This video discusses key numerical methods concepts including diagonal dominance conditions for matrix stability, Gauss-Jacobi and Gauss-Seidel iterative methods for solving linear systems, and numerical integration techniques such as Simpson's 1/3 rule, Simpson's 3/8 rule, and the trapezoidal rule, along with their respective applications and limitations in approximating solutions to mathematical problems.
Deep Dive
Prerequisite Knowledge
- No data available.
Where to go next
- No data available.
Deep Dive
AMAT කුප්පිය | Numerical Methods - II | Past Paper Discussion - 20/21 | 2024 - 03 - 31Added:
fore [Music] no fore fore for Max maximum XI X maximum for Matrix of equation [Music] x for l [Music] for for to make following Matrix uh to be diagonally dominant to be diagonal dominant the value of P needs to be value of P needs to be El greater than or equal to 13 a greater than or equal to 13 of the following assumptions of job meod The coent Matrix has no Zer in main diagonal the rate of concy is quite slow compared to other no Zer on it main [Music] diagonal Assumption of of compared to with other methods Matrix has Zer in its main diagonal has zici mat has no Zer on non leing diagonal the positive Def associated with the form [Music] Q fore fore need XT [Music] MX XT m [Music] x positive def by X X3 1 by3 X sorry sorry re XY XY sorry sorry sorry um XY uh X said sorry uh X for [Music] for which is the highest polinomial order that allow Simpsons 38 rule to the obtain exact value for integration highest polom Simpsons [Music] 3 which the local transation midpoint method step size scale local G mid point e triple Das B uh 3 B [Music] what is the correct mat form of for [Music] l for for sorry sorry sorry [Music] X2 K minus one Reina a13 X3 K minus one 212 x 2 3 x 311 3x uh a n x b [Music] for [Music] B for d d for inverse U consider the m for for f uh T half y i half find why [Music] [Music] when y z 3 y z equal y y uh [Music] f333 foree f t t halfa y half y this is what is limitation of GA Sidle method it cannot be usedful matrices with none non zement more [Music] comp it doesn't guarante forx it's Ana technique for using the formula in the usual [Music] notation for put in equation equation fore why [Music] for uh y y1 y 2 x n minus 2 n n x x YX YX y for y1 Y 2 Y3 y5 uh y n minus one y 2 the y 6 y n minus 2 [Music] foree uh e e e e e for fore fore for in equation equation that is by replacing the curve by by of third Delta y [Music] note for for Y3 Y2 y1 y spee similar similarly X3 X6 YX y 6 it was finally X YX y for X Y DX uh xn y DX y y1 y Y3 Y3 y4 Y3 sorry y5 Y6 the following table is the values of showing all workings and maintain inmes in all estimate theal rle two for for y1 y y y inter make two intervals inter s S 5 make y y1 y 2 Y3 for for y y one y 2s fore oh Simpsons one rule with 16s SS one Ru with six intervals Simpsons 13 rule six intervals six inter 5 make a y1 make a y 2 make a Y3 make a y4 make y5 y six six inters seven points sorry y y Y3 y y yorry for Simpson 38 r with three intervals inters s y z y1 Y2 y 3 3 h i sorry y sorry in the results in a and b for Sol which is more accurate and Y uh compare the results uh uh [Music] and going answer from B is more accurate why yute for for so that for approximating the solution of line system xB right uh L XK D B consist of a strictly below the the this diagonal matrix consist of dial a r consist of elements of a strictly above the consist of elements of a strictly below the DI for a b lower sorry lower triang triang lower triangular DX X D inverse l u x k d inverse the proposed iteration to approximate solution solution system mod okay the Matrix a a is strictly diagonally dominant hence jaob meod is [Music] convergent to the solution of B system another write down the system in the form [Music] d x l x k uh B 2 fore X1 X2 X3 k carry out three iterations to find solution of the system you are expected to maintain for Dees in answer X uh X1 X2 X3 k k k k [Music] [Music] for [Music] [Music] for foreign fore X3 foreign speee for [Music] Fore foreign fore [Music] for thir 0 0 12 X1 X2 X3 fore [Music] spee X1 X2 X3 for X1 for [Music] fore for r fore they briefly explain the difference uh briefly explain the difference in approach used by to [Music] Sol at the beginning of the interval is assumed to is assumed to apply across the entire interval the of beginning of inter is assum to apply across [Music] the take two take two derivatives as as one at the beginning n and one at the end end and obtain an average average improv en inter entire interval midpoint midpoint again the slope is is approximated at the middle of f dra all [Music] [Music] to find value [Music] of [Music] spee use using Oiler Oiler for y1 y1 HF t y t y foree for for for mid sorry from method point methode for 2 f y ft not y node FT1 y y f fore [Music] for why not know FT1 y1 [Music] 0 1-us 1.46 [Music] 0.55 for y atal 0.5 for 4 Y 2 y [Music] t0.5 for Fore foreign [Music] foree foring coins coins using coins uh Y 2 2 y1 Y 2 T1 y1 d f T1 sorry T2 Y2 1 for for [Music] for fore mid point mid point1 for for point me to find value of y when y i f t y right y i+ 1 y i t half y half h h for equ for y y t y f for f y f y1 y y0 [Music] [Music] fore t t f d i y i if f t i half y i half [Music] [Music] h T1 F T1 y1 y1 y1 y1 [Music] y1 fore [Music] f h y y1 for for for for foree but oh
Related Videos
Olympiad Mathematics | Indian | Can You Solve This One?
PhilCoolMath
650 views•2026-06-03
Escaping the Fog
LogicLemurGaming
760 views•2026-06-03
A Brutal Radical Expression Made Easy! The Shortcut Changes Everything.
tamoshop
112 views•2026-06-02
V : jee main /advance class 11 mathematics : Binomial Theorem class-1 ( 29 may 2026 )
dcamclassesiitjeemainsadva9953
125 views•2026-05-29
Is This Pentomino Tileable?
3cycle
241 views•2026-05-30
This Sudoku Has Many Lines!!
CrackingTheCryptic
2K views•2026-05-29
Olympiad Mathematics | Indian Can You Solve This One?
PhilCoolMath
268 views•2026-06-02
Olympiad Mathematics | Indian | Can You Solve This?
PhilCoolMath
669 views•2026-06-02











