What this book covers

Chapter 1, Numerical Linear Algebra, presents an overview of the role of matrices to solve problems in scientific computing. It is a crucial chapter for understanding most of the processes and ideas of subsequent chapters. You will learn how to construct and store large matrices effectively in Python. We then proceed to reviewing basic manipulation and operations on them, followed by factorizations, solutions of matrix equations, and the computation of eigenvalues/eigenvectors.

Chapter 2, Interpolation and Approximation, develops advanced techniques to approximate functions, and their applications to scientific computing. This acts as a segway for the next two chapters.

Chapter 3, Differentiation and Integration, explores the different techniques to produce derivatives of functions and, more importantly, how to compute areas and volumes effectively by integration processes. This is the first of two chapters devoted to the core of numerical methods in scientific computing. This second part is also an introduction to Chapter 5, Initial Value Problems for Ordinary Differential Equations that mentions ordinary differential equations.

Chapter 4, Nonlinear Equations and Optimization, is a very technical chapter in which we discuss the best methods of obtaining the roots and extrema of systems of functions depending on the kinds of functions involved.

Chapter 5, Initial Value Problems for Ordinary Differential Equations, is the first of five chapters on applications to real-world problems. We show you, by example, the most popular techniques to solve systems of differential equations, as well as some applications.

Chapter 6, Computational Geometry, takes a tour of the most significant algorithms in this branch of computer science.

Chapter 7, Descriptive Statistics, is the first of two chapters on statistical computing and its applications to Data Analysis. In this chapter, we focus on probability and data exploration.

Chapter 8, Inference and Data Analysis, is the second chapter on Data Analysis. We focus on statistical inference, machine learning, and data mining.

Chapter 9, Mathematical Imaging, is the last chapter of this book. In it, we explore techniques for image compression, edition, restoration, and analysis.