Introduction to Analysis 1st Edition  (English, Hardcover, Mattuck Arthur P.)

Designed for a one-semester undergraduate analysis course, this new text is written in a conversational, accessible style offering a great deal of examples. It gradually ascends in difficulty to help the student avoid hitting a wall.

Salient Features

• Moves rapidly into the substance of analysis to avoid extensive talk about real numbers beyond what is immediately needed.
• Offers a simplified presentation of limits, based on the approximation idea and the use of “for n >>1” and “for x …¢ a.” Helped along by the Limit Demon, students can write correct and readable limit arguments from the beginning. Warnings about common pitfalls to avoid are provided.
• Uses Applications to show how the basic theorems are used in differential equations, Fourier analysis, advanced calculus, numerical analysis, number theory, inscribing equilateral triangles in closed convex curves, and slicing Danish ham sandwiches.
• Presents analysis in a unified way as the mathematics based on inequalities, estimations, and approximations. The point-set topology viewpoint is presented late and used minimally.
• Offers a flexible structure: after the basic material, there are different goals at which the course may be aimed- e.g., differentiation of power series, an introduction to the Lebesgue integral, point-set topology, differentiation of improper integrals (e.g., Laplace transform), the existence and uniqueness theorem for differential equations.
• Includes simplified and meaningful proofs. Proofs, plausibility arguments, and intuitive explanations are written and arranged on the page so as to try for maximum clarity.
• Features Exercises and Problems at the end of each chapter, as well as Questions at the end of each section with full answers/solutions at the end of each chapter.