CBCGS [2017 - current]
CBGS [2013 - 2016]
Old [2000 - 2012]
Topics with syllabus and resources
1 Module 1
1.01 Laplace Transform (Lt) of Standard Functions
- Definition. unilateral and bilateral Laplace Transform
- LT of sin(at), cos(at), eat ,tn , sinh(at), cosh(at), erf(t)
- Heavi-side unit step
- dirac-delta function
- LT of periodic function.
1.02 Properties of Laplace Transform
- Linearity,
- first shifting theorem,
- second shifting theorem,
- multiplication by tn , division by t ,
- Laplace Transform of derivatives and integrals,
- change of scale,
- convolution theorem,
- initial and final value theorem,
- Parsavel‘s identity.
1.03 Inverse Laplace Transform
- Partial fraction method
- long division method
- residue method.
1.04 Applications of Laplace Transform
- Solution of ordinary differential equations.
2 Module 2
2.01 Introduction
- Definition
- Dirichlet‘s conditions
- Euler‘s formulae.
2.02 Fourier Series of Functions
- Exponential, trigonometric functions, even and odd functions, half range sine and cosine series.
- Complex form of Fourier series, orthogonal and orthonormal set of functions, Fourier integral representation.
3 Module 3
3.01 Solution of Bessel Differential Equation
- Series method, recurrence relation, properties of Bessel function of order +1/2 and -1/2 Generating function, orthogonality property.
- Bessel Fourier series of functions.
4 Module 4
4.01 Scalar and Vector Product
- Scalar and vector product of three and four vectors and their properties.
4.02 Vector Differentiation
- Gradient of scalar point function
- divergence and curl of vector point function.
4.03 Properties
- Solenoidal and irrotational vector fields
- conservative vector field.
4.04 Vector Integral
- Line integral
- Green‘s theorem in a plane
- Gauss‘ divergence theorem
- Stokes‘ theorem.
5 Module 5
5.01 Complex Variable
- Analytic Function: Necessary and sufficient conditions, Cauchy.
- Reiman equation in polar form.
- Harmonic function, orthogonal trajectories.
5.02 Mapping
- Conformal mapping.
- bilinear transformations.
- cross ratio.
- fixed points.
- bilinear transformation of straight lines and circles.
