Engineering math formula for GATE/BARC/ISRO

Engineering MathematicsΒ is one of the scoring sections inΒ GATE/BARC/ISRO Exam. Looking at your requirement, we are sharing with you Important Engineering Mathematics Formulas & Shortcuts for Competitive Exam as well as Engineering exam.

  1. IfΒ π‘Ÿβ‰ π‘Ÿβ€², no solution, ifΒ π‘Ÿ=π‘Ÿβ€²=𝑛, unique solution ifΒ π‘Ÿ=π‘Ÿβ€²<𝑛, many solutions. (non-homogeneous)
  2. IfΒ π‘Ÿ=𝑛, trivial solution, ifΒ π‘Ÿ<𝑛 ,then (π‘›βˆ’π‘Ÿ) linearly independent solutions. (Many solutions) and ifΒ π‘š<𝑛, then many solutions.
  3. 𝑓(π‘₯+β„Ž) =𝑓(π‘₯) +β„Žπ‘“β€²(π‘₯) +β„Ž22!𝑓′′(π‘₯) +β„Ž33!𝑓′′′(π‘₯) + β€¦β€¦β€¦βˆž
  4. IfΒ π‘Ÿπ‘‘βˆ’π‘ 2>0 andΒ π‘Ÿ<0 𝑓(π‘₯,𝑦) have maximum, ifΒ π‘Ÿπ‘‘βˆ’π‘ 2>0 andΒ π‘Ÿ>0 𝑓(π‘₯,𝑦) have minimum at(π‘Ž,𝑏) and ifΒ π‘Ÿπ‘‘βˆ’π‘ 2<0, then saddle point. IfΒ π‘Ÿπ‘‘βˆ’π‘ 2=0,π‘“π‘’π‘Ÿπ‘‘β„Žπ‘’π‘ŸΒ investigation is required to decide.
  5. βˆ«π‘(βˆ…π‘‘π‘₯+πœ“π‘‘π‘¦)=∫∫𝐸(πœ•πœ“πœ•π‘₯βˆ’πœ•βˆ…πœ•π‘¦)𝑑π‘₯𝑑𝑦 (Green’s)
  6. βˆ«π‘π‘­.𝑑ℝ=βˆ«π‘†π‘π‘’π‘Ÿπ‘™π‘­.𝑁𝑑𝑠 (Stokes)
  7. βˆ«π‘†π‘­.𝑁𝑑𝑠=βˆ«πΈπ‘‘π‘–π‘£π‘­π‘‘π‘£Β (Gauss)
  8. π‘¦π‘’βˆ«π‘ƒπ‘‘π‘₯=βˆ«π‘„π‘’βˆ«π‘ƒπ‘‘π‘₯𝑑π‘₯+𝑐
  9. If 𝑀 𝑑π‘₯+𝑁 𝑑𝑦=0 be a homogeneous equation inΒ π‘₯Β and 𝑦, then 1𝑀 π‘₯+𝑁 𝑦 𝑖𝑠 an integrating factor
  10. If the equation of the type 𝑓1(π‘₯𝑦)𝑦 𝑑π‘₯+𝑓2(π‘₯𝑦)π‘₯ 𝑑𝑦=0. If the equation 𝑀 𝑑π‘₯+𝑁 𝑑𝑦=0 be of this type then 1𝑀 π‘₯βˆ’π‘Β π‘¦Β is an integrating factor
  11. IfΒ πœ•π‘€πœ•π‘¦βˆ’πœ•π‘πœ•π‘₯𝑁 be a function of x only = 𝑓(π‘₯) say thenΒ π‘’βˆ«π‘“(π‘₯)𝑑π‘₯Β is an integrating factor

 

