o W. F. Ames ( G I T ) – for the Mathematical Reviews , AMS :
Any analyst is always concerned about good counterexamples to use in lectures and research. Here is a book with a collection of counterexamples in the areas of continuity, differentiability, extrema, existence, uniqueness, stability, regularity, periodicity, etc. They have been collected from a variety of books and journals. The collection should prove useful to analysts interested in the main topic of differential equations. There is a reasonable bibliography and both a subject and an author index. This is a valuable book for students and researchers alike.
o G.C.Rota (M.I.T.) for the World Scientific :
The author knows his business : he has chosen the right counterexamples at the right time. The section on plane autonomous systems is particularly felicitous, and should be consulted by whoever teaches elementary differential equations ( some of the examples are really cute and we will use them in our 400-student course next year ). Why can't mathematicians write more books like this one ?
BOOKS [In Greek]
PUBLICATIONS SYMMETRY, ATHENS
Author: John M. Rassias
ΒΙΒΛΙΑ [ΣΤΑ ΕΛΛΗΝΙΚΑ]
ΕΚΔΟΣΕΙΣ ΣΥΜΜΕΤΡΙΑ, ΑΘΗΝΑ
Συγγραφέας: Ιωάννης Μ. Ρασσιάς
ΜΑΘΗΜΑΤΙΚΗ ΑΝΑΛΥΣΗ Τόμος Ι - ΔΙΑΦΟΡΙΚΟΣ ΛΟΓΙΣΜΟΣ
(MATHEMATICAL ANALYSIS Volume I-DIFFERENTIAL CALCULUS)
|
ΡΑΣΣΙΑΣ ΙΩΑΝΝΗΣ Μ.
(RASSIAS JOHN Μ.)
Σελ. /pp. 1-212 |
ΜΑΘΗΜΑΤΙΚΗ ΑΝΑΛΥΣΗ Τόμος ΙI - ΟΛΟΚΛΗΡΩΤΙΚΟΣ ΛΟΓΙΣΜΟΣ
(MATHEMATICAL ANALYSIS Volume II – INTEGRAL CALCULUS
|
ΡΑΣΣΙΑΣ ΙΩΑΝΝΗΣ Μ.
(RASSIAS JOHN Μ.)
Σελ. /pp. 213-470 |
ΜΑΘΗΜΑΤΙΚΗ ΑΝΑΛΥΣΗ Τόμος ΙΙΙ - ΛΟΓΙΣΜΟΣ ΠΟΛΛΩΝ ΜΕΤΑΒΛΗΤΩΝ
(MATHEMATICAL ANALYSIS Volume III –CALCULUS OF SEVERAL VARIABLES)
|
ΡΑΣΣΙΑΣ ΙΩΑΝΝΗΣ Μ.
(RASSIAS JOHN Μ.)
Σελ. /pp. 471-786 |
ΕΦΑΡΜΟΣΜΕΝΗ ΑΝΑΛΥΣΗ Τόμος Ι - ΔΙΑΦΟΡΙΚH ΓΕΩΜΕΤΡΙΑ
(APPLIED ANALYSIS Volume I –DIFFERENTIAL GEOMETRY)
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ΡΑΣΣΙΑΣ ΙΩΑΝΝΗΣ Μ.
(RASSIAS JOHN Μ.)
Σελ. /pp. 1-288 |
ΕΦΑΡΜΟΣΜΕΝΗ ΑΝΑΛΥΣΗ Τόμος ΙΙ - ΜΕΡΙΚΕΣ ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ
(APPLIED ANALYSIS Volume II – PARTIAL DIFFERENTIAL EQUATIONS)
|
ΡΑΣΣΙΑΣ ΙΩΑΝΝΗΣ Μ.
(RASSIAS JOHN Μ.)
Σελ. /pp. 289-701 |
ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ ΚΑΙ ΓΡΑΜΜΙΚΟΣ ΠΡΟΓΡΑΜΜΑΤΙΣΜΟΣ
(LINEAR ALGEBRA AND LINEAR PROGRAMMING
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ΡΑΣΣΙΑΣ ΙΩΑΝΝΗΣ Μ.
(RASSIAS JOHN Μ.)
Σελ. /pp. 1-269 |
ΘΕΩΡΙΑ ΑΡΙΘΜΩΝ
(NUMBER THEORY)
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ΡΑΣΣΙΑΣ ΙΩΑΝΝΗΣ Μ.
(RASSIAS JOHN Μ.)
Σελ. /pp. 1-377 |
ΘΕΩΡΙΑ ΠΙΘΑΝΟΤΗΤΩΝ ΚΑΙ ΣΤΑΤΙΣΤΙΚΗΣ
(THEORY OF PROBABILITY AND STATISTICS)
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ΡΑΣΣΙΑΣ ΙΩΑΝΝΗΣ Μ.
(RASSIAS JOHN Μ.)
Σελ. /pp. 1-489 |
BOOKS [In English]
Author : John Michael Rassias
MIXED TYPE PARTIAL DIFFERENTIAL EQUATIONS
Wold Scientific Publishing Co. Pte. Ltd, Singapore
1990, 1-144
Contents:
• The Dynamical Equation of Mixed Type
• The Tricomi Problem
• Regularity of Solutions (in the sense of Tricomi)
• Fundamental Idea of Tricomi
• The Bitsadze-Lavrentjev Problem
• The Gellerstedt Problem
• The Frankl Problem
• Quasi-Regularity of Solutions (in the sense of Protter)
• The a, b, c Energy Integral Method
• Weak (or Strong) Solutions in the Classical Sense
• Well Posedness
• A Selection of New Results
• Open Problems
• Basic Books
COUNTER EXAMPLES IN DIFFERENTIAL EQUATIONS
AND RELATED TOPICS
Wold Scientific Publishing Co. Pte. Ltd, Singapore
1991, 1-192
Contents:
• Continuity and Linearity
• Differentiability and Analyticity
• Extrema
• Existence
• Uniqueness
• Stability
• Singularities
• Dynamical Systems
• Integral Equations
• Other Topics
• Open Problems
