M3 Numerical Methods — Formula Sheet kuch kuch important topics
M3 Numerical Methods — Formula Sheet 1. Newton-Raphson Method x n + 1 = x n − f ( x n ) f ′ ( x n ) \boxed{x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}} x n + 1 = x n − f ′ ( x n ) f ( x n ) Yaad rakho: New x = Old x − Function Derivative \boxed{\text{New }x=\text{Old }x-\frac{\text{Function}}{\text{Derivative}}} New x = Old x − Derivative Function 2. Regula-Falsi Method Pehle interval ( a , b ) (a,b) ( a , b ) choose karo such that: f ( a ) f ( b ) < 0 \boxed{f(a)f(b)<0} f ( a ) f ( b ) < 0 Formula: x = a f ( b ) − b f ( a ) f ( b ) − f ( a ) \boxed{x=\frac{a f(b)-b f(a)}{f(b)-f(a)}} x = f ( b ) − f ( a ) a f ( b ) − b f ( a ) Equivalent form: x = a − f ( a ) ( b − a ) f ( b ) − f ( a ) \boxed{x=a-\frac{f(a)(b-a)}{f(b)-f(a)}} x = a − f ( b ) − f ( a ) f ( a ) ( b − a ) Phir f ( x ) f(x) f ( x ) ka sign check karke a a a ya b b b replace karte hain. 3. Newton Forward Interpolation Kab? Jab required x x x , table ke beginni...