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Week
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Topics
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Study Metarials
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1
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Basic equations and concepts, classification of partial differential equations, integral curves of vector fields
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R1) Lecture notes
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2
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Constructing integral curves of a vector field
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R1) Lecture notes
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3
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Constructing integral surfaces of a vector field containing a given curve
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R1) Lecture notes
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4
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First order quasilinear equations
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R1) Lecture notes
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5
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Classification of second order equations with two variables, canonical forms, equations of mathematical physics, wellposed problems
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R1) Lecture notes
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6
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Cauchy-Kowalewskaya theorem, initial value problem for one dimensional wave equation, d`Alembert formula, domain of dependence
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R1) Lecture notes
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7
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Initial-boundary value problems for one dimensional wave equation
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R1) Lecture notes
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8
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Fourier series and their convergence, Fourier sine and cosine series
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R1) Lecture notes
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9
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Separation of variables, initialboundary value problem for one-dimensional wave equation, existence and uniqueness of the solution
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R1) Lecture notes
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10
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Initial-boundary value problem for one-dimensional heat equation, existence and uniqueness of the solution
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R1) Lecture notes
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11
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Nonhomogeneous problems
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R1) Lecture notes
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12
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Boundary value problems, Laplace equation, harmonic functions, maximum and minimum principles, uniqueness and continuity of Dirichlet problem
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R1) Lecture notes
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13
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Dirichlet problem for a circle, mean value theorem, Dirichlet problem for a circular annulus
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R1) Lecture notes
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14
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Neumann problem for a circle, Dirichlet and Neumann problems for a rectangle
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R1) Lecture notes
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