Link of book on Hydrodynamics ( MTH - 407)

Guys, here's the link of a book named "Theoretical Hydrodynamic" by L M Milne Thomson.

Here's the link .

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Link of book on Mathematical Economics

Hey friends, here's the link of the book "Introduction to Mathematical Economics" of Schaum's Outline Series.

Schaum’s Introduction to Mathematical Economics, 3rd ed. 

Summary: McGraw-Hill | English | Aug 30 2000 | ISBN: 007135896X | 523 pages | PDF | 42 MB

 

Table of Contents:
Review.
Economic Applications of Graphs and Equations.
The Derivative and the Rules of Differentiation.
Uses of the Derivative in Mathematics and Economics.
Calculus of Multivariable Functions.
Caculus of Multivariable Functions in Economics.
Exponential and Logarithmic Functions in Economics.
Differentiation of Exponential and Logarithmic Functions.
The Fundamentals of Linear (or Matrix) Algebra.
Matrix Inversion.
Special Determinants and Matrices and Their Use in Economics.
Comparative Statics and Concave Programming.
Integral Calculus: The Indefinite Integral.
Integral Calculus: The Definite Integral.
First-Order Differential Equations.
First Order Difference Equations.
Second-Order Differential Equations and Difference Equations.
Simultaneous Differential and Difference Equations.
The Calculus of Variations.
Optimal Control Theory.

Here's the link .

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Link of books on Nonlinear Programming

Hey friends, here's the links of two books on Nonlinear Programming.

1)Schaum's Outline of Operations Research, 2nd ed.

Summary:

McGraw-Hill | English | July 1 1997 | ISBN: 0070080208 | 464 pages | PDF | 29 MB

Table of Contents:
Chapter 1 Mathematical Programming
Chapter 2 Linear Programming: Basic Concepts
Chapter 3 Linear Programming: The Simplex And The Dual Simplex Methods
Chapter 4 Linear Programming: Duality And Sensitivity Analysis
Chapter 5 Linear Programming: Extensions
Chapter 6 Integer Programming: Branch-And-Bound Algorithm
Chapter 7 Integer Programming: Cut Algorithms
Chapter 8 Integer Programming: The Transportation Algorithm
Chapter 9 Integer Programming: Scheduling
Chapter 10 Nonlinear Programming: Single-Variable Optimization
Chapter 11 Nonlinear Programming: Multivariable Optimization Without Constraints
Chapter 12 Nonlinear Programming: Multivariable Optimization With Constraints
Chapter 13 Network Analysis
Chapter 14 Project Planning Using Pert/Cpm
Chapter 15 Inventory Models
Chapter 16 Forecasting
Chapter 17 Game Theory
Chapter 18 Decision Theory
Chapter 19 Dynamic Programming
Chapter 20 Finite Markov Chains
Chapter 21 Markovian Birth-Death Processes
Chapter 22 Queueing Systems
Chapter 23 M/M/1 Systems System
Chapter 24 Other Systems With Poisson-Type
Answers To Supplementary Problems
Index 

Here's the link

2) David G. Luenberger - Linear and Nonlinear Programming 2nd Edition

Summary:

Addison-Wesley | 1984 | ISBN: 0201157942 | Pages: 560 | DJVU | 3.34 MB

Here's  link1 & link2

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Link of book on Differential Geometry.

Guys, here's another book on Differential Geometry.

Differential Geometry Of Three Dimensions (1955)

Author: C.E.WEATHERBURN
Publisher: Cambridge At the University Press

Click here or here to download the book.

Enjoy :)

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Link of book on Differential Geometry.

Hey guys, here's another book on Differential Geometry.

Lectures on Classical Differential Geometry: Second Edition

 By Dirk J. Struik

• Publisher: Dover Publications
• Number Of Pages: 240
• Publication Date: 1988-04-01
• ISBN-10 / ASIN: 0486656098
• ISBN-13 / EAN: 9780486656090

Product Description:
Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, geometry on a surface, envelopes, conformal mapping, minimal surfaces, more. Well-illustrated, with abundant problems and solutions. Bibliography.

Here's the link1 (djvu) & link2 (pdf)

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Link of books on Mathematical Finance

Here's a link of a book on Mathematical Finance for the course MTH-414 : Mathematical Modeling of Business & Finance. Sorry as I couldn't give a screen shot of the book. But I give you a summary of this book.

