Introduction to Engineering and Scientific Computing with Python

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
List of Examples
Preface
Acknowledgments
Authors
Chapter 1 Engineering and Scientific Calculations
	Chapter Objectives
	1.1 Numerical Quantities
		1.1.1 Positional and Scientific Notation
		1.1.2 Accuracy and Precision
		1.1.3 Significant Figures
		1.1.4 Rounding
	1.2 Mathematical Functions
		1.2.1 Absolute Value and Sign Functions
		1.2.2 Exponents and Logarithms
		1.2.3 Trigonometric Functions
		1.2.4 Hyperbolic Functions
	1.3 Complex Numbers
	1.4 Engineering Units
	1.5 Organizing and Planning Solutions to Problems
	Problems
Chapter 2 Computer-Based Calculations
	Chapter Objectives
	2.1 Numerical Quantities as Stored in the Computer
		2.1.1 Integer Numbers
		2.1.2 Real Numbers
	2.2 How the Computer Stores Text
	2.3 Boolean True/False Information
	2.4 Computer Storage Evolution and Terminology
	Problems
Chapter 3 Python Basics
	Chapter Objectives
	3.1 The Spyder/IPython Environment
	3.2 Mathematical Functions
	3.3 Variables and Assignment
	3.4 Objects, Attributes, Methods, and Data Types
		3.4.1 Boolean Type
		3.4.2 Character Type
	3.5 Collections of Data
	3.6 Creating Plots
	3.7 The Spyder Editor
	3.8 Input and Output
		3.8.1 Console Input and Output
		3.8.2 File Input and Output
		3.8.3 Formatting Output
	3.9 Obtaining Help
	Problems
Chapter 4 Structured Programming with Python
	Chapter Objectives
	4.1 An Overview of Program Structure
	4.2 Implementing Decision Structures with Python
	4.3 Implementing Repetition Structures with Python
		4.3.1 The General Loop Structure
		4.3.2 The List-Driven and Count-Controlled Loop Structures
		4.3.3 The break and Continue Statements with the for Loop
	4.4 User-Defined Functions in Python
		4.4.1 lambda Functions
		4.4.2 Function Arguments
		4.4.3 Variable Scope
	Problems
Chapter 5 Graphics—Matplotlib
	Chapter Objectives
	5.1 Introduction to Matplotlib
	5.2 Customizing Line and Scatter Plots
	5.3 Using Figure Window Objects
	5.4 Creating Bar Plots Including Histograms
	5.5 Creating Other Plots of Interest
	5.6 Contour and Surface Plots
	Problems
Chapter 6 Array and Matrix Operations
	Chapter Objectives
	6.1 Creating Arrays in Python
		6.1.1 Creating Special Arrays
		6.1.2 Combining, Stacking, and Splitting Arrays
		6.1.3 Reshaping Arrays
	6.2 Indexing: Array Subscripts
	6.3 Array Operations
	6.4 Vector/Matrix Operations
		6.4.1 Matrix/Vector Multiplication
		6.4.2 Transpose
		6.4.3 Matrix Inversion
	Problems
Chapter 7 Solving Single Algebraic Equations
	Chapter Objectives
	7.1 The Nature of Single, Nonlinear Equations in One Unknown
	7.2 Bracketing Methods—Bisection
	7.3 Bracketing Methods—False Position
	7.4 Open Methods—Newton-Raphson
	7.5 Open Methods—Modified Secant
	7.6 Circular Methods—Fixed-Point Iteration
	7.7 Circular Methods—The Wegstein Method
	7.8 A Hybrid Approach—Brent’s Method
	7.9 Solving for the Roots of Polynomials
	7.10 Case Study: Trajectories of Projectiles in Air
	Problems
Chapter 8 Solving Sets of Algebraic Equations
	Chapter Objectives
	8.1 Systems of Linear Algebraic Equations
	8.2 Solving Small Numbers of Linear Algebraic Equations
		8.2.1 Graphical Method
		8.2.2 Determinants and Cramer’s Rule
			8.2.2.1 Determinants
			8.2.2.2 Cramer’s Rule
		8.2.3 Elimination of Unknowns
	8.3 Gaussian Elimination
		8.3.1 Naive Gaussian Elimination
		8.3.2 Gaussian Elimination Computer Algorithm
			8.3.2.1 Naive Gaussian Elimination Algorithm
			8.3.2.2 Adding Determinant Evaluation
			8.3.2.3 Partial Pivoting
			8.3.2.4 Detecting Singular and Ill-Conditioned Systems
	8.4 Solving Sets of Linear Equations with the NumPy linalg Module
	8.5 Solving Sets of Nonlinear Algebraic Equations
		8.5.1 Solution of Nonlinear Algebraic Equations by Successive Substitution
		8.5.2 The Newton-Raphson Method for Nonlinear Systems of Equations
	8.6 Use of the root Function from the SciPy optimize Module to Solve Nonlinear Equations
	Problems
Chapter 9 Solving Differential Equations
	Chapter Objectives
	9.1 Describing Differential Equations
	9.2 Quadrature – Finding the Area under the Curve
		9.2.1 Pre-computer Methods
		9.2.2 Quadrature for Continuous Functions
		9.2.3 The quad Function from SciPy’s integrate Module
		9.2.4 Quadrature for Discrete Data
	9.3 Solving Differential Equations with Initial Conditions
		9.3.1 Euler’s Method
		9.3.2 Heun’s Method
		9.3.3 Systems of Differential Equations
	9.4 Solving Differential Equations with the solve_ivp Function from SciPy’s integrate Module
	Problems
Chapter 10 Working with Data
	Chapter Objectives
	10.1 Characterizing Data Sets: Initial Observations and Sample Statistics
		10.1.1 General Data Concepts
		10.1.2 Sample Statistics: Central Tendency and Dispersion
			10.1.2.1 Central Tendency
			10.1.2.2 Spread or Dispersion
		10.1.3 Using Boxplots to Diagnose Outliers
	10.2 Distributions
		10.2.1 Several Important Distributions
			10.2.1.1 Uniform Distribution
			10.2.1.2 Normal Distribution
			10.2.1.3 Weibull Distribution
		10.2.2 Python and Distributions
		10.2.3 Random Numbers
	10.3 Making Claims Based on Data
		10.3.1 Comparison of Data with a Standard
		10.3.2 Comparison between Two Samples
		10.3.3 Determining Whether Data Are Normally Distributed
	10.4 Fitting Mathematical Models to Data
		10.4.1 Straight-line Linear Regression
		10.4.2 Fitting Polynomials
		10.4.3 General Issues and Precautions
	Problems
References
Index
Index of Python Terminology