Link of books on Tensor Analysis: Tensor Analysis With Applications

Hi Guys, today I'm giving you the link of another book on Tensor Analysis named "Tensor Analysis With Applications - A I Borisenko"

 Here is the link

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Link of books on Tensor Analysis

Guys, Happy Friendship Day :) Today I'm giving you the link of a book on Tensor Analysis.


Vector Analysis by Schaum's Outline Series

Here is the link.

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Link of books on Differential Geometry.

Hey guys, I've found two books on differential geometry. 

The first book is by Schaum's Outline Series

Here is the Link
Here is another link .


The second book is An Introduction to Differential Geometry

Here is the link1 & link2 .
This book needs DJVU reader to be opened. Here's the link for the DJVU reader.

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Link of book on Number Theory

Hey, here is a link of a book on Number Theory. Here's the link :)

NumberTheory

Enjoy :D

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Link of book on Partial Differential Equation

Hey guys, I've got a link of a book on PDE. It's just 3.32 MB. Go check it, here's the link 
 

Introduction to Partial Differential Equations and Hilbert Space Methods

Go to this website & click on "Request download ticket" at the bottom of the page & then click on "download". You'll get it.

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Assignment 15 : ADAMS 4TH ORDER PREDICTOR-CORRECTOR METHOD

      PROGRAM PCMET
      OPEN(1,'INPUT.DAT')
      OPEN(2,'OUTPUT.DAT')
      READ(1,*)A,B,N,Y0
      CALL PCM(A,B,N,Y0)
      END PROGRAM

      SUBROUTINE PCM(A,B,N,Y0)
      F(T,Y)=Y-T*T+1
      G(T)=(T+1)**2-0.5*EXP(T)
      REAL::T(0:N),W(0:N),K1,K2,K3,K4
      WRITE(2,*)'ADAMS 4TH ORDER PC METHOD:'
      WRITE(2,10)
  10  FORMAT(3X,'T',9X,'W',8X,'EXACT',5X,'ERROR')
      H=(B-A)/N
      T(0)=A
      W(0)=Y0
      WRITE(2,11)T(0),W(0),G(T(0)),ABS(W(0)-G(T(0)))
  11  FORMAT(2X,F4.2,2X,F9.6,2X,F9.6,2X,F9.6)
      DO I=0,2
      K1=H*F(T(I),W(I))
      K2=H*F(T(I)+0.5*H,W(I)+0.5*K1)
      K3=H*F(T(I)+0.5*H,W(I)+0.5*K2)
      K4=H*F(T(I)+H,W(I)+K3)
      W(I+1)=W(I)+(K1+2*K2+2*K3+K4)/6
      T(I+1)=A+(I+1)*H
      WRITE(2,11)T(I+1),W(I+1),G(T(I+1)),ABS(W(I+1)-G(T(I+1)))
      END DO
      DO I=3,N-1
      T(I+1)=A+(I+1)*H
      W(I+1)=W(I)+H*(55*F(T(I),W(I))-59*F(T(I-1),W(I-1))+37*F(T(I-2),W(
     1I-2))-9*F(T(I-3),W(I-3)))/24
      W(I+1)=W(I)+H*(9*F(T(I+1),W(I+1))+19*F(T(I),W(I))-5*F(T(I-1),W(I-1
     1))+F(T(I-2),W(I-2)))/24
      WRITE(2,11)T(I+1),W(I+1),G(T(I+1)),ABS(W(I+1)-G(T(I+1)))
      END DO
      END SUBROUTINE

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Assignment 14 : Adam - Moulton 4 Step Implicit Method

      PROGRAM AMMET
      OPEN(1,'INPUT.DAT')
      OPEN(2,'OUTPUT.DAT')
      READ(1,*)A,B,N,Y0
      CALL AMM(A,B,N,Y0)
      END PROGRAM

      SUBROUTINE AMM(A,B,N,Y0)
      F(T,Y)=Y-T*T+1
      G(T)=(T+1)**2-0.5*EXP(T)
      REAL::T(0:N),Y(0:N),W(0:N),K1,K2,K3,K4
      WRITE(2,*)'AM IMPLICIT METHOD:'
      WRITE(2,10)
  10  FORMAT(3X,'T',9X,'W',8X,'EXACT',5X,'ERROR')
      H=(B-A)/N
      T(0)=A
      W(0)=Y0
      Y(0)=Y0
      WRITE(2,11)T(0),Y(0),G(T(0)),ABS(Y(0)-G(T(0)))
  11  FORMAT(2X,F4.2,2X,F9.6,2X,F9.6,2X,F9.6)
      DO I=0,N-1
      K1=H*F(T(I),W(I))
      K2=H*F(T(I)+0.5*H,W(I)+0.5*K1)
      K3=H*F(T(I)+0.5*H,W(I)+0.5*K2)
      K4=H*F(T(I)+H,W(I)+K3)
      W(I+1)=W(I)+(K1+2*K2+2*K3+K4)/6
      T(I+1)=A+(I+1)*H
      IF(I<3) THEN
      Y(I+1)=W(I+1)
      ELSE
          Y(I+1)=Y(I)+H*(251*F(T(I+1),W(I+1))+646*F(T(I),W(I))-264*F(T(I-1),W(I-1))+106*F(T(I-2),W(I-2))-19*F(T(I-3),W(I-3)))/720
      END IF
      WRITE(2,11)T(I+1),Y(I+1),G(T(I+1)),ABS(Y(I+1)-G(T(I+1)))
      END DO
      END SUBROUTINE

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Assignment 13 : Adam - Bashforth 4 Step Explicit Method

