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What’s the point of calculating definite integrals since you can’t possibly do them all? What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book, now in its second edition, is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you. New material in the second edition includes 25 new challenge problems and solutions, 25 new worked examples, simplified derivations, and additional historical discussion.
This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.
An introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. The 3-part treatment begins with concepts and theorems encountered in the theory of quadrature and then explores the problem of calculation of definite integrals and methods for the calculation of indefinite integral. 1962 edition.
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This book, first published in 2004, uses the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics.
How to put Ken Wilber’s Integral Theory—which synthesizes the teachings of the world’s great wisdom traditions—into practice in all aspects of everyday life, so you can reach your full human potential “A masterpiece guide of grounded, intelligent, self-transforming wisdom integrating the insights of all the great traditions of truth.” —Caroline Myss, author of Anatomy of the Spirit Over the last thirty-five years, Ken Wilber has developed an Integral “theory of everything” that makes sense of how all the world’s knowledge systems—East and West; ancient, modern, and postmodern—fit together and can elevate our awareness. Drawing on science, psychology, human development, spirituality, religion, and dozens of other fields, Integral Theory is a revolutionary framework for understanding ourselves and the world we live in. Now there is a way to not just think Integrally, but to embody an Integral worldview in your everyday life. Integral Life Practice is not just a new approach to self-development and higher awareness, but a way of making sense of—and making best use of—the existing treasure trove of insights, methods, and practices for cultivating a more enlightened life. It offers a uniquely adaptive approach to awakened living that’s suitable for everyone: people with busy careers and families, college students, retirees, even hardcore athletes and yogis. It’s geared for devout—and irreverent—people of any religion, or no religion! This highly flexible system will help you develop your physical health, spiritual awareness, emotional balance, mental clarity, relational joy, and energy level, within a framework that integrates all aspects of your life. Combining original exercises, vivid examples, cutting-edge theory, and illustrative graphics, Integral Life Practice is the ultimate handbook for realizing freedom and fullness in the 21st century.
Authoritative, well-written treatment of extremely useful mathematical tool with wide applications. Topics include Volterra Equations, Fredholm Equations, Symmetric Kernels and Orthogonal Systems of Functions, more. Advanced undergraduate to graduate level. Exercises. Bibliography.
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Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.