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MTH-203 (A) | Laplace Transforms

F.Y.B.Sc. | Sem II | Mathematics

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F.Y.B.Sc. | Sem II | MTH-203 (A)
Laplace Transforms

We feel great pleasure in bringing out this books. The book has been written according to revised syllabus of KBC North Maharashtra University, Jalgaon for F.Y.B.Sc. Mathematics, MTH – 203 (A) – laplace transforms which is implemented form June 2022 (CBCS Pattern).
Each topic has been written in a very simple and lucid language to enable the students to understand the subject thoroughly. There are many worked examples with detailed steps. The problems in the exercises have been complied taking into consideration the academic background of students. We hope that the text will be equally appreciated by the students and the teachers.

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


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