by Victor Guillemin, Shlomo Sternberg
Publisher: Harvard University 2012
Number of pages: 488
In semi-classical analysis many of the basic results involve asymptotic expansions in which the terms can by computed by symbolic techniques and the focus of these lecture notes will be the 'symbol calculus' that this creates.
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This book is devoted to a rapidly developing branch of the qualitative theory of difference equations with or without delays. It presents the theory of oscillation of difference equations, exhibiting classical as well as recent results in that area.
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This text introduces the interesting and valuable concept of continued fractions. Contents: Two Historical Puzzles; Formation of Continued Fractions; Convergents; Non-terminating Continued Fractions; Approximation of Real Numbers.
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Contents: Notation, Undefined Concepts, Examples; Fields; Induction and Integers; Complexification of a Field; Real Numbers; Complex Numbers; Complex Sequences; Continuity; Properties of Continuous Functions; Derivative; Infinite Series; etc.
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This collection of problems and exercises in mathematical analysis covers the maximum requirements of general courses in higher mathematics for higher technical schools. It contains over 3,000 problems covering all branches of higher mathematics.