book

Python For Engineering and Scientific Computing

Name: Python For Engineering and Scientific Computing
ISBN: 9781806106059

by Rheinwerk Publishing, Inc, Veit Steinkamp

June 2025

Intermediate to advanced

515 pages

17h 5m

English

Packt Publishing

Read now

Unlock full access

Notes on Usage
Table of Contents
1 Introduction
1.1 Development Environments1.1.1 IDLE1.1.2 Thonny1.1.3 Spyder1.1.4 Pip
1.2 The Modules of Python
1.2.1 NumPy1.2.2 Matplotlib1.2.3 SymPy1.2.4 SciPy1.2.5 VPython
1.3 The Keywords of Python
1.4 Your Path through This Book
2 Program Structures
2.1 Linear Program Structures2.1.1 Linear Programs without Function Calls
2.2 Functions
2.2.1 Built-In Functions2.2.2 Functions without Parameters and without Return Values2.2.3 Functions with Parameters and a Return2.2.4 Functions with Multiple Return Values2.2.5 Functions Call Other Functions
2.3 Branching Structures
2.3.1 Single Selection2.3.2 Multiple Selection
2.4 Repetitive Structures
2.4.1 The while Loop2.4.2 The for Loop

2.5 Data Structures
2.5.1 Tuples2.5.2 Lists2.5.3 Dictionaries2.5.4 Sets
2.6 Functional Program Style
2.7 Object-Oriented Program Style
2.7.1 Objects and Classes2.7.2 Inheritance
2.8 Project Task: Dimensions of a Shaft
2.9 Tasks
3 Numerical Calculations Using NumPy
3.1 NumPy Functions3.1.1 Creating One-Dimensional Arrays Using arange() and linspace()3.1.2 Creating Two-Dimensional Arrays Using array()3.1.3 Slicing3.1.4 Mathematical NumPy Functions3.1.5 Statistical NumPy Functions
3.2 Vectors
3.2.1 Addition of Vectors3.2.2 Scalar Product3.2.3 Cross Product3.2.4 Triple Product3.2.5 Dyadic Product
3.3 Matrix Multiplication
3.3.1 Chain Shape with B Parameters3.3.2 Usage Example: Calculating the Energy of a Rotating Rigid Body in Space
3.4 Linear Systems of Equations
3.4.1 Systems of Equations with Real Coefficients3.4.2 Systems of Equations with Complex Coefficients
3.5 Project Task: Lightning Protection System
3.6 Tasks
4 Function Plots and Animations Using Matplotlib
4.1 2D Function Plots4.1.1 Basic Structure of a Function Plot4.1.2 Gridlines4.1.3 Labels4.1.4 Line Styles4.1.5 Designing Axes4.1.6 Coloring Areas4.1.7 Subplots4.1.8 Parameter Representation4.1.9 Changing Function Parameters Interactively4.1.10 Contour Plots
4.2 3D Function Plots
4.2.1 Helical Line4.2.2 Circular Ring4.2.3 Combining a 3D Plot with a Contour Plot
4.3 Vectors
4.3.1 Vector Addition4.3.2 Vector Field
4.4 Displaying Figures, Lines, and Arrows
4.4.1 Rectangles4.4.2 Circles and Lines4.4.3 Arrows4.4.4 Polygons4.4.5 Usage Example: A Metal Rod in a Magnetic Field
4.5 Animations
4.5.1 A Simple Animation: Shifting a Sine Function4.5.2 Animated Oblique Throw4.5.3 Animated Planetary Orbit
4.6 Project Task: Stirling Cycle
4.7 Project Task: Animating a Thread Pendulum
4.8 Project Task: Animating a Transmission
4.9 Tasks
5 Symbolic Computation Using SymPy
5.1 Basic Mathematical Operations5.1.1 Addition5.1.2 Multiplication of Terms5.1.3 Multiplication of Linear Factors5.1.4 Division5.1.5 Exponentiation5.1.6 Usage Example: Analyzing an Electrical Power Transmission System
5.2 Multiplying Matrixes
5.2.1 Calculation Rule5.2.2 Transmission Function of a Catenary Circuit
5.3 Equations
5.3.1 Linear Systems of Equations5.3.2 Nonlinear Systems of Equations
5.4 Simplifications of Terms
5.5 Series Expansion
5.6 Partial Fractions
5.7 Continued Fractions
5.8 Limits
5.8.1 Limits of Sequences5.8.2 Limits of Functions5.8.3 Differential Quotient
5.9 Differentiation
5.9.1 Usage Example: Curve Sketching
5.10 Integrations
5.10.1 Indefinite Integral5.10.2 Definite Integral5.10.3 Usage Example: Stored Electrical Energy
5.11 Differential Equations
5.11.1 Linear First-Order Differential Equations5.11.2 General Solution of a Second-Order Differential Equation5.11.3 Special Solution of a Second-Order Differential Equation
5.12 Laplace Transform
5.12.1 Solving Differential Equations5.12.2 Analyzing Networks with Transmission Functions
5.13 Project Task: Step Response of a Catenary Circuit
5.14 Project Task: Bending a Beam That Is Fixed at One End
5.14.1 Second Moment of Area5.14.2 Equation of the Bending Line
5.15 Project Task: Reaction Kinetics
5.16 Project Task: Dual Mass Oscillator
5.17 Tasks
6 Numerical Computations and Simulations Using SciPy
6.1 Numerical Computation of Zeros
6.2 Optimizations
6.3 Interpolations
6.4 Numerical Differentiation
6.4.1 Methods of Numerical Differentiation6.4.2 Drawing a Tangent Slope6.4.3 Derivative of a Sine Function6.4.4 Usage Example: Free Fall
