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**About this book :- **
**Matrices in Engineering Problems ** written by
** Marvin J Tobias, Steven Krantz **.

This book is intended as an undergraduate text introducing matrix methods as they relate to engineering problems. It begins with the fundamentals of mathematics of matrices and determinants. Matrix inversion is discussed, with an introduction of the well known reduction methods. Equation sets are viewed as vector transformations, and the conditions of their solvability are explored. Orthogonal matrices are introduced with examples showing application to many problems requiring three dimensional thinking. The angular velocity matrix is shown to emerge from the differentiation of the 3-D orthogonal matrix, leading to the discussion of particle and rigid body dynamics. The book continues with the eigenvalue problem and its application to multi-variable vibrations. Because the eigenvalue problem requires some operations with polynomials, a separate discussion of these is given in an appendix. The example of the vibrating string is given with a comparison of the matrix analysis to the continuous solution. Table of Contents: Matrix Fundamentals / Determinants / Matrix Inversion / Linear Simultaneous Equation Sets / Orthogonal Transforms / Matrix Eigenvalue Analysis / Matrix Analysis of Vibrating Systems

(Marvin J Tobias, Steven Krantz)

**Book Detail :- **
** Title: ** Matrices in Engineering Problems
** Edition: **
** Author(s): ** Marvin J Tobias, Steven Krantz
** Publisher: ** Morgan
** Series: ** Synthesis Lectures on Mathematics and Statistics
** Year: ** 2011
** Pages: ** 141
** Type: ** PDF
** Language: ** English
** ISBN: ** 9781608456581,1608456587
** Country: ** US

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**About Author :- **

Author **Marvin J Tobias ** is graduated in Mechanical Engineering (ME) from the University of Utah.

He joined the General Electric Company and began a series of rotating assignments through various Departments in the East, initially in the General Engineering Laboratory, then in the Jet Engine Department. In the fall, Marv successfully applied for a three year intensive training program the Advanced Engineering Program. During the latter years of the program his assignments were in radar signal and data processing.

Assignments in both ME and EE proved the need for further education and training in mathematics, so the middle year (B course—applied mathematics) was particularly interesting. Over the years, Marv became a lecturer for the B course, developing many notes on matrix algebra and calculus. As the PC became more powerful, with sophisticated word processing and graphics software, those notes became the content of this book.

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**Book Contents :- **
**Matrices in Engineering Problems ** written by
** Marvin J Tobias, Steven Krantz **
cover the following topics.

1. Matrix Fundamentals

2. Determinants

3. Matrix Inversion

4. Linear Simultaneous Equation Sets

5. Orthogonal Transforms

6. Matrix Eigenvalue Analysis

7. Matrix Analysis of Vibrating Systems

A Partial Differentiation of Bilinear and Quadratic Forms

B Polynomials

C The Vibrating String

D Solar Energy Geometry

E Answers to Selected Exercises

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**WORKSHEETS (Solved):- **

**SHORTCUT TRICKS (Division):- **

- Divisible by 2 Shortcut trick
- Divisible by 3 Shortcut trick
- Divisible by 4 Shortcut trick
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- Divisible by 6 Shortcut trick
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- Divisible by 9 Shortcut trick
- Divisible by 10 Shortcut trick

**SHORTCUT TRICKS (Prime Number):- **

- Find the prime number from 1 to 100 just in 5 second (MATH PRIME NUMBER SHORTCUT TRICK from 1 to 100 number) ?
- Find a large number "A" is prime number or not (MATH PRIME NUMBER SHORTCUT TRICK By using Square Root method) ?
- Find the composite number from 1 to 100 just in 5 second (MATH COMPOSITE NUMBER SHORTCUT TRICK from 1 to 100 number) ?