This document is an assignment for an advanced engineering mathematics course on partial differential equations. It discusses D'Alembert's formula, which provides the general solution to the one-dimensional wave equation. Specifically, it introduces new variables that allow the wave equation to be solved elegantly by rewriting the dependent variable u as a function of the new independent variables, one involving position x and time t added, and the other involving their difference. The assignment is for a third year civil engineering student named Vaani Pathak and is guided by their professor Jalpa Ma'am.

1. Advanced Engineering Mathematic
(2130002)
Active Learning Assignment
“PDE;D’Alembert’s Solution of the Wave Equation”
Branch : CE
Sem (Div) : 3rd- B3
Student’s Name :Vaani Pathak
Enrollment No.:170120107131
Guided By:Prof. Jalpa Ma’am.

2. D’Alembert’s Formula
• In mathematics ,and specifically partial
differential equations, D’Alembert’s
formula is the general solution to the
one-dimensional wave equation.
• There is an elegant approach to solve
wave equation by introducing new
variables:
v=x+ct, z=x-ct, u(x,t)=u(v,z) { }.

4. CONTINUE………

6. CONTINUE……..