Mathematical Methods For Digital Computers

This advanced undergraduate textbook presents a new approach to teaching mathematical methods for scientists and engineers. It provides a practical, pedagogical introduction to utilizing Python in Mathematical and Computational Methods courses. Both analytical and computational examples are integrated from its start. Each chapter concludes with a set of problems designed to help students hone their skills in mathematical techniques, computer programming, and numerical analysis. The book places less emphasis on mathematical proofs, and more emphasis on how to use computers for both symbolic and numerical calculations. It contains 182 extensively documented coding examples, based on topics that students will encounter in their advanced courses in Mechanics, Electronics, Optics, Electromagnetism, Quantum Mechanics etc.

Manufacturing computers in series was quite a feat in the 1950s. As mathematical as it gets, the machines discussed here were called X1 and X8.

In this age of omnipresent digital computers and their capacity for implementing numerical methods, no applied mathematician, physical scientist, or engineer can be considered properly trained without some understanding of those methods.

As our society grows ever more reliant on computers, so it also becomes more vulnerable to computer crime. Cyber attacks have been plaguing computer users since the 1980s, and computer security experts are predicting that smart telephones and other mobile devices will also become the targets of cyber security threats in the future.

In the period following World War II, it began to be recognized that there were a large number of interesting and significant activities which could be classified as multistage decision processes. It was soon seen that the mathematical problems that arose in their study stretched the conventional confines of analysis, and required new methods for their successful treatment.