Preface

It was a giant leap for academia when Stephen Wolfram, a theoretical physicist, thought of creating software that links computational science with mathematics. From time immemorial, philosophers have tried to explicate the relationship between mathematics and physics. From them, we have understood well that if mathematics is an essential tool for physics, then physics is a rich source of inspiration and insight for mathematics. Throughout our career in research and teaching, we have realized this truth. Mathematica is the most befitting proof of this fact. Today, it has over three million users around the globe, and hundreds of books have already been written on it. There are also several periodicals that are devoted exclusively to Mathematica. The Wolfram Research Foundation, which owns the Mathematica website,1 contains thousands of pages of material and is being constantly updated. Mathematica can be used by everyone, from a high school student to a researcher in mathematics. Mathematica is a symbolic mathematical computation program, sometimes called a computer algebra program, used extensively by scientists and engineers in academic and research institutes. The visualizations and graphical capabilities of Mathematica make it very useful for plotting all kinds of data and functions. Mathematica has a very good system for documentation with all its built-in functions. Mathematica is good at handling numerical work, and it is a perfect programming system where symbolic manipulation is easy.

When we started writing this book, what we had in our minds was to equip the students at master's level and researchers from a science and engineering backgrounds with the necessary mathematical techniques. We have remained faithful to our original intention. While doing so we have taken note of the needs of the beginners too. The book has been developed from our lecture notes and research work, which has been continuously modified and improved over the years while interacting with the students and having discussions with researchers. It bridges the gap between the elementary books written on Mathematica and the reference books written for advanced users. The book makes an attempt to present a wide variety of topics in mathematics with an emphasis on application in divergent areas. Throughout the book, the examples follow the introduction of the new commands. More than 400 problems have been worked out in the book, which helps the student understand the crux of the topic under consideration. A large number of problems on matrices, the Laplace and Fourier transformations, the Dirac Delta function, and quantum mechanics worked out here are tested and appreciated by students in the classroom. Most of these are exercises in standard textbooks on physics, mathematics, and engineering that demonstrate standard theorems and are absolutely essential for understanding the subjects. These have been illustrated with suitable figures too. The book has a variety of illustrated examples chosen meticulously from different fields. It gives an introduction to matrices, a detailed account of special matrices, linear equations, the eigenvalue problem, and bilinear and quadratic forms. The approach of this book is pedagogical where both teaching and learning dimensions have been taken care of. The best way to use the book is to replicate the examples worked out in the book, try to make modifications, and investigate the results. We would like to mention here that a user of any version of Mathematica would be comfortable utilizing this work.

The book is spread out into 17 chapters. Chapter 1 gives a general account and information about Mathematica, and Chapter 2 gives several commands to perform algebraic and trigonometric manipulations. Chapter 3 gives a good account of constructing and extracting the elements of the table. Chapters 4-6 are devoted to graphics. Chapter 7 gives the method to construct matrices and works out examples to illustrate the elementary properties of the matrices. Chapter 8 is devoted to solving algebraic and transcendental equations. Chapter 9 introduces the eigenvalue and vectors of a matrix and elaborates the matrix diagonalization. Chapter 10 gives the applications of Mathematica in differential calculus, whereas Chapter 11 deals with integral calculus. Chapter 12 is on the Dirac delta function where the properties and the limiting forms of the delta function have been plotted and discussed. Chapter 13 discusses the various properties of the Fourier transforms and their applications. Chapter 14 deals with Laplace transforms and the techniques to solve the differential equations using the Laplace transforms. Chapters 15 and 16 deal with vectors and linear vector spaces, respectively, which are vital for a proper understanding of quantum mechanics. Chapter 17 gives a brief account of the applications of Mathematica in quantum mechanics.

