Introduction to AnalysisBrooks/Cole Publishing Company, 1993 - 246 páginas This text gives students an introduction to the basic vocabulary and concepts necessary for further study in analysis. Definitions and theorems are presented. It motivates proofs and explains how a mathematician develops a proof. It lays the set-theoretical foundations for the real number system, including induction and well-ordering. |
Contenido
Preliminaries | 1 |
Sequences | 35 |
Limits of Functions | 63 |
Derechos de autor | |
Otras 6 secciones no mostradas
Términos y frases comunes
1-1 function a₁ absolutely convergent accumulation point alternating series test An+1 anbn b₂ calculus Cauchy sequence Chapter compact continuous at xo converges absolutely converges to xo converges to zero converges uniformly countable set Define f differentiable at xo diverges Exercise f dx f(xn f(xo fact finite number fn(x function f ƒ and g ƒ dx ƒ is continuous ƒ is differentiable hence implies infinite series irrational number lemma Let f lim f(x limit at xo limit at zero lower bound mathematical induction Mean-Value Theorem n=1 converges N₁ neighborhood nonempty number of terms partition polynomial positive integer positive real number power series Proof Suppose Prove that ƒ radius of convergence rational numbers Riemann-integrable Rolle's Theorem sequence converges series converges set of real show that ƒ subset Suppose f Taylor's Theorem THEOREM Let THEOREM Suppose uniformly continuous well-ordering principle x-xo хо