D’Alembert’s Solution of the Wave Equation
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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.
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D’Alembert’s Solution of the Wave Equation
- 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……..