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Math books

  1. Mathematical Analysis
    • Walter Rudin. Principles of Mathematical Analysis.
      Russian translation: У. Рудин. Основы математического анализа, 1976.
  2. 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.
  3. 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.
  4. Partial differential equations
    • Lawrence Evans. Partial Differential Equations.
  5. 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.
  6. Other
    • G. Polya, G. Szegö – Aufgaben und Lehrsätze aus der Analysis
      Russian translation: Г. Полиа, Г. Сеге. Задачи и теоремы из анализа.