Advanced Calculus, by Patrick M. Fitzpatrick, is a comprehensive and rigorous textbook that covers the topics typically found in a two-semester advanced calculus course. The book is part of The Sally Series, a collection of mathematics textbooks aimed at advanced undergraduate and beginning graduate students.
The book begins with a review of basic calculus concepts and then progresses to more advanced topics, such as metric spaces, continuous functions, differentiation and integration of functions of several variables, and differential forms. The author provides detailed proofs of theorems and exercises, making the book suitable for self-study or as a text for a course.
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The first part of the book focuses on the real number system and its properties, as well as the topology of Euclidean spaces. The author then moves on to more abstract topics, such as metric spaces and topology. The chapter on continuous functions covers topics such as uniform continuity and the intermediate value theorem.
The book then moves on to differentiation, starting with the basics of partial derivatives and moving on to higher-order derivatives, the chain rule, implicit differentiation, and the inverse function theorem. The chapter on integration covers the Riemann integral, improper integrals, and Fubini’s theorem. The author then introduces differential forms and covers topics such as Stokes’ theorem and the generalized Stokes’ theorem.
Overall, Advanced Calculus by Patrick M. Fitzpatrick is a comprehensive and challenging textbook that covers the topics of an advanced calculus course. The author provides detailed proofs and exercises, making the book suitable for self-study or as a text for a course.
Genres:
Advanced Calculus by Patrick M. Fitzpatrick is a mathematics textbook aimed at advanced undergraduate and beginning graduate students. The book falls under the genres of mathematics textbooks and educational literature.
There are no main characters in Advanced Calculus by Patrick M. Fitzpatrick, as it is a textbook.
Read Time:
The length of time it takes to read Advanced Calculus by Patrick M. Fitzpatrick will vary depending on the reader’s mathematical background and familiarity with the material. For someone with a strong background in calculus, the book could be read in a few weeks. For someone who is less familiar with the material, it could take several months.
- Publisher : American Mathematical Society; 2nd Revised edition (January 13, 2009)
- Language : English
- Hardcover : 590 pages
- ISBN-10 : 0821847910
- ISBN-13 : 978-0821847916
- Item Weight : 2.63 pounds
- Dimensions : 6.25 x 1 x 9 inches
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Patrick Fitzpatrick
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Advanced Calculus by Patrick M. Fitzpatrick is a comprehensive and rigorous textbook that covers the topics typically found in a two-semester advanced calculus course. The author provides detailed proofs and exercises, making the book suitable for self-study or as a text for a course.
The book is part of The Sally Series, a collection of mathematics textbooks aimed at advanced undergraduate and beginning graduate students. Overall, Advanced Calculus is a challenging but rewarding book for anyone interested in advanced calculus.
