Science and Nature

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Core Python Codes for Numerical Applications

A Hands-On Practical Approach to Numerical Methods and Programming for Engineers and ScientistsBy Ana Lucia Ferreiro

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Length13h 13m

About this audiobook

You do not really understand a numerical method until you have watched yours diverge. This book has you write each algorithm yourself in clear Python, measure its error, then compare it with the library routine you will use at work. You will implement bisection and Newton-Raphson and see their convergence orders in a table, factorise matrices with pivoting and learn what a condition number costs you, fit and interpolate data without falling into the Runge trap, integrate with Simpson, Romberg and Gauss quadrature, and solve initial value, boundary value and partial differential problems including stiff systems. Closing case studies cover heat exchangers, beam deflection, reaction kinetics and circuit transients. For engineers, scientists and students who want working code and honest error analysis together. What you will learn: • Implement bisection, Newton-Raphson and other root-finding methods, and verify their convergence orders • Solve systems of linear equations with pivoting and understand the impact of condition numbers • Apply iterative solvers and eigenvalue algorithms for large-scale problems • Fit and interpolate data using regression, splines and polynomial interpolation without Runge oscillations • Differentiate and integrate numerically with finite differences, Simpson, Romberg and Gauss quadrature • Solve initial value problems, including stiff systems, with explicit and implicit methods • Tackle boundary value and partial differential problems using finite differences • Optimise functions and apply numerical methods to engineering case studies This book is for engineers, scientists and students who want to write their own numerical code, understand the errors involved, and compare their implementations with standard library routines. Whether you are a practising professional or a student, you will gain practical skills to solve real-world problems with confidence.

Audiobook details

GenreScience and Nature, Technology

Length13 hrs 13 mins

Narrated byListen with 1,000+ voices

FormateBook with Audio

Publish dateSep 27, 2026

LanguageEnglish

1Core Python Codes for Numerical Applications

2Foreword

3Preface

4About This Book

5Chapter 1: Python for Computation

Show all chapters

61.1 Why Scripts Beat Spreadsheets

71.2 Numbers, Text and Truth Values

81.3 Control Flow: Branching and Loops

91.4 Functions, Arguments and Scope

101.5 Modules, Imports and Project Layout

111.6 Formatting, Files and Reproducible Runs

12Chapter 2: NumPy Arrays and Vectorisation

132.1 Creating and Inspecting Arrays

142.2 Elementwise Operations and Universal Functions

152.3 Broadcasting and Reshaping

162.4 Reductions, Sorting and Selection

172.5 Memory Layout and Timing

18Chapter 3: Floating-Point Arithmetic and Error

193.1 How Floating-Point Numbers Are Stored

203.2 Round-Off and Truncation Error

213.3 Error Propagation and Catastrophic Cancellation

223.4 Conditioning of a Problem

233.5 Stability and Summation Strategies

24Chapter 4: Roots of Equations

254.1 Bracketing and the Bisection Method

264.2 Fixed-Point Iteration

274.3 Newton-Raphson and the Secant Method

284.4 Measuring Convergence Order Empirically

29Chapter 5: Systems of Linear Equations

305.1 Gauss Elimination with Partial Pivoting

315.2 LU and Cholesky Factorisation

325.3 Tridiagonal and Banded Systems

335.4 Condition Number and Error Bounds

34Chapter 6: Iterative Solvers and Eigenvalues

356.1 Jacobi and Gauss-Seidel Iteration

366.2 Successive Over-Relaxation

376.3 The Power Method and Inverse Iteration

386.4 QR Iteration and the Library Route

39Chapter 7: Curve Fitting and Regression

407.1 Least Squares and the Normal Equations

417.2 Polynomial Regression and Basis Choice

427.3 Nonlinear Regression and Linearisation

437.4 Residual Diagnostics and Goodness of Fit

44Chapter 8: Interpolation and Splines

458.1 Lagrange and Newton Divided-Difference Interpolation

468.2 The Runge Phenomenon and Node Placement

478.3 Cubic Splines

48Chapter 9: Numerical Differentiation

499.1 Finite-Difference Formulas and Truncation Error

509.2 The Step-Size Trade-Off

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