 

Mathematical Finance: Theory, Modeling, Implementation Summary:

Christian Fries, Mathematical Finance: Theory, Modeling, Implementation
Wiley | ISBN: 0470047224 | August 24, 2007 | 544 pages | PDF | 15 Mb
A balanced introduction to the theoretical foundations and real-world applications of mathematical finance. The ever-growing use of derivative products makes it essential for financial industry practitioners to have a solid understanding of derivative pricing. To cope with the growing complexity, narrowing margins, and shortening life-cycle of the individual derivative product, an efficient, yet modular, implementation of the pricing algorithms is necessary. Mathematical Finance is the first book to harmonize the theory, modeling, and implementation of today's most prevalent pricing models under one convenient cover. Building a bridge from academia to practice, this self-contained text applies theoretical concepts to real-world examples and introduces state-of-the-art, object-oriented programming techniques that equip the reader with the conceptual and illustrative tools needed to understand and develop successful derivative pricing models.
Utilizing almost twenty years of academic and industry experience, the author discusses the mathematical concepts that are the foundation of commonly used derivative pricing models, and insightful Motivation and Interpretation sections for each concept are presented to further illustrate the relationship between theory and practice. In-depth coverage of the common characteristics found amongst successful pricing models are provided in addition to key techniques and tips for the construction of these models. The opportunity to interactively explore the book's principal ideas and methodologies is made possible via a related Web site that features interactive Java experiments and exercises.
While a high standard of mathematical precision is retained, Mathematical Finance emphasizes practical motivations, interpretations, and results and is an excellent textbook for students in mathematical finance, computational finance, and derivative pricing courses at the upper undergraduate or beginning graduate level. It also serves as a valuable reference for professionals in the banking, insurance, and asset management industries.

Here's the link .

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Link of books on Tensor Analysis: Tensor Calculus By Barry Spain

Hey Guys, here's another book on Tensor Analysis :)

Tensor Calculus - Barry Spain

Here's the link1 & here's the link2 .
The book is in zipped format. You need 7zip or Winrar to extract it & to get the pdf file. While extracting, it may require a password. The password is following :)

password: twistedmath

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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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Fortran Program For Jacobi, Gauss-Seidel and SOR Method

 The code is following
 PROGRAM  ITVMET
      PARAMETER (N=3)
      INTEGER::I,J
      REAL::A(10,10),A1(10,10),A2(10,10),B(10),B1(10),B2(10)
      REAL::X0(10),X01(10),X02(10),TOL,W
      OPEN(1,'INPUT.DAT')
      OPEN(2,'OUTPUT.DAT')
      READ(1,*)((A(I,J),J=1,N),I=1,N)
      READ(1,*)(B(I),I=1,N)
      READ(1,*)(X0(I),I=1,N)
      READ(1,*)TOL,W
      DO I=1,N
      B1(I)=B(I)
      B2(I)=B(I)
      X01(I)=X0(I)
      X02(I)=X0(I)
      DO J=1,N
      A1(I,J)=A(I,J)
      A2(I,J)=A(I,J)
      END DO
      END DO
      CALL JM(A,B,X0,N,TOL)
      CALL GSM(A1,B1,X01,N,TOL)
      CALL SOR(A2,B2,X02,N,TOL,W)
      END PROGRAM

      SUBROUTINE JM(A,B,X0,N,TOL)
      REAL::A(10,10),B(10),X0(10),X(10),NORM,SUM1
      INTEGER::K=1
      WRITE (2,*)'RESULT FOR JACOBI METHOD'
  10  DO I=1,N
      SUM1=0.0
      DO J=1,N
      IF (J.NE.I) SUM1=SUM1+A(I,J)*X0(J)
      END DO
      X(I)=(B(I)-SUM1)/A(I,I)
      END DO
      WRITE (2,12)K,(X(I),I=1,N)
  12  FORMAT(2X,I3,3(2X,F9.6))
      K=K+1
      NORM=ABS(X(1)-X0(1))
      DO I=2,N
      IF (ABS(X(I)-X0(I)).GT.NORM) NORM=ABS(X(I)-X0(I))
      END DO
      IF (NORM.LT.TOL) GOTO 11
      DO I=1,N
      X0(I)=X(I)
      END DO
      GO TO 10
   11 END SUBROUTINE

