An Invitation to Mathematical Physics and Its History

1. Front Matter

   Pages i-xix

   PDF

2. Introduction

   • Jont Allen

   Pages 1-17

3. Stream 1: Number Systems

   • Jont Allen

   Pages 19-68

4. Algebraic Equations: Stream 2

   • Jont Allen

   Pages 69-176

5. Stream 3A: Scalar Calculus

   • Jont Allen

   Pages 177-226

6. Stream 3B: Vector Calculus

   • Jont Allen

   Pages 227-290

7. Back Matter

   Pages 291-379

   PDF

This state of the art book takes an applications based approach to teaching mathematics to engineering and applied sciences students. The book lays emphasis on associating mathematical concepts with their physical counterparts, training students of engineering in mathematics to help them learn how things work. The book covers the concepts of number systems, algebra equations and calculus through discussions on mathematics and physics, discussing their intertwined history in a chronological order. The book includes examples, homework problems, and exercises.  This book can be used to teach a first course in engineering mathematics or as a refresher on basic mathematical physics. Besides serving as core textbook, this book will also appeal to undergraduate students with cross-disciplinary interests as a supplementary text or reader.

• Algebraic Equations
• Scalar and Vector Calculus
• Number Systems
• Eigenanalysis
• Group Theory
• Hypercomplex Numbers
• Non-Euclidean Geometry
• Combinatronics

• Electrical & Computer Engineering, University of Illinois at Urbana Champaign, Urbana, USA

  Jont Allen

Jont Allen is a Professor in the Department of Electrical and Computer Engineering, University of Illinois. After completing his Ph.D. from the University of Pennsylvania, Philadelphia in 1970, he went to Bell Labs, where he enjoyed a 32 year AT&T Bell Labs career. At AT&T Allen specialized in nonlinear cochlear modeling, auditory and cochlear speech processing, and speech perception. Since joining University of Illinois in 2003, he has taught and worked with his students on the theory and practice of human speech recognition, for both normal and hearing impaired hearing as well as reading disabilities in young children. Prof Allen has more than 20 US patents on hearing aids, signal processing and middle ear measurement diagnostics.  

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