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Calculus / Analysis Takeoff *****

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How drive Calculus engines to take off?

 

 

 

 

LEVEL 0. Best way to learn how to use Calculus (i.e. 'check the airport')

This basic level is covered by any "Calculus" book with many color figures and examples ( e.g. Thomas EN *****).  There are many collections of suplementary examples to solve ( e.g. Schaum's EN *** ). This level is acceptable for anybody who wants a simple overview of Calculus.

 

LEVEL 1. Instead of learning how to use Calculus one can learn what Calculus (Analysis) is in fact (i.e. 'board the jet and follow the runway')

It means to study  one of those cute great books where the author leads the reader through great ideas and serves the beauty of clever pure math (e.g. Spivak Calculus EN ***** with its Answer book EN ). These books should be suplemented by some advanced examples. One can use some collection dealing with technical part of Calculus ( e.g. Demidovich EN **** ) and some collection dealing with the math theory ( e.g. Klymchuk EN ***** ).

 

LEVEL 2. And finally one MUST get some reward! ('TAKEOFF!!!')

One must read a book where one can find some math which is unbelievably clever, sexy, smart and beautiful, some math science 'par exellence' (e.g. "baby Rudin" EN*****, with solutions EN ).

 

LEVEL 3. DONE.

There is no way back Smile

 

 

Remarks.

(A) Students which have chosen to study Honors classes ( wiki EN ) should skip LEVEL 0.

 

(B) The proposed Thomas - Schaum's - Spivak - Demidovich - Klymchuk - baby Rudin choice can be altered to anyone of the References

Depends only on one's taste Wink

 

(C) It would be nice ...

As time does on we see that some part in each particular book could be improved (errata, simpler proof discovered, ...). If the great authors of studied books make a statement that their work can be a subject of modifications/ addons etc, this would be great.

 

 

References

 

Level 0

George B. Thomas, Maurice D. Weir, Joel Hass, Thomas' Calculus

Daniel A. Murray, Differential and integral calculus

Ron Larson, Bruce H. Edwards, Calculus

C. Henry Edwards, David E. Penney, Calculus

Examples & Problems:

Schaum's Outlines ( wiki EN ) ... solved problems series

 

Level 1

Michael Spivak - Calculus

Michael Spivak - Answer book for calculus

Herbert Amann, Joachim Escher, Analysis

Robert G. Bartle,  Donald R. Sherbert, Introduction to Real Analysis

David Alexander Brannan, A First Course in Mathematical Analysis

Kazimierz Kuratowski, Introduction to Calculus.

Steven G. Krantz, Real Analysis and Foundations

Richard Courant, Differential and Integral Calculus, Vol. 1

Richard Courant, Differential and Integral Calculus, Vol. 2

Tom M. Apostol, Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra

Tom M. Apostol, Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications

Vojtech Jarnik, Differential calculus, Integral Calculus ( CZ )

Examples & Problems:

Boris P. Demidovich, Problems in Mathematical Analysis

Ilja Cerny, Introduction into Intelligent Calculus ( CZ )

Sergiy Klymchuk, Counterexamples in calculus

Ivan Netuka, Jiri Vesely, Examples from Mathematical Analysis ( CZ )

 

Level 2

Walter Rudin, Principles of Mathematical Analysis

Charalambos D. Aliprantis, Owen Burkinshaw, Problems In Real Analysis, A Workbook with Solutions (of problems in Rudin's Principles)

Harold M. Edwards, Advanced Calculus - a Differential Forms Approach

Examples & Problems:

Paolo Ney de Souza, Jorge Nuno Silva, Berkeley Problems in Mathematics

Bernard R. Gelbaum, John M. H. Olmsted, Counterexamples in Analysis

 

Smile