Welcome to Vibrationdata
Mathematics & Numerical Analysis Page

 Tutorials



Table of Laplace Transforms:  Laplace.pdf  

Partial Fractions in Shock and Vibration Analysis: partial.pdf
Complex Functions and Trigonometric Identities: trig.pdf
This tutorial also derives formulas for the natural logarithm, square root, and cube root of a complex number.
Integration of the Normal Distribution Curve: int_pdf.pdf
Roots of a Cubic Polynomial: cubic.pdf

Newton-Raphson Method Applied to Vibration Problems: Newrap.pdf

The Cosine Integral: cosine_integral.pdf

Solution of the Terminal Velocity Ordinary Differential Equation: terminal_velocity_ode.pdf

EIGENVALUE PROBLEM
The Generalized Eigenvalue Problem:  eigen.pdf  


Dr. Edward L. Wilson, The Eigenvalue Problem (Berkeley Link )

 Mathematics Software

 Executable

 Source

Solution of a set of linear equations of the form Ax=b, using Gaussian elimination.
 linear.exe

 _
 Inverse of a Real Matrix
 inverse.exe
 inv_con.cpp
 Inverse of a Complex Matrix
 inv_comp.exe
 inv_comp.cpp
 Newton-Raphson Method
 nr.exe

  _
Prime Number Generation:
 prime.exe
prime.cpp
 Integer factorization:
 factor.exe
 factor.cpp
Greatest Common Factor (GCF) of two integers
 gcf.exe
 gcf.cpp
Least Common Multiple (LCM) of two integers
 lcm.exe
 lcm.cpp
Factorial of a number, including non-integers.
 factorial.exe
 factorial.cpp
Gamma function of a rational number. 
 gamma.exe
 gamma.cpp
Engineering Math Calculator:

1. Vectors
2. Complex Numbers
3. Roots of quadratic, cubic, and quartic polynomials
 EngMath.exe

 _
Fraction Calculator
fraction.exe
_
Evaluation of the Cosine Integral.
S (1/x)cos(x)dx
cosine_integral.exe
cosine_integral.cpp


 Laplace Transform Books

Schaum's Outline of Laplace Transforms

The Laplace Transform : Theory and Applications (Undergraduate Texts in Mathematics)

 Other Mathematics Books

3000 Solved Problems in Calculus (Schaum's Solved Problems Series)
Jan Tuma, Engineering Mathematics Handbook
The Fast Fourier Transform and its Applications

Statistics Explained

William Press, et al, Numerical Recipes The Art of Scientific Computing

Frank Bowman, Introduction to Bessel Functions

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Please send comments and questions to Tom Irvine at: tomirvine@aol.com