Ordinary Differential Equations and Partial Differential Equations
24EST407 · S4 · 4 credits
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Module 01Homogenous linear differential equation of second orderexpand
superposition principle, general solution, homogenous linear ODEs with constant coefficients-general solution. Solution of Euler-Cauchy equations (second order homogeneous only).
Module 02Ordinary Differential Equations IIexpand
Non-homogenous linear ODEs-general solution, solution by the method of undetermined coefficients (for the right-hand side of forms 𝑥𝑛, 𝑒𝑘𝑥, 𝑠𝑖𝑛𝑎𝑥, 𝑐𝑜𝑠𝑎𝑥, 𝑒𝑎𝑥𝑠𝑖𝑛𝑎𝑥, 𝑒𝑎𝑥𝑐𝑜𝑠𝑎𝑥 and their linear combinations), method of variation of parameters. Solution of higher order equations-homogeneous linear ODE with constant coefficients.
Module 03Ordinary Differential Equations IIIexpand
Systems of First-Order Equations - Introduction, Linear Systems, Homogeneous Linear systems with constant coefficients.
Module 04Partial Differential Equations Iexpand
Introduction, Formation of partial differential equations -elimination of arbitrary constants-elimination of arbitrary functions, Solutions of partial differential equations, Equations solvable by direct integration.
Module 05Linear equations of the first orderexpand
Lagrange's linear equation, Solution of equation by the method of separation of variables.
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