SE MECHANICAL SEM 3 – ENGINEERING MATHEMATICS III

Module 1 – Laplace Transform
12 Topics
1.3 – Properties of Laplace Transform
1.1.a – Definition of Laplace Transform
1.1.b – Condition of Existence of Laplace Transform
1.2 – Laplace Transform (L) of Standard Functions like eat, sin(at), cos(at), sinh(at), cosh(at) and tn , where n>_0.
1.3.a – Linearity
1.3.b – First Shifting Theorem
1.3.c – Second Shifting Theorem
1.3.d – Change of Scale Property
1.3.e – Multiplication by t
1.3.f – Division by t
1.3.g – Laplace Transform of Derivatives and Integrals (Properties without proof)
1.4 – Evaluation of Integrals by using Laplace Transformation
Module 2 – Inverse Laplace Transform
6 Topics
2.1.b – Linearity Property
2.1.a – Inverse Laplace Transform
2.1.c – Use of Standard Formulae to Find Inverse Laplace Transform
2.1.d – Finding Inverse Laplace Transform using Derivative
2.2 – Partial Fractions Method & First Shift Property to Find Inverse Laplace Transform
2.3 – Inverse Laplace Transform using Convolution Theorem ( without proof)
Module 3 – Fourier Series
5 Topics
3.1.a – Dirichlet’s conditions
3.1.b – Definition of Fourier series and Parseval’s Identify (without proof)
3.2 – Fourier Series of Periodic Function with Period 2pi and 2l
3.3 – Fourier Series of Even and Odd Functions
3.4 – Half Range Sine and Cosine Series
Module 4 – Complex Variables
7 Topics
4.1.a – Function f(z) of Complex Variable, Limit, Continuity and Differentiability of f(z)
4.1.b – Analytic Function
4.1.c – Necessary and Sufficient Conditions for f(z) to be Analytic (without proof)
4.2 – Cauchy-Riemann Equations in Cartesian Co-ordinates (without proof)
4.3 – Milne-Thomson Method to Determine Analytic Function f(z) when Real part (u) or Imaginary part (v) or its Combination (u+v or u-v) is given
4.4.a – Harmonic Function
4.4.b – Harmonic Conjugate and Orthogonal Trajectories
Module 5 – Matrices
8 Topics
5.1.a – Characteristic Equation
5.1.b – Eigen values and Eigen vectors
5.1.c – Properties of Eigen values and Eigen vectors
5.2.a – Cayle-Hamilton Theorem (without proof)
5.2.b – Application to Find The Inverse of The given Square Matrix and to Determine The given Higher Degree Polynomial Matrix
5.3 – Functions of Square Matrix
5.4.a – Similarity of Matrices
5.4.b – Diagonalization of Matrices
Module 6 – Numerical methods for PDE
6 Topics
6.1.a – Introduction of Partial Differential Equations
6.1.b – Method of Separation of Variables
6.1.c – Vibrations of String
6.1.d – Analytical Method for One Dimensional Heat and Wave Equations
6.2 – Crank Nicholson Method
6.3 – Bender Schmidt Method
Previous Topic
Next Topic

2.1.c – Use of Standard Formulae to Find Inverse Laplace Transform

SE MECHANICAL SEM 3 – ENGINEERING MATHEMATICS III Module 2 – Inverse Laplace Transform 2.1.c – Use of Standard Formulae to Find Inverse Laplace Transform
Previous Topic
Back to Lesson
Next Topic