Python programming and numerical methods : a guide for engineers and scientists

Python Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the goal of helping the students to develop good computational problem-solving techniques through the use of numerical methods and the Python programming language. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level that allows students to quickly apply results in practical settings. Includes tips, warnings and "try this" features within each chapter to help the reader develop good programming practice Summaries at the end of each chapter allow for quick access to important information Includes code in Jupyter notebook format that can be directly run online Contents Figures Preface PURPOSE PREREQUISITES ORGANIZATION HOW TO READ THIS BOOK? WHY PYTHON? PYTHON AND PACKAGE VERSIONS PYTHON BASICS GETTING STARTED WITH PYTHON PYTHON AS A CALCULATOR MANAGING PACKAGES INTRODUCTION TO JUPYTER NOTEBOOK LOGICAL EXPRESSIONS AND OPERATORS SUMMARY AND PROBLEMS VARIABLES & BASIC DATA STRUCTURES CONTENTS VARIABLES AND ASSIGNMENT DATA STRUCTURE – STRING DATA STRUCTURE – LIST DATA STRUCTURE – TUPLE DATA STRUCTURE – SET DATA STRUCTURE – DICTIONARY INTRODUCING ARRAYS SUMMARY AND PROBLEMS FUNCTIONS CONTENTS FUNCTION BASICS LOCAL VARIABLES AND GLOBAL VARIABLES NESTED FUNCTIONS LAMBDA FUNCTIONS FUNCTIONS AS ARGUMENTS TO FUNCTIONS SUMMARY AND PROBLEMS BRANCHING STATEMENTS CONTENTS IF-ELSE STATEMENTS TERNARY OPERATORS SUMMARY AND PROBLEMS ITERATION CONTENTS FOR-LOOPS WHILE LOOPS COMPREHENSIONS SUMMARY AND PROBLEMS RECURSION CONTENTS RECURSIVE FUNCTIONS DIVIDE-AND-CONQUER SUMMARY AND PROBLEMS OOP CONTENTS INTRODUCTION TO OOP CLASS AND OBJECT INHERITANCE, ENCAPSULATION, AND POLYMORPHISM SUMMARY AND PROBLEMS COMPLEXITY CONTENTS COMPLEXITY AND BIG-O NOTATION COMPLEXITY MATTERS THE PROFILER SUMMARY AND PROBLEMS REPRESENTATION of NUMBERS CONTENTS BASE-N AND BINARY FLOATING POINT NUMBERS ROUND-OFF ERRORS SUMMARY AND PROBLEMS ERRORS, GOOD PROGRAMMING PRACTICES & DEBUGGING CONTENTS ERROR TYPES AVOIDING ERRORS TRY/EXCEPT TYPE CHECKING DEBUGGING SUMMARY AND PROBLEMS READING & WRITING DATA CONTENTS TXT FILES CSV FILES PICKLE FILES JSON FILES HDF5 FILES SUMMARY AND PROBLEMS VISUALIZATION & PLOTTING CONTENTS D PLOTTING WORKING WITH MAPS ANIMATIONS AND MOVIES SUMMARY AND PROBLEMS PARALLELIZE PYTHON CONTENTS PARALLEL COMPUTING BASICS MULTIPROCESSING USING JOBLIB SUMMARY AND PROBLEMS LINEAR ALGEBRA & SYSTEMS OF LINEAR EQUATIONS CONTENTS BASICS OF LINEAR ALGEBRA LINEAR TRANSFORMATIONS SYSTEMS OF LINEAR EQUATIONS SOLUTIONS TO SYSTEMS OF LINEAR EQUATIONS SOLVING SYSTEMS OF LINEAR EQUATIONS IN PYTHON MATRIX INVERSION SUMMARY AND PROBLEMS EIGENVALUES & EIGENVECTORS CONTENTS EIGENVALUES AND EIGENVECTORS PROBLEM STATEMENT THE POWER METHOD THE QR METHOD EIGENVALUES AND EIGENVECTORS IN PYTHON SUMMARY AND PROBLEMS LEAST SQUARES REGRESSION CONTENTS LEAST SQUARES REGRESSION PROBLEM STATEMENT LEAST SQUARES REGRESSION DERIVATION (LINEAR ALGEBRA) LEAST SQUARES REGRESSION DERIVATION (MULTIVARIATE CALCULUS) LEAST SQUARES REGRESSION IN PYTHON LEAST SQUARES REGRESSION FOR NONLINEAR FUNCTIONS SUMMARY AND PROBLEMS INTERPOLATION CONTENTS INTERPOLATION PROBLEM STATEMENT LINEAR INTERPOLATION CUBIC SPLINE INTERPOLATION LAGRANGE POLYNOMIAL INTERPOLATION NEWTON’S POLYNOMIAL INTERPOLATION SUMMARY AND PROBLEMS TAYLOR SERIES CONTENTS EXPRESSING FUNCTIONS USING A TAYLOR SERIES APPROXIMATIONS USING TAYLOR SERIES DISCUSSION ABOUT ERRORS SUMMARY AND PROBLEMS ROOT FINDING CONTENTS ROOT FINDING PROBLEM STATEMENT TOLERANCE BISECTION METHOD NEWTON–RAPHSON METHOD ROOT FINDING IN PYTHON SUMMARY AND PROBLEMS NUMERICAL DIFFERENTIATION CONTENTS NUMERICAL DIFFERENTIATION PROBLEM STATEMENT USING FINITE DIFFERENCE TO APPROXIMATE DERIVATIVES APPROXIMATING OF HIGHER ORDER DERIVATIVES NUMERICAL DIFFERENTIATION WITH NOISE SUMMARY AND PROBLEMS NUMERICAL INTEGRATION CONTENTS NUMERICAL INTEGRATION PROBLEM STATEMENT RIEMANN INTEGRAL TRAPEZOID RULE SIMPSON’S RULE COMPUTING INTEGRALS IN PYTHON SUMMARY AND PROBLEMS ODEs INITIAL-VALUE PROBLEMS CONTENTS ODE INITIAL VALUE PROBLEM STATEMENT REDUCTION OF ORDER THE EULER METHOD NUMERICAL ERROR AND INSTABILITY PREDICTOR–CORRECTOR AND RUNGE–KUTTA METHODS PYTHON ODE SOLVERS ADVANCED TOPICS SUMMARY AND PROBLEMS BOUNDARY-VALUE PROBLEMS for ODEs CONTENTS ODE BOUNDARY VALUE PROBLEM STATEMENT THE SHOOTING METHOD THE FINITE DIFFERENCE METHOD NUMERICAL ERROR AND INSTABILITY SUMMARY AND PROBLEMS FOURIER TRANSFORM CONTENTS THE BASICS OF WAVES DISCRETE FOURIER TRANSFORM (DFT) FAST FOURIER TRANSFORM (FFT) FFT IN PYTHON SUMMARY AND PROBLEMS Python in Windows A.1 GETTING STARTED WITH PYTHON IN WINDOWS Index "Python Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the goal of helping the students to develop good computational problem-solving techniques through the use of numerical methods and the Python programming language. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level that allows students to quickly apply results in practical settings." --From publisher's description