INTRODUCTION TO SCIENTIFIC COMPUTATION

This book introduces scientific computation in an accessible and interactive way for undergraduates, especially those in the sciences, engineering, and mathematics. No prior programming experience is expected. Readers can begin directly from the introductory chapters, which cover basic elements of the Python programming language, then progress to the main chapters where techniques of scientific computation are presented and applied to specific problems. Examples and exercises are included in detail, covering diverse topics from various branches of science. These include cellular automata, the driven damped pendulum, Euler–Bernoulli beam theory, Newton's law of cooling, and many others.

Rather than using established routines as a black box to memorize, this book delves into foundational concepts and encourages readers to apply fundamental principles to hands-on problems. Extensive use of scientific Python libraries and Jupyter Notebooks reinforce the student's understanding. This book is well-suited for a first exposure to scientific computation, but also to bridge introductory programming classes with advanced coursework in scientific modeling.

Contents:

• Getting Started
• Python Basics
• Control Structures
• Libraries, Arrays, and Plots
• Indexing Lists and Arrays
• Data Types and Variable Assignment
• Functions and More Loops
• Random Topics
• Programming Practice
• Symbolic Computation with SymPy
• Root Finding
• Curve Fitting and Interpolation
• Numerical Integration I
• Numerical Integration II
• Linear Algebra
• Numerical Differentiation
• Ordinary Differential Equations I
• Ordinary Differential Equations II
• Driven Damped Pendulum and Chaos
• Boundary Value Problems
• Partial Differential Equations I
• Partial Differential Equations II
• Fourier Analysis

Readership: First-year and second-year undergraduates in physics, engineering and mathematics.