Transcription of Partial Differential Equations
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Partial Differential Equations Victor Ivrii Department of Mathematics, University of Toronto c by Victor Ivrii, 2017, Toronto, Ontario, Canada Contents Contents i Preface .. iv 1 Introduction 1. PDE Motivations and Context .. 1. Initial and Boundary Value Problems .. 4. Classification of Equations .. 6. Origin of some Equations .. 10. Problems to Chapter 1 .. 14. 2 1-dimensional waves 16. first order PDEs .. 16. Appendix .. 20. first order PDEs (continued) .. 25. Homogeneous 1D Wave equation .. 29. 1D Wave equation reloaded: characteristic coordinates .. 35. Wave equation reloaded (continued) .. 39.
2. Ordinary Di erential Equations First order equations (a)De nition, Cauchy problem, existence and uniqueness; (b)Equations with separating variables, integrable, linear. Higher order equations (c)De nition, Cauchy problem, existence and uniqueness; Linear equations of order 2 (d)General theory, Cauchy problem, existence and uniqueness;
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Differential equations, First Order Equations, Linear First Order Equations, Equations, First Order Differential Equations Linear Equations, Linear first order differential equations, First order differential equations, Differential, First Order, Linear, Linear equations, Order, Order equations, Second Order Differential Equations, Second order linear, Second order linear equations, Solutions of Linear Differential Equations, Numerical Methods for Partial Differential Equations