It is our bounden duty to remember here many to whom we are indebted for this work. We are thankful to Prof. Fionn Murtagh (professor of data science and director at the Centre for Mathematics and Data Science, University of Huddersfield), Prof. K. S. Mallesh (professor of physics, Regional Institute of Education, Mysore), and Prof. M. V. Satyanarayana (professor of physics, IIT Chennai) for going through the entire manuscript and giving useful suggestions that increased the readability of the book. We thank Prof. B. A. Kagali (retired professor, Bangalore University), Prof. J. S. Bhat (director, IIIT Surat), Prof. P. Paulose (professor of physics, IIT Guwahati), Prof. Kamal Kanti Nandi (director, Zeldovich International Centre for Astrophysics, Moscow), Prof. Shashank Bhatnagar (Department of Physics, University Institute of Science, Chandigarh University), Prof. Jayanta Kumar Sarma (professor of physics, Tezpur University, Assam), Dr. J. N. Pandya (assistant professor of applied physics, Maharaja Sayajirao University of Baroda), Prof. Anindya Sarkar (Department of Geology and Geophysics, Indian Institute of Technology, Kharagpur), Prof. Jithesh R. Bhatt, Prof. Janardhan Padmanabhan, Prof. A. S. Joshipura (Physical Research Laboratory, Ahmedabad) for their support to this work. We also thank all the authors and their publishers for allowing us to use many diagrams from their published books. We remember particularly here Prof. Ajoy Ghatak (retired professor, IIT, Delhi) for encouraging us.

KBV expresses his gratitude to Dr. Stephane Pepin (Federal Agency for Nuclear Control, Health and Environment Department, Brussels, Belgium) for the help he rendered in his research. KBV acknowledges Prof. Michael Birse and Dr. Judith McGovern (Department of Physics and Astronomy, University of Manchester) for introducing Mathematica to solve certain problems in high-energy physics, when he was a Commonwealth fellow at the University of Manchester from 1998 to 1999. KBV wishes to express his deep gratitude to Shri Vinaya Hegde, President, Nitte Education Trust & Chancellor, Nitte (Deemed to be University), the president of the Nitte Education Trust, Shri Vishal Hegde, Pro-Chancellor, Nitte, deemed-to-be university, and Dr. Satheesh Bhandary, Vice-Chancellor, Nitte, deemed-to-be university, for having provided an opportunity to work in NMAMIT, Nitte. KBV is grateful to Prof. Niranjan N. Chiplunkar (principal, NMAMIT, Nitte, Karkala) for his interest in the Mathematica book and for his constant encouragement, which accelerated the progress of the book. KBV is thankful to Mr. A. Yogeesh Hegde, Director (CM&D), Nitte Campus, Nitte, deemed-to-be university, for providing logistical support, the management and faculty members of NMAMIT for providing an excellent environment for completing the book, and to Mangalore University for providing a conducive environment for writing the manuscript. Most of the book was written while KBV was working at Mangalore University. KBV is grateful to his family members for their constant moral support, and he is particularly thankful to his wife, Dr. Veena Devi V. Shastrimath, and his son, Mr. K. V. Adithya for their constant encouragement and support in preparing the manuscript. KBV expresses his gratitude to all his PhD students for their collaboration in research.

APM is deeply indebted to the Most Rev. P. P. Saldanha (bishop, Diocese of Mangalore), Rev. Ronald Dsouza (manager, Codialbail Press), Rev. Lawrence Mascarenhas (correspondent, St. Philomena College, Puttur), Leo Noronha (former principal, St. Philomena College), Dr. A. P. Radhakrishna (Head, Department of Physics, St. Philomena College, Puttur), Dr. Praveen P. D Souza (assistant professor of physics, St. Philomena College, Puttur), Mr. Vinay D. R., and Mr. Sujith S. for their inspiration, support, and insights in preparing the manuscript. We are thankful to Mr. Vipin Naik N. S. (assistant professor of physics, St. Philomena College, Puttur) for going through the manuscript critically.

We are also greatly thankful to Vision Group on Science and Technology (VGST), Department of IT, BT, and S&T, Government of Karnataka for funding our research projects and through which we availed Mathematica software.

We gratefully acknowledge Wiley-VCH GmbH for accepting to publish our book. We would like to express our gratitude to Dr. Martin Preuss, Associate Publisher, for his support and encouragement throughout the process. We are thankful to Ms. Farhath Fathima, content refinement specialist, Wiley-VCH, for doing the significant job of proofreading very efficiently.

It is our hope that this book exposes...