6.5 Numerical Integration
6.5.1 Methods of Numerical Integration6.5.2 Definite Integral6.5.3 Integrating a Constant6.5.4 Usage Example: Free Fall6.5.5 Improper Integral6.5.6 Calculating Arc Lengths6.5.7 Volume and Surfaces of Rotating Bodies6.5.8 Double Integrals6.5.9 Triple Integrals
6.6 Solving Differential Equations Numerically
6.6.1 Numerical Solution of Differential Equations6.6.2 First-Order Linear Differential Equation6.6.3 Second-Order Linear Differential Equation6.6.4 Nonlinear Second-Order Differential Equation6.6.5 Second-Order Differential Equation System: Coupled Spring-Mass System6.6.6 Nonlinear Second-Order Differential Equation System: Double Pendulum
6.7 Discrete Fourier Transform
6.7.1 Basic Use of the Fast Fourier Transform Algorithm6.7.2 Frequency Spectra of Non-Sinusoidal Periodic Signals6.7.3 Reconstructing a Noisy Signal
6.8 Writing and Reading Sound Files
6.8.1 Generating and Saving Signals6.8.2 Reading and Displaying Signals
6.9 Signal Processing
6.9.1 Frequency Response of a Butterworth Lowpass6.9.2 Frequency Response of a Crossover6.9.3 Filtering Signals
6.10 Project Task: Simulation of a Rolling Bearing Damage
6.11 Project Task: Predator-Prey Model
6.11.1 Exponential Growth6.11.2 Logistic Growth6.11.3 Predator-Prey Relationship for Exponential Growth6.11.4 Predator-Prey Relationship for Logistic Growth
6.12 Project Task: Simulation of an Epidemic
6.13 Tasks
7 3D Graphics and Animations Using VPython
7.1 The Coordinate System
7.2 Basic Shapes, Points, and Lines
7.2.1 Cylinder7.2.2 Cuboid7.2.3 Points7.2.4 Lines7.2.5 Sphere7.2.6 Penetration7.2.7 Composite Bodies
7.3 Bodies in Motion
7.3.1 Vertical Movement7.3.2 Horizontal Movement7.3.3 Movement in Space7.3.4 Composite Motion7.3.5 Rotational Motion7.3.6 Random Motion
7.4 Animation of Oscillations
7.4.1 Simple Pendulum7.4.2 Spring Pendulum
7.5 Event Processing
7.6 Project Task: Animation of a Coupled Spring Pendulum
7.7 Project Task: Animation of Two Coupled Simple Pendulums
7.8 Tasks
8 Computing with Complex Numbers
8.1 Mathematical Operations
8.2 Euler’s Formula
8.2.1 Symbolic Method
8.3 Calculating with Complex Resistors
8.4 Function Plots with Complex Magnitudes
8.4.1 Complex Frequency Response of a Series Resonant Circuit8.4.2 Locus Curves
8.5 Project Task: Electric Power Transmission System
8.5.1 Task8.5.2 Equivalent Circuit Diagram of a Three-Phase Power Line
8.6 Tasks
9 Statistical Computations
9.1 Generating, Saving, and Reading Measurement Values9.1.1 Generating Measurement Values9.1.2 Converting a Measurement Series into a Table9.1.3 Writing Measurement Values to a File9.1.4 Reading Measurement Values from a File
9.2 Frequency Distribution
9.2.1 Frequency Tables9.2.2 Histograms
9.3 Location Parameters
9.3.1 Arithmetic Mean9.3.2 Mode, Median, Harmonic Mean, and Geometric Mean
9.4 Dispersion Parameters
9.5 Normal Distribution
9.5.1 Graphical Representation of the Density Function9.5.2 Probability Distribution
9.6 Skew
9.7 Regression Analysis
9.7.1 Computing the Regression Parameters9.7.2 Representing the Scatter Plot and the Regression Line
9.8 Project Task: Simulation of a Quality Control Chart
9.9 Tasks
10 Boolean Algebra
10.1 Logical Operations10.1.1 Conjunction10.1.2 Disjunction10.1.3 Negation
10.2 Laws of Boolean Algebra
10.2.1 Simple Postulates10.2.2 De Morgan’s Laws10.2.3 Distributive Law
10.3 Circuit Synthesis
10.3.1 Simplifying Logic Functions by Factoring Out10.3.2 Simplification Using the Disjunctive Normal Form10.3.3 Simplification Using the Conjunctive Normal Form
10.4 Project Task: Seven-Segment Coding
10.5 Tasks
11 Interactive Programming Using Tkinter
11.1 Interactions with Command Buttons, Textboxes, and Labels11.1.1 Labels11.1.2 Textboxes and Command Buttons
11.2 The Layout Manager of Tkinter
11.2.1 The pack Method11.2.2 The grid Method11.2.3 Summary
11.3 Selection with Radio Button
11.4 Slider
11.5 The Canvas Drawing Area
11.5.1 Representing Lines11.5.2 Function Plots11.5.3 Querying Mouse Coordinates
11.6 Project Task: Rotational Frequency Control of an Externally Excited DC Motor
11.7 Tasks
A Appendix
A.1 Glossary: Basic Applied Computer Science Terminology
A.2 Derivatives of Elementary Functions
A.3 Antiderivative of Elementary Functions
A.4 Fourier Series of Important Electrotechnical Voltage Characteristics
A.5 Correspondence Table of Important Inverse Laplace Transforms
A.6 Bibliography
B The Author
Index
Service Pages
Legal Notes

