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Math books
- Mathematical Analysis
- Walter Rudin. Principles of Mathematical Analysis.
Russian translation: У. Рудин. Основы математического анализа, 1976.
- Ordinary differential equations
- Gerald Teschl. Ordinary Differential Equations and Dynamical Systems, 2012.
A modern introduction to the ODEs and dynamical systems. Note that in this book only classical (i.e. smooth) solutions are studied.
- Vladimir Arnold. Ordinary differential equations.
Russian translation: В. Арнольд. Обыкновенные дифференциальные уравнения.
- For Caratheodory theory you can consult, e.g. E.A. Coddington, N. Levinson "Theory of ordinary differential equations", Chapter 2.
- Functional Analysis
- Shlomo Sternberg. Theory of functions of a real variable, 2005.
I've enjoyed reading this book which provides a comprehensive introduction into the subject. Its disadvantage is, however, the lack on the exercises for the reader.
- Kosaku Yoshida. Functional Analysis.
Russian translation: К. Иосида. Функциональный анализ, 1967.
- Tosio Kato. Perturbation theory for linear operators, 1995.
Although the main topic of the book is a perturbation theory, but the first chapters are a concise introduction to the theory of linear operators with many beautiful exercises for active readers. Russian translation: Т. Като. Теория возмущений линейных операторов, 1972.
- Partial differential equations
- Lawrence Evans. Partial Differential Equations.
- Control and systems theory
- Jerzy Zabczyk. Mathematical Control Theory: An Introduction (last edition in 2007)
- V. Alekseev, V. Tikhomirov, S. Fomin. Optimal Control, 1987.
Russian original: В. М. Алексеев, В. М. Тихомиров, С. В. Фомин. Оптимальное управление, 1979.
- Other
- G. Polya, G. Szegö – Aufgaben und Lehrsätze aus der Analysis
Russian translation: Г. Полиа, Г. Сеге. Задачи и теоремы из анализа.
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