“An Introduction to Differential Equations” BY R K Ghosh, K C Maity, and D K Ghosh. (NCBA)

Name: "An Introduction to Differential Equations" BY R K Ghosh, K C Maity, and D K Ghosh. (NCBA) - Booksbp.com
SKU: 9788173817342
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SKU: 9788173817342

1. Core Ordinary Differential Equations (ODEs)

Preliminary Notions: Understanding the fundamental concept of ordinary differential equations, defining independent/dependent variables, order, and degree.
Equations of First Order and First Degree: Methods for solving basic differential equations, including variables separable, homogeneous equations, exact equations, and integrating factors.
Linear Equations with Constant Coefficients: Focused techniques for finding Complementary Functions (C.F.) and Particular Integrals (P.I.) using differential operators.
Equations of First Order but Not of First Degree: Specialized methods for solving equations solvable for \(p\) (where \(p = \frac{dy}{dx}\)), solvable for \(x\), solvable for \(y\), and Clairaut’s form.

2. Advanced Analytical Techniques

Method of Undetermined Coefficients & Variation of Parameters: Robust procedures used to determine particular solutions of higher-order linear differential equations.
Sturm-Liouville Theory: Analysis of boundary value problems, establishing properties of eigenvalues and corresponding orthogonal eigenfunctions.
Laplace and Inverse Laplace Transformations: Mathematical transforms used to simplify linear differential equations into algebraic equations, typically applied to initial value problems.

3. Structural & Boundary Value Methods

Green’s Functions: Integral equations and constructions used to solve inhomogeneous boundary value problems.
Existence and Uniqueness Theory: Strict mathematical proofs (such as Picard’s iteration method) verifying whether a given initial value problem has a unique solution.
Partial Differential Equations (PDEs): Introduction to equations involving multiple independent variables, Lagrange’s linear equation method, and Charpit’s method.