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Mathematics - iii (Differential Calculus) - Vol 1
The Laplace Transform is a fundamental technique in electrical engineering that simplifies the analysis of circuits by converting differential equations into algebraic equations using the frequency domain. It handles initial conditions naturally and is particularly useful for linear time-invariant systems and transient response analysis. The application of Laplace Transforms allows for easier solution of complex circuit behaviors, enabling the determination of voltage and current responses to various inputs.
19 Chapters
4 weeks
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Course Chapters
Chapter 1
Laplace Transforms & Applications - Definition of Laplace Transform
Chapter 2
Linearity Property of Laplace Transform
Chapter 3
Topic 3: First Shifting Theorem
Chapter 4
Second Shifting Theorem
Chapter 5
Laplace Transform of Derivatives
Chapter 6
Laplace Transform of an Integral
Chapter 7
Multiplication by tn (Power of t)
Chapter 8
Division by t (Inverse of Multiplication by s)
Chapter 9
Laplace Transform of Unit Step Function
Chapter 10
The Dirac Delta Function (Impulse Function)
Chapter 11
Laplace Transform of Periodic Functions
Chapter 12
Inverse Laplace Transform
Chapter 13
Convolution Theorem
Chapter 14
Initial Value Theorem
Chapter 15
Final Value Theorem
Chapter 16
Application to Ordinary Differential Equations (ODEs)
Chapter 17
Application to Simultaneous Linear Differential Equations
Chapter 18
Application to Integral Equations
Chapter 19