FE SEM 2 – ENGINEERING MATHS II Course Content Expand All Module 1 – Differential Equations of First Order and First Degree 2 Topics Expand Lesson Content 0% Complete 0/2 Steps 1.1 Exact differential Equations, Equations reducible to exact form by using integrating factors. 1.2 Linear differential equations (Review), equation reducible to linear form, Bernoulli’s equation. Module 2 – Linear Differential Equations With Constant Coefficients and Variable Coefficients Of Higher Order 2 Topics Expand Lesson Content 0% Complete 0/2 Steps 2.1 Linear Differential Equation with constant coefficient‐ complementary function, particular integrals of differential equation of the type f(D)y = X where X is , sin(ax+b) , cos (ax+b), x^n ,e^axV,xV? 2.2 Method of variation of parameters. Module 3 – Beta and Gamma Function, Differentiation Under Integral Sign & Rectification 3 Topics Expand Lesson Content 0% Complete 0/3 Steps 3.1 Beta and Gamma functions and its properties. 3.2 Differentiation under integral sign with constant limits of integration. 3.3 Rectification of plane curves.(Cartesian and polar) Module 4 – Multiple Integration I 3 Topics Expand Lesson Content 0% Complete 0/3 Steps 4.1 Double integration‐definition, Evaluation of Double Integrals.(Cartesian & Polar) 4.2 Evaluation of double integrals by changing the order of integration. 4.3 Evaluation of integrals over the given region.(Cartesian & Polar) Module 5 – Multiple Integration II 3 Topics Expand Lesson Content 0% Complete 0/3 Steps 5.1 Evaluation of double integrals by changing to polar coordinates. 5.2 Application of double integrals to compute Area 5.3 Triple integration definition and evaluation (Cartesian, cylindrical and spherical polar coordinates). Module 6 – Numerical Solution Of Ordinary Differential Equations Of First Order, First Degree & Numerical Integration 2 Topics Expand Lesson Content 0% Complete 0/2 Steps 6.1 Numerical solution of ordinary differential equation using (a) Euler’s method (b) Modified Euler method, (c) Runge‐Kutta fourth order method 6.2 Numerical integration‐ by (a) Trapezoidal (b) Simpson’s 1/3rd (c) Simpson’s 3/8th rule
