UG : TRB - MATHS - UNIT - 3 - IMPORTANT TOPIC - PROPERTY OF LAPLACE TRANSFORM

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UNIT – 3

1) HOMOGENEOUS EQUATIONS – EXACT EQUATIONS – INTEGRATING FACTORS – LINEAR EQUATIONS – REDUCTION OF ORDER – SECOND ORDER DIFFERENTIAL EQUATIONS – GENERAL SOLUTION OF HOMOGENEOUS EQUATIONS

2) HOMOGENEOUS EQUATION WITH CONSTANT COEFFICIENTS – METHOD OF UNDETERMINED COEFFICIENTS – METHOD OF VARIATION OF PARAMETERS – SYSTEM OF FIRST ORDER EQUATIONS – LINEAR SYSTEMS – HOMOGENEOUS LINEAR SYSTEMS WITH CONSTANT COEFFICIENTS

3) FORMATION OF PDE BY ELIMINATING ARBITRARY CONSTANTS AND ARBITRARY FUNCTIONS COMPLETE INTEGRAL – SINGULAR INTEGRAL – GENERAL INTEGRAL

4) SOLVING PDES: COMPLETE INTEGRAL – SINGULAR INTEGRAL – GENERAL INTEGRAL – LAGRANGE’S EQUATION Pp + Qq = R - CHARPIT’S METHOD AND SPECIAL TYPES OF FIRST ORDER EQUATIONS

5) LAPLACE TRANSFORM OF ELEMENTARY FUNCTIONS LAPLACE TRANSFORM OF SPECIAL FUNCTIONS LIKE UNIT STEP FUNCTION DIRAC DELTA FUNCTION – EVALUATION OF INTEGRALS USING LAPLACE TRANSFORM

6) INITIAL VALUE THEOREM – FINAL VALUE THEOREM - LAPLACE TRANSFORM OF PERIODIC FUNCTIONS – INVERSE LAPLACE TRANSFORMS – CONVOLUTION THEOREM – APPLICATION OF LAPLACE TRANSFORMATIONS IN SOLVING FIRST AND SECOND ORDER LINEAR DIFFERENTIAL EQUATION AND SIMULTANEOUS LINEAR ODES
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