  1. IfΒ πœ•π‘πœ•π‘₯βˆ’πœ•π‘€πœ•π‘¦π‘€Β be a function of y only = 𝑓(𝑦) say thenΒ π‘’βˆ«π‘“(𝑦)𝑑𝑦 is an integrating factor.
  2. βˆ«π‘€π‘‘π‘₯𝑦=π‘π‘œπ‘›π‘‘Β +∫terms of N not containing x dy=c
  3. 𝑃.𝐼.=1𝑓(𝐷)π‘’π‘Žπ‘₯=1𝑓(π‘Ž)π‘’π‘Žπ‘₯Β , 𝑓(π‘Ž)β‰ 0, if 𝑓(π‘Ž)=0,π‘‘β„Žπ‘’π‘›Β π‘ƒ.𝐼.=π‘₯1𝑓′(π‘Ž)π‘’π‘Žπ‘₯,𝑓′(π‘Ž)β‰ 0
  4. 𝑃.𝐼=1𝑓(𝐷2)sin(π‘Žπ‘₯+𝑏)= 1𝑓(βˆ’π‘Ž2), 𝑓(βˆ’π‘Ž2)β‰ 0, if 𝑓(βˆ’π‘Ž2)=0,

then 𝑃.𝐼. =π‘₯1𝑓′(βˆ’π‘Ž2)sin(π‘Žπ‘₯+𝑏), 𝑓′(βˆ’π‘Ž2)β‰ 0

  1. 𝑃.𝐼.=1𝑓(𝐷)π‘’π‘Žπ‘₯𝑉=Β π‘’π‘Žπ‘₯1𝑓(𝐷+π‘Ž)𝑉
  2. 𝑃.𝐼=1𝑓(𝐷)π‘₯π‘š=[𝑓(𝐷)]βˆ’1π‘₯π‘š,
  3. (1+π‘₯)βˆ’1=1βˆ’π‘₯+π‘₯2βˆ’β‹―
  4. (1βˆ’π‘₯)βˆ’1=1+π‘₯+π‘₯2+β‹―
  5. π‘₯𝑛𝑑𝑛𝑦𝑑π‘₯𝑛+π‘˜1π‘₯π‘›βˆ’1π‘‘π‘›βˆ’1𝑦𝑑π‘₯π‘›βˆ’1+β‹―π‘˜π‘›βˆ’1π‘₯𝑑𝑦𝑑π‘₯+π‘˜π‘›π‘¦=𝑋,Β π‘₯=𝑒𝑑 ,Β π‘₯𝑑𝑦𝑑π‘₯=𝐷𝑦,Β π‘₯2𝑑2𝑦𝑑π‘₯2=𝐷(π·βˆ’1)𝑦,Β π‘₯3𝑑3𝑦𝑑π‘₯3=D(Dβˆ’1)(Dβˆ’2)
  6. πœ•πœ•π‘₯(βˆ«β„Ž(𝑑,π‘₯)𝑑𝑑𝑔(π‘₯)𝑓(π‘₯))=βˆ«πœ•πœ•π‘₯β„Ž(𝑑,π‘₯)𝑑𝑑𝑔(π‘₯)𝑓(π‘₯)+𝑑𝑔𝑑π‘₯Β β„Ž[𝑔(π‘₯),π‘₯]βˆ’π‘‘π‘“π‘‘π‘₯Β β„Ž[𝑓(π‘₯),π‘₯]
  7. 𝐿{𝑓(𝑑)}=βˆ«π‘’βˆ’π‘ π‘‘βˆž0 𝑓(𝑑)𝑑𝑑
  8. 𝐿(1)=1𝑠
  9. 𝐿(𝑑𝑛)=𝑛!𝑠𝑛+1
  10. 𝐿(π‘’π‘Žπ‘‘)=1π‘ βˆ’π‘Ž
  11. 𝐿(sinπ‘Žπ‘‘)=π‘Žπ‘ 2+π‘Ž2
  12. 𝐿(cosπ‘Žπ‘‘)=𝑠𝑠2+π‘Ž2
  13. 𝐿(sinhπ‘Žπ‘‘)=π‘Žπ‘ 2βˆ’π‘Ž2
  14. 𝐿(coshπ‘Žπ‘‘)=𝑠𝑠2βˆ’π‘Ž2
  15. 𝐿{π‘’π‘Žπ‘‘π‘“(𝑑)}= 𝑓̅(π‘ βˆ’π‘Ž)
  16. 𝑓(𝑑+𝑇)=𝑓(𝑑) then 𝐿{𝑓(𝑑)}= βˆ«π‘’βˆ’π‘ π‘‘Β π‘“(𝑑)𝑑𝑑𝑇01βˆ’π‘’βˆ’π‘ π‘‡
  17. 𝐿{𝑓′(𝑑)}=𝑠𝑓̅(𝑠)βˆ’π‘“(0)