Content preview from Python For Engineering and Scientific Computing

6.6 Solving Differential Equations Numerically

Numerous types of differential equations cannot be solved analytically. These equations include, among others, nonlinear differential equations. However, these types of differential equations can be solved numerically with sufficient accuracy and relatively little effort. A particular advantage of numerical solution methods is that the initial values are a necessary part of the solution algorithm. Thus, the initial value problem no longer needs to be solved explicitly. Another advantage of numerical solution methods is that the calculated solution set is available as an array and can thus be visualized using the plot method.

6.6.1 Numerical Solution of Differential Equations

If a differential ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.

Read now

Unlock full access

More than 5,000 organizations count on O’Reilly

O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.

Julian F.

Head of Cybersecurity

I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.

Addison B.

Field Engineer

I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.

Amir M.

Data Platform Tech Lead

I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.

Mark W.

Embedded Software Engineer

Publisher Resources

ISBN: 9781806106059

Cloud Computing

Data Engineering

Data Science

AI & ML

Programming Languages

Software Architecture

IT/Ops

Security

Design

Business

Soft Skills

Python For Engineering and Scientific Computing

by Rheinwerk Publishing, Inc, Veit Steinkamp

6.6 Solving Differential Equations Numerically

6.6.1 Numerical Solution of Differential Equations

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.