      SUBROUTINE GSM(A1,B1,X01,N,TOL)
      REAL::A1(10,10),B1(10),X01(10),X(10),NORM,SUM1,SUM2
      INTEGER::K=1
      WRITE (2,*)'RESULT FOR GAUSS-SEIDEL METHOD'
  11  DO I=1,N
      SUM1=0.0
      SUM2=0.0
      DO J=1,N
      IF (J.LT.I) SUM1=SUM1+A1(I,J)*X(J)
      IF (J.GT.I) SUM2=SUM2+A1(I,J)*X01(J)
      END DO
      X(I)=(B1(I)-SUM1-SUM2)/A1(I,I)
      END DO
      WRITE (2,20)K,(X(I),I=1,N)
  20  FORMAT(2X,I3,3(2X,F9.6))
      K=K+1
      NORM=ABS(X(1)-X01(1))
      DO I=2,N
      IF (ABS(X(I)-X01(I)).GT.NORM) NORM=ABS(X(I)-X01(I))
      END DO
      IF (NORM.LT.TOL) GO TO 12
      DO I=1,N
      X01(I)=X(I)
      END DO
      GO TO 11
   12 END SUBROUTINE

      SUBROUTINE SOR(A2,B2,X02,N,TOL,W)
      REAL::A2(10,10),B2(10),X02(10),X(10),NORM,SUM1,SUM2,W
      INTEGER::K=1
      WRITE(2,*)'RESULT FOR SOR METHOD'
  13  DO I=1,N
      SUM1=0.0
      SUM2=0.0
      DO J=1,N
      IF (J.LT.I) SUM1=SUM1+A2(I,J)*X(J)
      IF (J.GT.I) SUM2=SUM2+A2(I,J)*X02(J)
      END DO
      X(I)=(1.0-W)*X02(I)+(W*(B2(I)-SUM1-SUM2))/A2(I,I)
      END DO
      WRITE(2,30)K,(X(I),I=1,N)
  30  FORMAT(2X,I3,3(2X,F9.6))
      K=K+1
      NORM=ABS(X(1)-X02(1))
      DO I=2,N
      IF(ABS(X(I)-X02(I)).GT.NORM) NORM=ABS(X(I)-X02(I))
      END DO
      IF (NORM.LT.TOL) GO TO 14
      DO I=1,N
      X02(I)=X(I)
      END DO
      GO TO 13
  14  END SUBROUTINE

For systems of higher numbers of unknowns, just change the number N in the PARAMETER field.
For any kind of problems, don't hesitate to contact me :)

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Fortran Program For Power Method

The FORTRAN code is following.     
       PROGRAM POWERMET
      PARAMETER (N=3)
      REAL::A(10,10),X(5)
      OPEN(1,'INPUT.DAT')
      OPEN(2,'OUTPUT.DAT')
      READ(1,*)((A(I,J),J=1,N),I=1,N)
      READ(1,*)(X(I),I=1,N)
      READ(1,*)TOL
      CALL POWER(A,X,N,TOL)
      CLOSE(1)
      CLOSE(2)
      END PROGRAM

      SUBROUTINE POWER(A,X,N,TOL)
      REAL::A(10,10),X(5),Y(5),Z(5),W(5),L1,L2
      K=0
      WRITE(2,11)
  11  FORMAT(10X,'ITE',16X,'EIGENVECTOR',20X,'EIGENVALUE')
      WRITE(2,*)K,(X(I),I=1,N)
  10  DO I=1,N
      W(I)=X(I)
      Y(I)=0
      DO J=1,N
      Y(I)=Y(I)+A(I,J)*X(J)
      END DO
      END DO
      K=K+1
      L1=ABS(Y(1))
      DO I=1,N
      IF(L1.LT.ABS(Y(I))) L1=ABS(Y(I))
     END DO
      DO I=1,N
      X(I)=Y(I)/L1
      Z(I)=X(I)-W(I)
      END DO
      WRITE(2,*)K,(X(I),I=1,N),L1
      WRITE(2,*)K,(X(I),I=1,N),L1
    WRITE(2,*)K,(X(I),I=1,N),L1
      L2=ABS(Z(1))
      DO I=1,N
      IF(L2.LT.ABS(Z(I))) L2=ABS(Z(I))
      END DO
      IF(L2.GT.TOL)  GO TO 10
      END SUBROUTINE

You need to input a 3X3 matrix, an initial approximation and desired tolerance level. To input a higher order matrix, change the PARAMETER value.

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Hellooooooooooooo

Hello friends :)
I made this blog for the students of the department of Mathematics of the University of Dhaka. Here I would try to provide stuffs for Mathematicians like books, assignments, FORTRAN codes and much more. But to take this blog further I need your help too. Please send me your mathematical stuffs and share with other students. No more today. Bye.

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