  18. 𝐿{𝑓𝑛(𝑑)}= 𝑠𝑛𝑓̅(𝑠)βˆ’π‘ π‘›βˆ’1𝑓(0)βˆ’π‘ π‘›βˆ’2𝑓′(0)βˆ’β‹―β€¦β€¦..π‘“π‘›βˆ’1(0)
  19. 𝐿{βˆ«π‘“(π‘₯)𝑑π‘₯𝑑0}= 1𝑆𝑓̅(𝑠)
  20. 𝐿{𝑑𝑛𝑓(𝑑)}=(βˆ’1)𝑛𝑑𝑛𝑑𝑠𝑛.[𝑓̅(s)]
  21. 𝐿{1𝑑𝑓(𝑑)}= βˆ«π‘“Μ…(s) βˆžπ‘†π‘‘π‘ 
  22. 𝑓(π‘₯)=π‘Ž02+ Ξ£π‘Žπ‘›βˆžπ‘›=1cos𝑛π‘₯+ Ξ£π‘π‘›βˆžπ‘›=1sin𝑛π‘₯
  23. π‘Ž0=1πœ‹βˆ«π‘“(π‘₯)𝑑π‘₯𝛼+2πœ‹π›Ό,Β π‘Žπ‘›=1πœ‹βˆ«π‘“(π‘₯) cos𝑛π‘₯𝑑π‘₯𝛼+2πœ‹π›Ό, 𝑏𝑛=1πœ‹βˆ«π‘“(π‘₯) sin𝑛π‘₯𝑑π‘₯𝛼+2πœ‹π›Ό
  24. 𝑓(π‘₯)=π‘Ž02+ Ξ£π‘Žπ‘›βˆžπ‘›=1cosπ‘›πœ‹π‘₯𝑐+ Ξ£π‘π‘›βˆžπ‘›=1sinπ‘›πœ‹π‘₯𝑐
  25. 40.Β π‘Ž0=1π‘βˆ«π‘“(π‘₯)𝑑π‘₯𝛼+2𝑐𝛼,Β π‘Žπ‘›=1π‘βˆ«π‘“(π‘₯) cosπ‘›πœ‹π‘₯𝑐𝑑π‘₯𝛼+2𝑐𝛼, 𝑏𝑛=1π‘βˆ«π‘“(π‘₯) sinπ‘›πœ‹π‘₯𝑐𝑑π‘₯𝛼+2𝑐𝛼
  26. 𝑓(π‘₯)= Ξ£π‘π‘›βˆžπ‘›=1sinπ‘›πœ‹π‘₯𝑐 , where 𝑏𝑛=2π‘βˆ«π‘“(π‘₯) sinπ‘›πœ‹π‘₯𝑐𝑑π‘₯𝑐0
  27. 𝑓(π‘₯)=Β π‘Ž02+ Ξ£π‘Žπ‘›βˆžπ‘›=1cosπ‘›πœ‹π‘₯𝑐 where,Β π‘Ž0=2π‘βˆ«π‘“(π‘₯)𝑑π‘₯𝑐0,Β π‘Žπ‘›=2π‘βˆ«π‘“(π‘₯) cosπ‘›πœ‹π‘₯𝑐𝑑π‘₯𝑐0
  28. πœ‡=Σ π‘₯𝑗𝑓(π‘₯𝑗)π‘—Β π‘Žπ‘›π‘‘Β πœ‡=∫π‘₯ 𝑓(π‘₯)𝑑π‘₯Β βˆžβˆ’βˆž
  29. 𝜎2=Ξ£ (π‘₯π‘—βˆ’πœ‡)2𝑓(π‘₯𝑗)Β π‘—π‘Žπ‘›π‘‘Β πœŽ2=∫(π‘₯βˆ’πœ‡)2 𝑓(π‘₯)𝑑π‘₯βˆžβˆ’βˆž
  30. π‘€π‘’π‘Žπ‘›:𝑛𝑝=πœ‡Β π‘‰π‘Žπ‘Ÿπ‘–π‘Žπ‘›π‘π‘’: 𝜎2=πœ‡Β (Poisson’s distribution)
  31. 𝑓(π‘₯)=1𝜎√2πœ‹π‘’βˆ’ 12(π‘₯βˆ’πœ‡πœŽ)2 (Normal distribution)
  32. 𝑦=π‘Ž+𝑏π‘₯, Σ𝑦=π‘›π‘Ž+𝑏Σπ‘₯, Ξ£π‘₯𝑦=π‘ŽΞ£π‘₯+𝑏Σπ‘₯2
  33. 𝑦=π‘Ž+𝑏π‘₯+𝑐π‘₯2, Σ𝑦=π‘›π‘Ž+𝑏.Ξ£π‘₯+𝑐.Ξ£π‘₯2, Ξ£π‘₯𝑦=π‘ŽΞ£π‘₯+𝑏.Ξ£π‘₯2+𝑐 Σπ‘₯3, Ξ£π‘₯2𝑦=π‘ŽΞ£π‘₯2+𝑏.Ξ£π‘₯3+𝑐 Σπ‘₯4
