Excursions in classical analysis : pathways to advanced problem solving and undergraduate research / Hongwei Chen.

Format:

Book

Author/Creator:

Chen, Hongwei.

Contributor:

Mathematical Association of America.

Series:

Classroom resource materials (Unnumbered)

Classroom resource materials

Language:

English

Subjects (All):

Mathematical analysis--Problems, exercises, etc.

Mathematical analysis.

Physical Description:

1 online resource (0 p.)

Edition:

1st ed.

Place of Publication:

Washington, D.C. : Mathematical Association of America, c2010.

Language Note:

English

Summary:

Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof. The author presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that at first glance, might not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis. The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order.

Contents:

Two classical inequalities

A new approach for proving inequalities

Means generated by an integral

The L'Hôpital monotone rule

Trigonometric identities via complex numbers

Special numbers

On a sum of cosecants

The gamma products in simple closed forms

On the telescoping sums

Summation of subseries in closed form

Generating functions for powers of Fibonacci numbers

Identities for the Fibonacci powers

Bernoulli numbers via determinants

On some finite trigonometric power sums

Power series of (arcsin x)²

Six ways to sum [zeta] 2

Evaluations of some variant Euler sums

Interesting series involving binomial coefficients

Parametric differentiation and integration

Four ways to evaluate the Poisson integral

Some irresistible integrals.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-88385-935-1

OCLC:

939263603