Advance Maths: Part I: Linear Differential Equations

This course covers all the details of Linear Differential Equations (LDE) which includes LDE of second and higher order with constant coefficients, homogeneous equations, variation of parameters, Euler's/ Cauchy's equations, Legendre's form, solving LDEs simultaneously, symmetrical equations, applications of LDE.

This course covers a major and important part of LDE with many solved examples and exercises for students for self assessment.  This course will undoubtedly help students in thorough preparation of this topic.

Exact differential equations, Equations reducible to exact form. Linear differential equations, Equations reducible to linear form, Bernoulli’s equation. Applications of Differential Equations to Orthogonal Trajectories, Newton’s Law of Cooling, Kirchhoff’s Law of Electrical Circuits, Rectilinear Motion, Simple Harmonic Motion, One dimensional Conduction of Heat.

1. Differential Equations of First Order and First Degree - 2. Linear Differential Equations with Constant Cofficients

LDE of nth order with constant coefficients, Method of variation of parameters, Cauchy’s & Legendre’s Differential Equations, Simultaneous & Symmetric simultaneous Differential Equations. Modeling of problems on bending of beams, whirling of shafts and mass spring systems.

Definition, To Find Complimentary Function, C.F. = YC , Particular Integral (P.I. = YP), Method of Variation of Parameters, Cauchy’s and Legendre’s Homogeneous Linear Differential Equations, Cauchy’s Homogeneous Linear Differential Equation, Legendre’s Homogeneous Equation, Modeling of Mass-Spring Systems, Free and Forced Damped and Undamped Systems, Introduction, Undamped and Damped Vibration