Principles of Differential and Integral Equations

Cover......Page 000a_0001.djvu
Title: Principles of Differential and Integral Equations......Page corduneanu-podaie-pp0001.djvu
@ Copyright 1971 ......Page corduneanu-podaie-pp0002.djvu
Contents ......Page corduneanu-podaie-pp0003.djvu
Preface ......Page corduneanu-podaie-pp0005.djvu
Introduction ......Page corduneanu-podaie-pp0007.djvu
§1.1. The Linear Equation of the First Order ......Page corduneanu-podaie-pp0011.djvu
§1.2. The Equation with Separable Variables......Page corduneanu-podaie-pp0013.djvu
§1.3. Exact Differential Equations ......Page corduneanu-podaie-pp0016.djvu
§1.4. The Uniqueness Problem: An Example ......Page corduneanu-podaie-pp0018.djvu
§1.5. Some Integral Inequalities......Page corduneanu-podaie-pp0020.djvu
PROBLEMS ......Page corduneanu-podaie-pp0022.djvu
§2.1. The First-Order Equation ......Page corduneanu-podaie-pp0025.djvu
§2.2. First-Order Differential Systems ......Page corduneanu-podaie-pp0030.djvu
§2.3. Equations and Systems of Higher Order ......Page corduneanu-podaie-pp0033.djvu
§2.4. Peano Existence Theorem......Page corduneanu-podaie-pp0036.djvu
§2.5. A Uniqueness Theorem ......Page corduneanu-podaie-pp0040.djvu
PROBLEMS ......Page corduneanu-podaie-pp0042.djvu
§3.1. Statement of the Problems......Page corduneanu-podaie-pp0045.djvu
§3.2. Global Uniqueness ......Page corduneanu-podaie-pp0047.djvu
§3.3. Global Existence and the Behavior of Saturated Solutions......Page corduneanu-podaie-pp0048.djvu
§3.4. Dependence of Solutions on Initial Values ......Page corduneanu-podaie-pp0052.djvu
§3.5. Differential Inequalities and the Comparison Method ......Page corduneanu-podaie-pp0055.djvu
§3.6. A Criterion of Global Existence ......Page corduneanu-podaie-pp0057.djvu
PROBLEMS ......Page corduneanu-podaie-pp0060.djvu
§4.1. Linear Systems: Generalities ......Page corduneanu-podaie-pp0063.djvu
§4.2. Linear Homogeneous Systems ......Page corduneanu-podaie-pp0066.djvu
§4.3. Nonhomogeneous Linear Systems ......Page corduneanu-podaie-pp0070.djvu
§4.4. Linear Equations of Higher Order ......Page corduneanu-podaie-pp0072.djvu
§4.5. Autonomous Systems......Page corduneanu-podaie-pp0075.djvu
§4.6. Linear Systems and Equations with Constant Coefficients......Page corduneanu-podaie-pp0079.djvu
PROBLEMS ......Page corduneanu-podaie-pp0087.djvu
5 Stability Theory of Ordinary Differential Systems ......Page corduneanu-podaie-pp0091.djvu
§5.1. Definitions and Examples ......Page corduneanu-podaie-pp0092.djvu
§5.2. Stability of Linear Systems ......Page corduneanu-podaie-pp0096.djvu
§5.3. Stability in the First Approximation ......Page corduneanu-podaie-pp0101.djvu
§5.4. Stability Theorems by Comparison Method ......Page corduneanu-podaie-pp0104.djvu
§5.5. Further Stability Results......Page corduneanu-podaie-pp0111.djvu
§5.6. Stability of Automatic Control Systems ......Page corduneanu-podaie-pp0116.djvu
PROBLEMS ......Page corduneanu-podaie-pp0119.djvu
§6.1. Existence and Uniqueness of Solution ......Page corduneanu-podaie-pp0125.djvu
§6.2. An Existence Theorem ......Page corduneanu-podaie-pp0128.djvu
§6.3. The Linear Equation......Page corduneanu-podaie-pp0129.djvu
§6.4. The First-Kind Linear Equation ......Page corduneanu-podaie-pp0131.djvu
§6.5. Some Problems on the Half-Axis ......Page corduneanu-podaie-pp0132.djvu
PROBLEMS ......Page corduneanu-podaie-pp0136.djvu
§7.1. The Resolvent Kernel ......Page corduneanu-podaie-pp0139.djvu
§7.2 The Entire Functions of Fredholm and Their Applications......Page corduneanu-podaie-pp0144.djvu
§7.3. A Glimpse on Hilbert Space Theory......Page corduneanu-podaie-pp0148.djvu
§7.4. Eigenvalues, Eigenfunctions and Adjoint Equations......Page corduneanu-podaie-pp0152.djvu
PROBLEMS ......Page corduneanu-podaie-pp0157.djvu
§8.1. Some Properties of an Integral Operator ......Page corduneanu-podaie-pp0161.djvu
§8.2. The Existence of Eigenvalues ......Page corduneanu-podaie-pp0163.djvu
§8.3. The Hilbert-Schmidt Expansion Theorem ......Page corduneanu-podaie-pp0166.djvu
§8.4. Complete Kernels and Systems ......Page corduneanu-podaie-pp0169.djvu
§8.5. The Sturm-Liouville Problem ......Page corduneanu-podaie-pp0170.djvu
§8.6. Reduction to an Integral Equation: The First Case ......Page corduneanu-podaie-pp0172.djvu
§8.7. Reduction to an Integral Equation: The Second Case ......Page corduneanu-podaie-pp0175.djvu
PROBLEMS ......Page corduneanu-podaie-pp0176.djvu
§9.1. Maximum and Minimum Solutions of Scalar Differential Equations ......Page corduneanu-podaie-pp0179.djvu
§9.2. A Theorem of Massera ......Page corduneanu-podaie-pp0181.djvu
§9.3. An Oscillation Theorem ......Page corduneanu-podaie-pp0183.djvu
§9.4. A Formula of Picone and Its Consequences ......Page corduneanu-podaie-pp0185.djvu
§9.5. The Lienard's Equation ......Page corduneanu-podaie-pp0188.djvu
§9.6. Differential Systems Without Uniqueness ......Page corduneanu-podaie-pp0192.djvu
§9.7. Abel's Integral Equation ......Page corduneanu-podaie-pp0196.djvu
B. Books on Differential Equations (Elementary and Intermediate) ......Page corduneanu-podaie-pp0199.djvu
C. Books on Differential Equations (Intermediate to Advanced) ......Page corduneanu-podaie-pp0200.djvu
D. Books on Stability Theory of Ordinary Differential Equations"......Page corduneanu-podaie-pp0201.djvu
F. Books on the Theory of Control Processes ......Page corduneanu-podaie-pp0202.djvu
H. Books on Integral Equations ......Page corduneanu-podaie-pp0203.djvu
I. Books Including the Theory of Integral Equations ......Page corduneanu-podaie-pp0204.djvu
Index ......Page corduneanu-podaie-pp0205.djvu
Back Cover......Page 000b_0001.djvu