The book offers an initiation into mathematical reasoning, and into the mathematician's mind-set and reflexes. Specifically, the fundamental operations of calculus--differentiation and integration of functions and the summation of infinite series--are built, with logical continuity (i.e., "rigor"), starting from the real number system. The first chapter sets down precise axioms for the real number system, from which all else is derived using the logical tools summarized in an Appendix. The discussion of the "fundamental theorem of calculus," the focal point of the book, especially thorough. The concluding chapter establishes a significant beachhead in the theory of the Lebesgue integral by elementary means.
Written for:
undergraduate math students
發表於2024-08-23
A First Course in Real Analysis 2024 pdf epub mobi 電子書 下載
圖書標籤: 實分析
A First Course in Real Analysis 2024 pdf epub mobi 電子書 下載