Analysis: With an Introduction to ProofFor courses in Real Analysis, Advanced Calculus, and Transition to Advanced Mathematics or Proofs course. Carefully focused on reading and writing proofs, this introduction to the analysis of functions of a single real variable helps students in the transition from computationally oriented courses to abstract mathematics by its emphasis on proofs. Student oriented and instructor friendly, it features clear expositions and examples, helpful practice problems, many drawings that illustrate key ideas, and hints/answers for selected exercises. *NEW - True/False questions - (More than 250 total) located at the beginning of the exercises for each section and relating directly to the reading. *NEW - 8 new illustrations of key concepts make this the most visually compelling analysis text. *Straightforward discussion of logic - As it applies to the proving of theorems in analysis (Ch. 1). Can be covered briefly or in depth, depending on the needs of students. *Practice problems - Scattered throughout the narrative (more than 140 total). These problems relate directly to what has just been presented. Includes complete answers at the end of each section. *Fill-in-the-blank proofs. Helps stude |
Contents
Sets and Functions | 31 |
The Real Numbers | 87 |
Ordered Fields | 95 |
Copyright | |
22 other sections not shown
Common terms and phrases
accumulation point apply assume axiom bijection bounded called Cauchy closed compact conclude consider contains continuous function contradiction converges uniformly countable defined definition denote derivative differentiable diverges element equal equivalence EXAMPLE Exercise exists Figure Find finite formula function f ƒ is continuous give given Hence holds implies increasing induction inequality infinite injective integrable interval Justify each answer Let f Let f(x lim sup limit Mark each statement mean mean value theorem metric space neighborhood nonempty obtain open set ordered particular partition positive Proof properties Prove radius of convergence rational real number relation result satisfies sequence statement True subsequence subset sums Suppose Suppose that ƒ surjective True or False uniform uniformly continuous upper bound write