This book is a self-contained treatment of all the mathematics needed by undergraduate and beginning graduate students of economics. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra and easily accessible introductions to optimization and dynamics. The emphasis throughout is on intuitive argument and problem-solving. All methods are illustrated by well-chosen examples and exercises selected from central areas of modern economic analysis. New features of the second edition include: - a thorough exposition of dynamic optimization in discrete and continuous time - an introduction to the rigorous mathematical analysis used in graduate-level economics.