University of Moratuwa

This note explains the series solution methods for second-order linear differential equations with variable coefficients, including solutions about ordinary and regular singular points using the Frobenius method. It introduces the indicial equation, discusses different root cases, and includes worked examples. Special functions such as Bessel functions are also covered, highlighting their importance in engineering applications.

This document offers a comprehensive guide to Partial Differential Equations (PDEs). It covers the definition, classification, and types of PDEs, including elliptic, parabolic, and hyperbolic equations. The notes explain key solution techniques such as direct integration, separation of variables, Fourier series methods, and the use of Laplace’s equation in both Cartesian and polar coordinates. Worked examples demonstrate applications to problems in heat conduction, wave motion, and steady-stat...

This document provides a detailed guide to solving differential equations using Fourier Series. It explains the fundamentals of Fourier series representation, including sine and cosine series, half-range expansions, and the complex form. The notes cover key theorems such as Dirichlet’s conditions and Parseval’s formula, along with generalized integration by parts. Numerous worked examples illustrate the step-by-step process of forming Fourier series for various periodic and piecewise functio...

This document provides a comprehensive guide to solving differential equations using Laplace Transforms. It covers fundamental Laplace Transform definitions, common transforms for standard functions, important theorems such as linearity, shifting, and convolution, as well as the inverse Laplace Transform. The notes include worked examples demonstrating the application of Laplace methods to solve ordinary differential equations (ODEs), including those with initial conditions, periodic inputs, and...

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Title: The Little Man Computer. This is a note that includes the exercises with answers.