V.I.Arnold 1937~2010

1. Ordinary Differential Equations
2. Lectures on Partial Differential Equations
3. Mathematical Methods of Classical Mechanics
4. Catastrophe Thoery
5. Symplectic Geometry and Topology
6. Mathematical Understanding of Nature
7. Memories of Arnold

Abel's Theorem in Problems And Solutions: Based on the lecture of Professor V.I.Arnold

Geometrical Methods in the Theory of Odinary Differential Equations

第一章 基本概念

1. Phase Spaces
2. Vector Fields on the Line
3. Linear Equations
4. Phase Flows
5. The Action of Diffeomorphism on Vector Fields and Direction Fields
6. Symmetries
7. Conservative fields

Bernoulli equation         Power series   

第二章 基本定理

1. Rectification Theorems
2. Applications to Equations of Higher Order
3. The Phase Curves of an Autonomous System
4. The Derivative n the Direction of a Vector Field and First Integrals
5. First-Order Linear and Quasi-linear Partial Differential Equations
6. the Conservative System with one Degree of Freedem

第三章 線性系統

1. Linear Problems
2. The Exponential Function
3. Properties of The Exponential
4. The Determinant of an Exponential
5. Practical Computation of The Matrix of an Exponential
6. Complexification and Realification
7. ...
8. Linear Systems
9. The Laplace transform

第四章 Proofs of The Main Theorems

第五章 Differential Equations on Manifolds

1. Differential Manifolds
2. The Tangent Bundle  Vector Fields on a Manifold
3. The Phase Flow defined by a Vector Field
4. The Indices of the Singular Points of a vector Field

Examination Topics      Sample Examination Problems      Supplementary Problems