I Existence and Uniqueness for the Initial Value Problem Under the Hypothesis of Lipschitz. - 1. General Results. - 2. Qualitative Properties of Solutions. - 3. Solutions as Functions of the Initial Data. - 4. Systems of Equations as Particular Transformations Between Function Spaces. - 5. Exercises. - 6. Bibliographical Notes. - II Linear Systems. - 1. Elements of Linear Algebra. - 2. Linear Systems of Ordinary Differential Equations. - 3. Operational Calculus. - 4. Linear Finite Differences Equations. - 5. Examples. - 6. Bibliography. - III Existence and Uniqueness for the Cauchy Problem Under the Condition of Continuity. - 1. Existence Theorem. - 2. The Peano Phenomenon. - 3. Questions of Uniqueness. - 4. Elements of G-Convergence. - 5. Bibliographical Notes. - IV Boundary Value Problems. - 1. Continuous Mappings on Euclidean Spaces. - 2. Geometric Boundary Value Problems. - 3. Sturm-Liouvilie Problems: Eigenvalues and Existence and Uniqueness Theorems. - 4. Periodic Solutions. - 5. Functional Boundary Value Problems. - 6. Bibliographical Notes. - V Questions of Stability. - 1. Stability of the Solutions of Linear Systems. - 2. Some Methods for the Determination of the Stability of Nonlinear Systems. - 3. Some Applications. - 4. The Method of Runge and Kutta. - 5. Bibliographical Notes. Language: English