Check out the full Syllabus for Engineering Mathematics 2 below -

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Module 1

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Differential Equations of First Order and First Degree

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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.
 

Self learning topics: Simple application of differential equation of first order and first degree to electrical and Mechanical Engineering problem

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Module 2

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Linear Differential Equations With Constant Coefficients and Variable Coefficients of Higher Order
 

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 ( ) ( ) .

2.2. Method of variation of parameters.
 

Self learning topics: Cauchy‘s homogeneous linear differential equation and Legendre‘s differential equation, Applications of Higher order differential equation.

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Module 3

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Beta and Gamma Function, Differentiation under Integral sign and Rectification

Pre-requisite: Tracing of curves
 

1.1 Beta and Gamma functions and its properties.
 

1.2 Differentiation under integral sign with constant limits of integration.

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1.3 Rectification of plane curves.(Cartesian and polar)
 

Self learning topics: Rectification of curve in parametric co-ordinates.

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Module 4

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Multiple Integration-1

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)
 

Self learning topics: Application of double integrals to compute Area, Mass.

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Module 5

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Multiple Integration-2
 

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).
 

Self learning topics: Application of triple integral to compute volume

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Module 6

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Numerical solution of ordinary differential equations of first order and first degree, and , Numerical Integration
 

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(all with proof).
 

Self learning topics: Numerical solution of ordinary differential equation using Taylor series method.

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