrary assume Bellman equation bounded C1 function characteristic equation coefficients column complex numbers Compute concave function Consider constraints continuous function converges convex set corresponding defined definition denote derivative determinant difference equation differential equation double integral economic eigenvalues eigenvectors equal equilibrium point Euler equation EXAMPLE exists a number Figure first-order fixed formula given gives globally asymptotically stable Hamiltonian hemicontinuous Hence implies inequality interior point interval Jacobian linear linearly independent lower hemicontinuous matrix maximizes maximum point maximum principle necessary conditions Note objective function obtain open set optimal control optimal solution optimization problems positive constants principal minors problem max PROBLEMS FOR SECTION proof prove quasiconcave real number result right-hand side satisfies sequence Solve the problem stationary point subset sufficient conditions Suppose unique solution upper hemicontinuous value function variables vector yields