Thursday, September 6, 2012

Supplements on Linear Algebra for the Essentials of Mathematical Methods in Science and Engineering (2008)

Supplements of the Essentials of Mathematical Methods in Science and Engineering (2008) concentrates on the needs of engineering and applied science students

The file named SUPPLEMENTS has three parts:
Part I: We discuss  m x n systems; row echelon forms; row, column and null spaces; rank and nullity; linear independence and basis vectors; linear transformations and their representations; etc.
Part II: We introduce numerical methods of linear algebra, where partial pivoting; LU- factorization; interpolation and numerical methods of finding solutions are among the interesting topics discussed.    
Part III: We give an interesting application of linear algebra from chemistry and chemical engineering, where we show how to find a set of independent chemical reactions and introduce the stoichiometric matrix.

The file named BAYIN(2008)-mathlab-files-JULY11-2010 has some matlab codes, where after a review of the basic commands,  we continue with matlab applications of the numerical methods of linear algebra. These codes were used in the lab section of a one semester sophomore math course for engineers that met four hours a week. Students had little or no prior experience with matlab.

Saturday, November 13, 2010

Supplements of Mathematical Methods in Science and Engineering

Supplements of the Mathematical Methods in Science and Engineering (2006) consists of solutions and hints to selected problems, some of which are from the book. You can also find extensive sections devoted to additional features of the methods introduced in the book:
Chapter 10:
  • Cartesian tensors and the theory of elasticity
  • Curvature
  • Interpretation of the metric tensor
Chapter 13:
  • Integral representation of Bessel functions
Chapter 14:
  • Caputo derivative
  • Riesz derivative
Chapter 15:
  • Method of steepest descent
  • Pade approximants
Chapter 16:
  • Discrete Fourier transforms
  • Fast Fourier transforms
Chapter 17:
  • Optimum control theory
Chapter 19:
  • Perturbation theory
Chapter 20:
  • Anomalous diffusion
  • Path integrals over Levy paths.

Thursday, October 7, 2010

Supplements of my books

Supplements of my books entitled Mathematical Methods in Science and Engineering (2006) and Essentials of Mathematical Methods in Science and Engineering (2008) are available to everybody. Their most up to date versions can be found in my website .

In the companion site for our book, Mathematical Methods in Science and Engineering  2006, we present solutions or hints to selected problems. These problems are not always chosen from the book. When they are directly taken from the book, or when they are related to a problem in the book, the corresponding problem number is given. Each problem is stated completely so that the interested reader can attempt to reach the solution before consulting the answers or the hints. It is assumed that the reader is familiar with the contents of the corresponding chapter in the book. Rather than presenting the complete solutions, we usually prefer to discuss the method and guide the reader through the crucial intermediate steps. In this regard, even with the help given, these problems remain challenging exercises, which can generally be assigned by instructors in the given format.