Unit 1 Laplace Transform and Their Basic Properties
1.1 Integral transform
1.2 Definition and existence of Laplace transform
1.3 Sectional or piecewise continuity
1.4 Functions of exponential order
1.5 Laplace transforms of elementary functions
1.6 Properties of Laplace transform
1.7 Laplace transform of derivatives
1.8 Laplace transform of integrals
1.9 Multiplication by tn
1.10 Division by t

Unit 2 Laplace Transform of Some Special Functions
2.1 Periodic function
2.2 The Gamma function
2.3 The Error and Complementary Error function
2.4 Unit step function
2.5 Unit impulse or Dirac-delta function
2.6 Null functions
2.7 Evaluation of Integrals by Laplace transforms

Unit 3 Inverse Laplace Transforms
3.1 Inverse Laplace transform
3.2 Properties of inverse Laplace transform
3.3 Inverse Laplace transforms of derivatives
3.4 Inverse Laplace transforms of integrals
3.5 Multiplication by sn
3.6 Division by s
3.7 Convolution Theorem
3.8 Evaluation of inverse Laplace transforms by using convolution theorem
3.9 Partial fraction method

Unit 4 Applications to Differential Equations
4.1 Solution of ordinary differential equation with constant coefficients
4.2 Ordinary differential equations with variable coefficients
4.3 Simultaneous ordinary differential equations