This best-selling classic has been used as an essential textbook for a transitional course from calculus to an analysis by thousands of students in the United States and around the world for over thirty years, making it one of the best-selling books of all time. Students majoring in mathematics who have little to no prior experience with rigorous proofs have found it to be an extremely helpful resource. Its approachable tone demystifies the process of constructing proofs while providing a thorough analysis of the theoretical foundations of calculus. The proofs are presented in their entirety, and the enormous number of carefully selected examples and exercises range in difficulty from easy to difficult.
The second version of the book maintains a clear and concise writing style, enlightening discussions, and straightforward, well-motivated proofs. The irrationality of pi, the Baire category theorem, Newton’s technique and the secant method, and continuous nowhere-differentiable functions are some new topics that have been added.