      PROGRAM ABMET
      OPEN(1,'INPUT.DAT')
      OPEN(2,'OUTPUT.DAT')
      READ(1,*)A,B,N,Y0
      CALL ABM(A,B,N,Y0)
      END PROGRAM

      SUBROUTINE ABM(A,B,N,Y0)
      F(T,Y)=Y-T*T+1
      G(T)=(T+1)**2-0.5*EXP(T)
      REAL::T(0:N),W(0:N),K1,K2,K3,K4
      WRITE(2,*)'AB EXPLICIT METHOD:'
      WRITE(2,10)
  10  FORMAT(3X,'T',9X,'W',8X,'EXACT',5X,'ERROR')
      H=(B-A)/N
      T(0)=A
      W(0)=Y0
      WRITE(2,11)T(0),W(0),G(T(0)),ABS(W(0)-G(T(0)))
  11  FORMAT(2X,F4.2,2X,F9.6,2X,F9.6,2X,F9.6)
      DO I=0,2
      K1=H*F(T(I),W(I))
      K2=H*F(T(I)+0.5*H,W(I)+0.5*K1)
      K3=H*F(T(I)+0.5*H,W(I)+0.5*K2)
      K4=H*F(T(I)+H,W(I)+K3)
      W(I+1)=W(I)+(K1+2*K2+2*K3+K4)/6
      T(I+1)=A+(I+1)*H
      WRITE(2,11)T(I+1),W(I+1),G(T(I+1)),ABS(W(I+1)-G(T(I+1)))
      END DO
      DO I=3,N-1
      T(I+1)=A+(I+1)*H
      W(I+1)=W(I)+H*(55*F(T(I),W(I))-59*F(T(I-1),W(I-1))+37*F(T(I-2),W(I-2))-9*F(T(I-3),W(I-3)))/24
      WRITE(2,11)T(I+1),W(I+1),G(T(I+1)),ABS(W(I+1)-G(T(I+1)))
      END DO
      END SUBROUTINE

Input is same as RK and Euler Methods as the function, that is, initial value problem is the same. But A-B method produces more accurate approximations.

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Assignment 12 : RK Method of Order 2 & 4

      PROGRAM RKMETS
      OPEN(1,'INPUT.DAT')
      OPEN(2,'OUTPUT.DAT')
      READ(1,*)A,B,N,Y0
      CALL RK2(A,B,N,Y0)
      CALL RK4(A,B,N,Y0)
      END PROGRAM

      SUBROUTINE RK2(A,B,N,Y0)
      F(T,Y)=Y-T*T+1
      G(T)=(T+1)**2-0.5*EXP(T)
      REAL::K1,K2
      WRITE(2,*)'R-K METHOD OF ORDER 2:'
      WRITE(2,10)
  10  FORMAT(4X,"T"98X,"W",8X,'EXACT',5X,'ERROR')
      H=(B-A)/N
      T=A
      Y=Y0
      WRITE(2,11)T,Y,G(T),ABS(Y-G(T))
  11  FORMAT(2X,F4.2,2X,F9.6,2X,F9.6,2X,F9.6)
      DO I=1,N
      K1=H*F(T,Y)
      K2=H*F(T+H,Y+K1)
      Y=Y+(K1+K2)/2
      T=A+I*H
      WRITE(2,11)T,Y,G(T),ABS(Y-G(T))
      END DO
      END SUBROUTINE

      SUBROUTINE RK4(A,B,N,Y0)
      F(T,Y)=Y-T*T+1
      G(T)=(T+1)**2-0.5*EXP(T)
      REAL::K1,K2,K3,K4
      WRITE(2,*)'R-K METHOD OF ORDER 4:'
      WRITE(2,10)
  10  FORMAT(4X,"T"98X,"W",8X,'EXACT',5X,'ERROR')
      H=(B-A)/N
      T=A
      Y=Y0
      WRITE(2,11)T,Y,G(T),ABS(Y-G(T))
  11  FORMAT(2X,F4.2,2X,F9.6,2X,F9.6,2X,F9.6)
      DO I=1,N
      K1=H*F(T,Y)
      K2=H*F(T+0.5*H,Y+0.5*K1)
      K3=H*F(T+0.5*H,Y+0.5*K2)
      K4=H*F(T+H,Y+K3)
      Y=Y+(K1+2*K2+2*K3+K4)/6
      T=A+I*H
      WRITE(2,11)T,Y,G(T),ABS(Y-G(T))
      END DO
      END SUBROUTINE

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Assignment 10 : Romberg Integration

      PROGRAM ROMINT
      DIMENSION R(20,20)
      OPEN(1,'IA10.DAT')
      OPEN(2,'OA10.DAT')
      READ(1,*)A,B,N
      CALL ROMBERG(A,B,N,R)
      END PROGRAM

      SUBROUTINE ROMBERG(A,B,N,R)
      F(X)=SIN(X)
      REAL::R(20,20)
      WRITE(2,*)'ROMBERG INTEGRATION'
      H=B-A
      R(1,1)=(H/2.0)*(F(A)+F(B))
      DO I=2,N
      S=0
      DO K=1,2**(I-2)
      S=S+F(A+((K-0.5)*H))
      END DO
      R(I,1)=0.5*(R(I-1,1)+(H*S))
      H=H/2.0
      END DO
      DO J=2,N
      DO I=J,N
      R(I,J)=R(I,J-1)+((R(I,J-1)-R(I-1,J-1))/(4**(J-1))-1)
      END DO
      END DO
      DO I=1,N
      WRITE(2,20)(R(I,J),J=1,I)
  20  FORMAT(6(2X,F12.6))
      END DO
      END SUBROUTINE

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