Topics in our Partial Differential Equations Notes PDF
In these “Partial Differential EquationsNotes PDF”, you will study how to form and solve partial differential equations and use them in solving some physical problems.
The topics we will cover will be taken from the following list:
First Order PDE and Method of Characteristics: Introduction, Classification, Construction and geometrical interpretation of first order partial differential equations (PDE), Method of characteristic and general solution of first order PDE, Canonical form of first order PDE, Method of separation of variables for first order PDE.
Mathematical Models and Classification of Second Order Linear PDE: Gravitational potential, Conservation laws and Burger’s equations, Classification of second order PDE, Reduction to canonical forms, Equations with constant coefficients, General solution.
The Cauchy Problem and Wave Equations: Mathematical modeling of vibrating string and vibrating membrane, Cauchy problem for second order PDE, Homogeneous wave equation, Initial boundary value problems, Non-homogeneous boundary conditions, Finite strings with fixed ends, Non-homogeneous wave equation, Goursat problem.
Method of Separation of Variables: Method of separation of variables for second order PDE, Vibrating string problem, Existence and uniqueness of solution of vibrating string problem, Heat conduction problem, Existence and uniqueness of solution of heat conduction problem, Non-homogeneous problem.
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