Advanced Calculus: A Differential Forms Approach (Modern Birkhäuser Classics) - Softcover

Edwards, Harold M. M.

Softcover

ISBN 10: 0817684115 ISBN 13: 9780817684112

Verlag: Birkhäuser, 2013

Inhaltsangabe

<P>IN A BOOK WRITTEN FOR MATHEMATICIANS, TEACHERS OF MATHEMATICS, AND HIGHLY MOTIVATED STUDENTS, HAROLD EDWARDS HAS TAKEN A BOLD AND UNUSUAL APPROACH TO THE PRESENTATION OF ADVANCED CALCULUS. HE BEGINS WITH A LUCID DISCUSSION OF DIFFERENTIAL FORMS AND QUICKLY MOVES TO THE FUNDAMENTAL THEOREMS OF CALCULUS AND STOKES’ THEOREM. THE RESULT IS GENUINE MATHEMATICS, BOTH IN SPIRIT AND CONTENT, AND AN EXCITING CHOICE FOR AN HONORS OR GRADUATE COURSE OR INDEED FOR ANY MATHEMATICIAN IN NEED OF A REFRESHINGLY INFORMAL AND FLEXIBLE REINTRODUCTION TO THE SUBJECT. FOR ALL THESE POTENTIAL READERS, THE AUTHOR HAS MADE THE APPROACH WORK IN THE BEST TRADITION OF CREATIVE MATHEMATICS.</P><P>THIS AFFORDABLE SOFTCOVER REPRINT OF THE 1994 EDITION PRESENTS THE DIVERSE SET OF TOPICS FROM WHICH ADVANCED CALCULUS COURSES ARE CREATED IN BEAUTIFUL UNIFYING GENERALIZATION. THE AUTHOR EMPHASIZES THE USE OF DIFFERENTIAL FORMS IN LINEAR ALGEBRA, IMPLICIT DIFFERENTIATION IN HIGHER DIMENSIONS USING THE CALCULUS OF DIFFERENTIAL FORMS, AND THE METHOD OF LAGRANGE MULTIPLIERS IN A GENERAL BUT EASY-TO-USE FORMULATION. THERE ARE COPIOUS EXERCISES TO HELP GUIDE THE READER IN TESTING UNDERSTANDING. THE CHAPTERS CAN BE READ IN ALMOST ANY ORDER, INCLUDING BEGINNING WITH THE FINAL CHAPTER THAT CONTAINS SOME OF THE MORE TRADITIONAL TOPICS OF ADVANCED CALCULUS COURSES. IN ADDITION, IT IS IDEAL FOR A COURSE ON VECTOR ANALYSIS FROM THE DIFFERENTIAL FORMS POINT OF VIEW.</P><P>THE PROFESSIONAL MATHEMATICIAN WILL FIND HERE A DELIGHTFUL EXAMPLE OF MATHEMATICAL LITERATURE; THE STUDENT FORTUNATE ENOUGH TO HAVE GONE THROUGH THIS BOOK WILL HAVE A FIRM GRASP OF THE NATURE OF MODERN MATHEMATICS AND A SOLID FRAMEWORK TO CONTINUE TO MORE ADVANCED STUDIES.</P><P><I>THE MOST IMPORTANT FEATURE...IS THAT IT IS FUN—IT IS FUN TO READ THE EXERCISES, IT IS FUN TO READ THE COMMENTS PRINTED IN THE MARGINS, IT IS FUN SIMPLY TO PICK A RANDOM SPOT IN THE BOOK AND BEGIN READING. THIS

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Críticas

"This book can serve as a delightful guide to advanced calculus, giving firm foundations to further studies." -Acta Sci. Math "An inviting, unusual, high-level introduction to vector calculus, based solidly on differential forms. Superb exposition: informal but sophisticated, down-to-earth but general, geometrically and physically intuitive but mathematically rigorous, entertaining but serious. Remarkably diverse applications, physical and mathematical." -The American Mathematical Monthly

Reseña del editor

This soft cover reprint of the original 1994 edition begins by with a lucid review of differential forms and proceeds to fundamental theorems of calculus and Stokes’ theorem. Covers differential forms in linear algebra, and more. Includes numerous exercises.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2013
• ISBN 10: 0817684115
• ISBN 13: 9780817684112
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 528