In this post, we will see the book Operational Methods by V. P. Maslov....This book is devoted to one, but sufficiently general operational method, which absorbs many operational methods known to date and allows for the uniform solution of both classical problems, involving differential equations with partial derivatives, and the absolutely new problems of mathematical physics, including those connected with non-linear equations in partial derivatives.  ...This book on operational methods should be accessible to senior course students of mathematics and physics faculties at universities and departments of applied mathematics. This means that only a knowledge of classical analysis is required of the reader. The book provides explanations in sufficient volume of such concepts as the theory of Banach algebras of distributions (Chapter I), the theory of linear differential and difference equations (Sees. 1, 2, and 3 of Introduction), the theory of non-linear equations of the first order with partial derivatives (Chapter IV). This material may be also of use to the reader who is already familiar with these questions, because rather often it is not presented in traditional style, and adapted for further reference. The reader who studies the book thoroughly will be equipped to carry on independent research in the modern theory of linear, non-linear differential and differential-difference equations with partial derivatives....This book has been written in such a way as to serve the widest possible circle of readers. It is suitable for two methods of study. The reader, who seeks to avoid fine assessments and passing to the limit and only wishes to master the practical techniques for obtaining asymptotic solutions, may omit that part of the book which is devoted to functional analysis. ...The most effective way of mastering the subject, however, consists rather in first reading Introduction and then reading all the book in succession. The reader should nevertheless be warned that all these methods are not at all easy, because the book provides a new operational calculus-the calculus of ordered operators.The book was translated from the Russian by V. Golo, N. Kulman and G. Voropaeva and was published by Mir in 1976.Credits to the original uploader for the scan, in this link we have converted to pdf from djvu, added bookmarks and cover.The Internet Archive LinkCONTENTSPreface 7 Introduction to Operational Calculus 13Sec. 1. Solution of Ordinary Differential Equations by the Heaviside Operational Method 13Sec. 2. Difference Equations 20 Sec. 3. Solution of Systems of Differential Equations by the Heaviside Operational Method 22 Sec. 4. Algebra of Convergent Power Series of Noncommutative Operators 24Sec. 5. Spectrum of a Pair of Ordered Operators 35 Sec. 6. Algebras with \mu-Structures 40 Sec. 7. An Example of a Solution of a Differential Equation 56Sec. 8. Passage of the Equation of Oscillations of a Crystal Lattice into a Wave Equation 58 Sec. 9. The Concept of a Quasi-Inverse Operator and Formulation ofthe Main Theorem 100Chapter I Functions of a Regular Operator 147Sec. 1. Certain Spaces of Continuous Functions and Related Spaces 149Sec. 2. Embedding Theorems 154Sec. 3. The Algebra of Functions of a Generator 158Sec. 4. The Extension of the Class of Possible Symbols 173Sec. 5. Homomorphism of Asymptotic Formulas. The Method of Stationary Phase 181 Sec. 6. The Spectrum of a Generator 188 Sec. 7. Regular Operators 194 Sec. 8. The Generalized Eigenfunctions and Associated Functions 198 Sec. 9. Self-Adjoint Operators as Transformers in the Schmidt Space 205Chapter II Calculus of Noncommutative Operators 210 Sec. 1. Preliminary Definitions 210 Sec. 2. The Functions of Two Noncommutative Self-Adjoint Operators 224 Sec. 3. The Functions of Noncommutative Operators 228 Sec. 4. The Spectrum of a Vector-Operator 231 Sec. 5. Theorem on Homomorphism 239 Sec. 6. Problems 242 Sec. 7. Differentiation of the Functions of an Operator Depending on a Parameter 251Sec. 8. Formulas of Commutation 256Sec. 9. Growing Symbols 261Sec. 10. The Factor-Spectrum 265Sec. 11. The Functions of Components of a Lie Nilpotent Algebra and Their Representations 266Chapter III Asymptotic Methods 273Sec. 1. Canonical Transformations of Pseudodifferential Operators 273Sec. 2. The Homomorphism of Asymptotic Formulas 294Sec. 3. The Geometrical Interpretation of the Method of StationaryPhase 301Sec. 4. The Canonical Operator on an Unclosed Curve 303Sec. 5. The Method of Stationary Phase 312Sec. 6. The Canonical Operator on the Unclosed Curve Depending on Parameters Defined Correct to 0 ( 1/\omega ) 315Sec. 7. V-Objects on the Curve 321Sec. 8. The Canonical Operator on the Family of Unclosed Curves 327Sec. 9. The Canonical Operator on the Family of Closed Curves 333Sec. 10. An Example of Commutation of a Canonical Operator with a Hamiltonian 339Sec. 11. Commutation of a Hamiltonian with a Canonical Operator 346Sec. 12. The General Canonical Transformation of the Pseudodifferential Operator 348Chapter IV Generalized Hamilton-Jacobi Equations 355Sec. 1. Hamilton-Jacobi Equations with Dissipation 356Sec. 2. The Lagrangean Manifold with a Complex Germ 360Sec. 3. y-Atlases and the Dissipativity Inequality 372Sec. 4. Solution of the Hamilton-Jacobi Equation with Dissipation 378Sec. 5. Preservation of the Dissipativity Inequality. Bypassing Focuses Operation 386Sec. 6. Solution of Transfer Equation with Dissipation 401Chapter V Canonical Operator on a Lagrangean Manifold with a Complex Germ and Proof of the Main Theorem 419Sec. 1. Quantum Bypassing Focuses Operation 419Sec. 2. Commutation Formulas for a Complex Exponential and a Hamiltonian 440Sec. 3. C-Lagrangean Manifolds and the Index of a Complex Germ 452Sec. 4. Canonical Operator 469Sec. 5. Proof of the Main Theorem 482Appendix to Sec. 5 493Sec. 6. Cauchy Problem for Systems with Complex Characteristics 503Sec. 7. Quasi-Inverse of Operators with Matrix Symbols 519Appendix. Spectral Expansion of T-products 545Index 557