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Table of Contents
Intro; Preface; Contents; 1 Complex Functions; 1.1 Complex Functions of Real Variable; 1.2 Complex Functions of Complex Variable; 1.3 Elementary Complex Functions; 1.4 Complex Integrals; 1.5 Complex Series; 2 Special Functions; 2.1 Euler's Functions; 2.2 Bessel's Functions; 2.3 Orthogonal Polynomials; 2.4 Legendre's Polynomials; 2.5 Chebyshev's Polynomials; 2.6 Hermite's Polynomials; 2.7 Laguerre's Polynomials; 3 Operational Calculus; 3.1 Laplace's Transform; 3.2 Operational Methods; 3.3 Applications; 3.4 Differential Equations with Constant Coefficients
3.5 Differential Equations with Variable Coefficients3.6 Integral Equations; 3.7 Partial Differential Equations; 3.8 Some Improper Integrals; 4 Fourier's Transform; 4.1 Fourier Series; 4.2 Fourier's Single Integral Formula; 4.3 Fourier's Transform in L1; 4.4 Fourier's Transform in L2; 5 Calculus of Variations; 5.1 Introduction; 5.2 Euler's Equation; 5.3 Generalizations of Euler's Equation; 5.4 Sufficent Conditions for Extremum; 5.5 Isoperimetric Problems; 5.6 Moving Boundary Problems; 6 Quasi-linear Equations; 6.1 Canonical Form for n=2; 6.2 Canonical Form for n>2; 7 Hyperbolical Equations
7.1 Problem of the Infinite Vibrating Chord7.2 Initial-Boundary Values Problems; 7.3 Cauchy's Problem; 7.4 Problem of the Finite Vibrating Chord; 8 Parabolical Equations; 8.1 The Finite Problem of Heat; 8.2 Initial-Boundary Value Problems; 8.3 Method of the Green's Function; 8.4 Cauchy's Problem; 9 Elliptic Partial Differential Equations; 9.1 Introductory Formulas; 9.2 Potentials; 9.3 Boundary Values Problems; 10 Optimal Control; 10.1 Preparatory Notions; 10.2 Problems of Optimal Control; 10.3 Linear Problems of Control; 10.4 Problems of Quadratic Control
3.5 Differential Equations with Variable Coefficients3.6 Integral Equations; 3.7 Partial Differential Equations; 3.8 Some Improper Integrals; 4 Fourier's Transform; 4.1 Fourier Series; 4.2 Fourier's Single Integral Formula; 4.3 Fourier's Transform in L1; 4.4 Fourier's Transform in L2; 5 Calculus of Variations; 5.1 Introduction; 5.2 Euler's Equation; 5.3 Generalizations of Euler's Equation; 5.4 Sufficent Conditions for Extremum; 5.5 Isoperimetric Problems; 5.6 Moving Boundary Problems; 6 Quasi-linear Equations; 6.1 Canonical Form for n=2; 6.2 Canonical Form for n>2; 7 Hyperbolical Equations
7.1 Problem of the Infinite Vibrating Chord7.2 Initial-Boundary Values Problems; 7.3 Cauchy's Problem; 7.4 Problem of the Finite Vibrating Chord; 8 Parabolical Equations; 8.1 The Finite Problem of Heat; 8.2 Initial-Boundary Value Problems; 8.3 Method of the Green's Function; 8.4 Cauchy's Problem; 9 Elliptic Partial Differential Equations; 9.1 Introductory Formulas; 9.2 Potentials; 9.3 Boundary Values Problems; 10 Optimal Control; 10.1 Preparatory Notions; 10.2 Problems of Optimal Control; 10.3 Linear Problems of Control; 10.4 Problems of Quadratic Control