by Henrik Aratyn (University of Illinois at Chicago, USA) & Constantin Rasinariu (Columbia College Chicago, USA)

Table of Contents (74k)
Preface (63k)
Chapter 1: Vectors and Vector Calculus (4,029k)

This unique book provides a streamlined, self-contained and modern text for a one-semester mathematical methods course with an emphasis on concepts important from the application point of view. Part I of this book follows the “paper and pencil” presentation of mathematical methods that emphasizes fundamental understanding and geometrical intuition. In addition to a complete list of standard subjects, it introduces important, contemporary topics like nonlinear differential equations, chaos and solitons. Part II employs the Maple software to cover the same topics as in Part I in a computer oriented approach to instruction. Using Maple liberates students from laborious tasks while helping them to concentrate entirely on concepts and on better visualizing the mathematical content. The focus of the text is on key ideas and basic technical and geometric insights presented in a way that closely reflects how physicists and engineers actually think about mathematics.

• Mathematical Methods:
  • Vectors and Vector Calculus
  • Matrices and Rotations
  • Differential Equations
  • Series Solutions of Differential Equations
  • Special Functions and the Generalized Fourier Series
  • Linear Systems of Differential Equations
  • Nonlinear Differential Equations
• Maple:
  • Vectors and Vector Calculus
  • Matrices and Rotations
  • Differential Equations
  • Power Series Solutions of Differential Equations
  • Special Functions and Generalized Fourier Series
  • Linear Systems of Differential Equations
  • Nonlinear Differential Equations