Download this PDF book: Numerical Methods with Python: for the Sciences (de Gruyter Textbook) by William Miles
Introduces students to appropriate use of computer programming within the scientific disciplines using Python. Discusses several common applications of programming and implementation using real world examples and hands on programming exercises.
Students learn how to model situations such as image recognition, medical diagnosis, spread of disease, and others.
The text could be used by students and lecturers for courses in Python, Numerical Methods, or as a first course in Data Science.
Introduction After years of mentoring undergraduate student research projects, it is clear that the most popular projects are applied in nature. It is also true that most “real-world” problems can not be solved explicitly.
That is, we cannot find a nice, neat formula to solve the problem. Because of this, we must use numerical techniques to determine a close approximation to the solution of the problem of interest.
These techniques often require us to repeat a process hundreds or thousands of times in order for the approximation to be “close enough” to the actual solution or for the approximation to evolve for the desired length of time.
In addition to such repeated processes, we also frequently need to handle large amounts of data or manipulate large matrices in order to arrive at a solution.
To solve the types of problems that arise in math and science, we frequently need to develop and implement an algorithm. An algorithm is the definition of a process that is to be used in solving a problem. Generally, algorithms are presented as a list of steps to be followed in order to arrive at a solution.
In this book, we introduce some of the fundamental ideas and methods that are used to solve scientific problems. Some of the most frequently occurring challenges include:
– the need to locate the extreme values of a function;
– the need to solve large linear systems;
– the need to solve differential equations (or systems of differential equations);
– the need to draw conclusions about a population based on a sample (inferential statistics);
– the need to find the “best” linear model for a set of data (linear regression); and
– the need to classify objects (logistic regression and neural networks).
Furthermore, from a mathematical standpoint, we need to be able to analyze functions, e. g.:
– graph a function;
– find and graph the derivative of a function;
– compute the definite integral of a function. This text addresses all of these issues to some degree.
The book is intended for math and science students who have had a semester of calculus. We will approach topics from an introductory level.
Because of this, we will have to exclude much of the rich theory that is available in the study of numerical methods. Our goal is to introduce students to the types of methods that are available and the basic ideas that motivate these methods.
In general, there are more advanced (and more efficient) methods available than the ones we cover. However, we seek to teach the student “how” to approach a problem within the context of computing. If a student wishes to pursue a topic more deeply, we reference avenues for such further study
About the book:
Publisher : De Gruyter (June 6, 2023)
Language : English
Pages : 190
File : PDF, 14MB
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