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.
