The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples it contains over 800 exercises. New stand-alone chapters give a systematic account of the ‘special functions’ of physical science cover an extended range of practical applications of complex variables and give an introduction to quantum operators. Further tabulations of relevance in statistics and numerical integration have been added. In this edition half of the exercises are provided with hints and answers and in a separate manual available to both students and their teachers complete worked solutions.
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The present edition of the book is strictly according to the revised curriculum of the C.B.S.E and latest N.C.E.R.T Text book for the session 2017-18. In this edition, we have given a separate NCERT Corner at the end of each chapter which contains all the examples and exercises of the NCERT Text Book alongwith answers and hints.It further includes NCERT exempler problems, latest C.B.S.E sample paper, HOTS & model test paper for practice.
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Version 5.0. A first course in rigorous mathematical analysis. Covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, sequences of functions, and metric spaces. Originally developed to teach Math 444 at University of Illinois at Urbana-Champaign and later enhanced for Math 521 at University of Wisconsin-Madison and Math 4143 at Oklahoma State University. The first volume is either a stand-alone one-semester course or the first semester of a year-long course together with the second volume. It can be used anywhere from a semester early introduction to analysis for undergraduates (especially chapters 1-5) to a year-long course for advanced undergraduates and masters-level students. See http: //www.jirka.org/ra/
Table of Contents (of this volume I):
1. Real Numbers
2. Sequences and Series
3. Continuous Functions
4. The Derivative
5. The Riemann Integral
6. Sequences of Functions
7. Metric Spaces
This first volume contains what used to be the entire book “Basic Analysis” before edition 5, that is chapters 1-7. Second volume contains chapters on multidimensional differential and integral calculus and further topics on approximation of functions.
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Version 2.0. The second volume of Basic Analysis, a first course in mathematical analysis. This volume is the second semester material for a year-long sequence for advanced undergraduates or masters level students. This volume started with notes for Math 522 at University of Wisconsin-Madison, and then was heavily revised and modified for teaching Math 4153/5053 at Oklahoma State University. It covers differential calculus in several variables, line integrals, multivariable Riemann integral including a basic case of Green’s Theorem, and topics on power series, Arzelà-Ascoli, Stone-Weierstrass, and Fourier Series. See http: //www.jirka.org/ra/
Table of Contents (of this volume II):
8. Several Variables and Partial Derivatives
9. One Dimensional Integrals in Several Variables
10. Multivariable Integral
11. Functions as Limits
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Weird Maths is a lively, accessible, fun book about mathematics, the maths that is all around us, that defines us, our intelligence, our curiosity. In this delightful journey of discovery, David Darling and Agnijo Banerjee explore the cutting edge of modern maths and delve into some fascinating questions: Is anything truly random? Does infinity actually exist? Can maths help us understand chaos? Can chess be solved with maths? If there are aliens and if they play music, would we like it? Packed with puzzles and paradoxes, mind-bending concepts and surprising solutions, Weird Maths is a book for anyone who is interested in maths or in popular science.
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A unique text and reference for pure and applied mathematicians, engineers, physicists, and chemists, this book was a landmark in the literature of computational methods in mathematical physics in the twentieth century. The treatment remains of great interest because of its thoroughness and scope. A valuable historic source for methods and approaches to problems of mathematical physics, this text is enhanced by many detailed, worked-out examples.
Topics include methods based on the representation of the solution as an infinite series, the approximate solution of the integral equations of Swedish mathematician Erik Ivar Fredholm, the method of nets, and variational methods. Additional subjects include the conformal transformation of regions, principles of the application of conformal transformation to the solution of the fundamental problems for canonical regions, and Polish mathematician Dr. Hermann Schwarz’s method.
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