  34. 𝑦=𝑓(π‘₯)=(π‘₯βˆ’π‘₯1)(π‘₯βˆ’π‘₯2)…(π‘₯βˆ’π‘₯𝑛)(π‘₯0βˆ’π‘₯1)(π‘₯0βˆ’π‘₯2)…(π‘₯0βˆ’π‘₯𝑛)𝑦0+(π‘₯βˆ’π‘₯0)(π‘₯βˆ’π‘₯2)…(π‘₯βˆ’π‘₯𝑛)(π‘₯1βˆ’π‘₯0)(π‘₯1βˆ’π‘₯2)…(π‘₯1βˆ’π‘₯𝑛)𝑦1+β‹―+(π‘₯βˆ’π‘₯1)(π‘₯βˆ’π‘₯2)…(π‘₯βˆ’π‘₯π‘›βˆ’1)(π‘₯π‘›βˆ’π‘₯0)(π‘₯π‘›βˆ’π‘₯1)…(π‘₯π‘›βˆ’π‘₯π‘›βˆ’1)𝑦𝑛
  35. (𝑑𝑦𝑑π‘₯)π‘₯0=1β„Ž[Δ𝑦0βˆ’12Ξ”2𝑦0+13Ξ”3𝑦0βˆ’14Ξ”4𝑦0+β‹―]
  36. (𝑑𝑦𝑑π‘₯)π‘₯𝑛=1β„Ž[βˆ‡π‘¦π‘›+12βˆ‡2𝑦𝑛+13βˆ‡3𝑦𝑛+14βˆ‡4𝑦𝑛+β‹―]
  37. π‘₯𝑛+1=π‘₯π‘›βˆ’π‘“(π‘₯𝑛)𝑓′(π‘₯𝑛) (Newton-Raphson)
  38. βˆ«π‘“(π‘₯)𝑑π‘₯π‘₯0+π‘›β„Žπ‘₯0=β„Ž2[𝑦0+𝑦𝑛+2(𝑦1+𝑦2+β‹―..+π‘¦π‘›βˆ’1)] (Trapezoidal)
  39. βˆ«π‘“(π‘₯)𝑑π‘₯π‘₯0+π‘›β„Žπ‘₯0=β„Ž3[(𝑦0+𝑦𝑛)+4(𝑦1+𝑦3+β‹―π‘¦π‘›βˆ’1)+2(𝑦2+𝑦4+β‹―π‘¦π‘›βˆ’2)] (Simpson’s)
  40. πΈπ‘Ÿπ‘Ÿπ‘œπ‘Ÿ=βˆ’π‘βˆ’π‘Ž12β„Ž2 𝑓′′(πœ‰)=𝑂(β„Ž2) (Trapezoidal)
  41. πΈπ‘Ÿπ‘Ÿπ‘œπ‘Ÿ=βˆ’π‘βˆ’π‘Ž180β„Ž4𝑓𝑖𝑣(πœ‰)=𝑂(β„Ž4) (Simpson’s)
  42. π‘¦π‘˜+1=π‘¦π‘˜+β„Ž.𝑓(π‘‘π‘˜,π‘¦π‘˜) where 𝑑𝑦𝑑π‘₯=𝑓(𝑑,𝑦) (Euler’s)

Hello friends, my name is Bipin Kumar, I am the Writer and Founder of this blog and share all the information related to Civil Engineering, Civil practical Knowledge, Site Execution Knowledge, latest information about construction and more through this website.

1 thought on “Engineering math formula for GATE/BARC/ISRO”

Leave a Comment

Pinterest
fb-share-icon
Instagram