This manual includes solutions to the odd-numbered exercises in Economic Dynamics in Discrete Time. Some exercises are purely analytical, while others require numerical methods. Computer codes are provided for most problems. Many exercises ask the reader to apply the methods learned in a chapter to solve related problems, but some exercises ask the reader to complete missing steps in the proof of a theorem or in the solution of an example in the book.

Solutions to the odd-numbered exercises in the second edition of Economic Dynamics in Discrete Time. This manual includes solutions to the odd-numbered exercises in the second edition of Economic Dynamics in Discrete Time. Some exercises are purely analytical, while others require numerical methods. Computer codes are provided for most problems. Many exercises ask the reader to apply the methods learned in a chapter to solve related problems, but some exercises ask the reader to complete missing steps in the proof of a theorem or in the solution of an example in the book.

A unified, comprehensive, and up-to-date introduction to the analytical and numerical tools for solving dynamic economic problems. This book offers a unified, comprehensive, and up-to-date treatment of analytical and numerical tools for solving dynamic economic problems. The focus is on introducing recursive methods—an important part of every economist's set of tools—and readers will learn to apply recursive methods to a variety of dynamic economic problems. The book is notable for its combination of theoretical foundations and numerical methods. Each topic is first described in theoretical terms, with explicit definitions and rigorous proofs; numerical methods and computer codes to implement these methods follow. Drawing on the latest research, the book covers such cutting-edge topics as asset price bubbles, recursive utility, robust control, policy analysis in dynamic New Keynesian models with the zero lower bound on interest rates, and Bayesian estimation of dynamic stochastic general equilibrium (DSGE) models. The book first introduces the theory of dynamical systems and numerical methods for solving dynamical systems, and then discusses the theory and applications of dynamic optimization. The book goes on to treat equilibrium analysis, covering a variety of core macroeconomic models, and such additional topics as recursive utility (increasingly used in finance and macroeconomics), dynamic games, and recursive contracts. The book introduces Dynare, a widely used software platform for handling a range of economic models; readers will learn to use Dynare for numerically solving DSGE models and performing Bayesian estimation of DSGE models. Mathematical appendixes present all the necessary mathematical concepts and results. Matlab codes used to solve examples are indexed and downloadable from the book's website. A solutions manual for students is available for sale from the MIT Press; a downloadable instructor's manual is available to qualified instructors.

Incorporating new problems and examples, the second edition of Linear Systems and Signals features MATLAB® material in each chapter and at the back of the book. It gives clear descriptions of linear systems and uses mathematics not only to prove axiomatic theory, but also to enhance physical and intuitive understanding.

An advanced treatment of modern macroeconomics, presented through a sequence of dynamic equilibrium models, with discussion of the implications for monetary and fiscal policy. This textbook offers an advanced treatment of modern macroeconomics, presented through a sequence of dynamic general equilibrium models based on intertemporal optimization on the part of economic agents. The book treats macroeconomics as applied and policy-oriented general equilibrium analysis, examining a number of models, each of which is suitable for investigating specific issues but may be unsuitable for others. After presenting a brief survey of the evolution of macroeconomics and the key facts about long-run economic growth and aggregate fluctuations, the book introduces the main elements of the intertemporal approach through a series of two-period competitive general equilibrium models—the simplest possible intertemporal models. This sets the stage for the remainder of the book, which presents models of economic growth, aggregate fluctuations, and monetary and fiscal policy. The text focuses on a full analysis of a limited number of key intertemporal models, which are stripped down to essentials so that students can focus on the dynamic properties of the models. Exercises encourage students to try their hands at solving versions of the dynamic models that define modern macroeconomics. Appendixes review the main mathematical techniques needed to analyze optimizing dynamic macroeconomic models. The book is suitable for advanced undergraduate and graduate students who have some knowledge of economic theory and mathematics for economists.

DISCRETE MATHEMATICS WITH APPLICATIONS, 5th Edition, Metric Edition explains complex, abstract concepts with clarity and precision and provides a strong foundation for computer science and upper-level mathematics courses of the computer age. Author Susanna Epp presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to today's science and technology.

An innovative textbook for use in advanced undergraduate and graduate courses; accessible to students in financial mathematics, financial engineering and economics. Introduction to the Economics and Mathematics of Financial Markets fills the longstanding need for an accessible yet serious textbook treatment of financial economics. The book provides a rigorous overview of the subject, while its flexible presentation makes it suitable for use with different levels of undergraduate and graduate students. Each chapter presents mathematical models of financial problems at three different degrees of sophistication: single-period, multi-period, and continuous-time. The single-period and multi-period models require only basic calculus and an introductory probability/statistics course, while an advanced undergraduate course in probability is helpful in understanding the continuous-time models. In this way, the material is given complete coverage at different levels; the less advanced student can stop before the more sophisticated mathematics and still be able to grasp the general principles of financial economics. The book is divided into three parts. The first part provides an introduction to basic securities and financial market organization, the concept of interest rates, the main mathematical models, and quantitative ways to measure risks and rewards. The second part treats option pricing and hedging; here and throughout the book, the authors emphasize the Martingale or probabilistic approach. Finally, the third part examines equilibrium models—a subject often neglected by other texts in financial mathematics, but included here because of the qualitative insight it offers into the behavior of market participants and pricing.

A significant new edition of a text that offers both tools and sample applications; extensive revisions and seven new chapters improve and expand upon the original treatment.