KBP Problem video for Graph theory

konigsberg bridge problems

Graph theory by Sonendra Gupta

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Unit Wise Study Material M2

Unit Wise Study Material

Unit	Topics	Click here to Download
Unit-1	Fourier Series & Fourier Transform	Download
Unit-2	Laplace transform, Inverse transform and Application	Download
Unit-3	Second order differential equation and Series Solution	Download
Unit-4	Partial differential equation	Download
Unit-5	Vector Calculus and Application	Download

      Engineering MathematicsII

        For BE/B.Tech

         Category

Study Material                |                 Paper's

    Engineering MathematicsI

 For BE/B.Tech

          

      Category

Study Material                    |                          Paper's

Study Material M2

Unit Wise

Unit I (Fourier Series and Fourier Transform)

Fourier Series 

• Introduction of Fourier series.
• Fourier series for Discontinuous functions.
• Fourier series for even and odd function.
• Half range series

Fourier Transform 

• Definition and properties of Fourier transform.
• Sine and Cosine transform.
             

Unit II (Laplace Transform and Application)

Laplace Transform       

• Introduction of Laplace Transform.
• Laplace Transform of elementary functions.
• Properties of Laplace Transform.
• Change of scale property, second shifting property.
• Laplace transform of the derivative.
• Inverse Laplace transform & its properties.
• Convolution theorem.
• Applications of L.T. to solve the ordinary differential equations.

Unit III (Second order differential equation and series solution)

Second order differential equation

• Second Order linear differential equation with variable coefficients
• Methods one integral is known.
• Removal of first derivative.
• Changing of independent variable and variation of parameter.

•  Series solution
• Solution by Series Method.

Unit Iv (Partial Differential Equation and Application of PDE)

Partial Differential Equation 

• Linear and Non Linear partial differential equation of first order.
• Formulation of  partial differential equations.
• Solution of equation by direct integration.
• Lagrange’s Linear equation.
• Charpit’s method.

 Application of PDE

• Linear partial differential equation of second and higher order.
• Linear homogeneous and Non homogeneous partial diff.
• Equation of nth order with constant coefficients.
• Separation of variable method for the solution of wave and heat equations.

Unit V (Vector and Application of Vector)

Vector Calculus 

• Differentiation of vectors.
• scalar and vector point function.
• Geometrical meaning of Gradient.
• Unit normal vector and directional derivative.
• Physical interpretation of divergence and Curl.
• Line integral.
• Surface integral and volume integral.
• Green’s, Stoke’s and Gauss divergence theorem.