Machine learning (ML) algorithms work on cleaned data. Usually, the data we collect for building ML models suffers from noise, missing values, inconsistent data types, and different data scales. This makes pre-processing of data a very important phase in preparing the data for building ML models. Pre-processing is when we apply transformations over the data before feeding it to the ML algorithm. In short, data pre-processing symbolizes a set of procedures applied to the data to make it fit for ML algorithms. It generally involves the following steps:

• Step 1—Importing libraries: It involves importing the necessary libraries that are required to carry out the subsequent data manipulation and cleaning tasks.

• Step 2—Loading the dataset: The dataset that needs to be pre-processed must be loaded.

• Step 3—Handling the missing values: Dataset often contains missing or null values; these values need to be handled appropriately.

• Step 4—Handling the categorical data: In the data pre-processing phase, it is crucial to address categorical attributes that often contain multiple categories. Handling categorical data becomes an important step to ensure proper treatment and transformation of these attributes.

• Step 5—Splitting the dataset into training and testing datasets: Training and testing is the most important part of ML; thus, we need to split the dataset into training and testing subsets before building the ML models.

• Step 6—Feature scaling: In datasets, the range of data often varies, or data is often of different scales. Thus, feature scaling needs to be done to ensure uniformity in results.

It is important to note that it is not necessary to apply all of these steps to pre-process the data. However, based on the nature of the dataset, some of these steps may be skipped for building the model. In the coming sections, we will discuss the importance or need of these steps and discuss how to perform these steps in Python.

6A Radiation as a photon gas

In the nineteenth century, physicists applied classical electromagnetic theory to explain the experimental results of black body radiation but were unable to provide an adequate explanation. This was a major problem to the physicists as classical theory predicted an infinite amount of energy of the radiation emitted from a black body. This gross disagreement was called the “ultraviolet catastrophe”. Max Planck presented a paper on December 14, 1900, in which he guessed the answer to this problem of black body radiation. This guess marked the very beginning of quantum mechanics.

The electromagnetic radiation inside a black body chamber exists as patterns of standing waves or modes. A single mode is like a standing wave on a guitar string and is characterized by a frequency. Planck made a bold hypothesis that the energy of such a mode is quantized, ithat is, only certain energies of these oscillation modes are allowed. Thus, the energy 𝐸𝑛 of 𝑛th mode is given by 𝐸𝑛 = (𝑛 + 12 ) ℏ𝜔 = (𝑛 + 12 ) ℎ𝜈, where 𝜈 is the oscillation frequency, ℎ is Planck's constant, and 𝑛 is an integer starting with 0. Thus, each oscillation mode can exist in any one of an infinite number of energy states whose energies are equally separated by the energy ℏ𝜔. In the discussion of the properties of the photon gas, for the time being, we shall ignore 12 in the expression for 𝐸𝑛 as it has no effect on the results we seek. Therefore, we take 𝐸𝑛 = 𝑛ℏ𝜔 as the energy of the 𝑛th mode whose (angular) frequency is 𝜔. When the energy of a mode is 𝐸𝑛, we say that there are 𝑛 photons in the mode. Each photon has energy equal to ℏ𝜔. Thus, according to the prescription of Max Planck, a black body radiation chamber consists of a number of photons in various energy states with different amounts of energy.

20.1 Neural Networks and Human Brain

The inspiration to build artificial neural networks (ANNs) has come from the deep desire to simulate the working of the human brain. As our understanding of the human brain is getting enriched and improved daily due to the ongoing research on this topic, researchers are also improving the ANNs accordingly. One such recent addition is the recurrent neural networks (RNNs) and the long short-term memory (LSTM). In this chapter, we will discuss these developments in a simplified manner so that our readers can understand this amazing technology and use it for their development projects.

Sections 20.1 and 20.2 draw their inspiration from the blog titled “The Ultimate Guide to Recurrent Neural Networks (RNN)” published by SuperDataScience Team. Most of the figures used in these sections are adapted from this blog.

For detailed information on the blog, please refer to the “Additional Resources” section of this chapter.

Research on the human brain gives us the idea that the human brain has three main parts: cerebrum, cerebellum, and brainstem, as shown in Figure 20.1. Let us briefly discuss the main functions of these parts and their components to understand the association between neural networks and the human brain.

Cerebrum

From Figure 20.1, we can understand that the cerebrum has four lobes. These are as follows.

rystallography

The science that deals with the geometrical structure and physical properties of crystalline solids is called crystallography.

Solids are classified into two categories:

• 1. Crystalline solids

• 2. Amorphous solids

CRYSTALLINE SOLIDS

Crystalline solids are those that contain the regular repeated pattern of atoms or molecules, as shown in Figure 10.1. The physical properties of crystalline solids are different in different directions. Therefore, crystalline solids are anisotropic. Examples are rock salt, quartz, calcite, sugar, and so on.

AMORPHOUS SOLIDS

Figure 10.2 illustrates an amorphous material, which lacks the regular arrangement of atoms or molecules. The amorphous solid's physical characteristics are uniform throughout. As a result, amorphous solids are isotropic. Examples are glass, rubber, polymers, and so on.

SPACE LATTICES

A crystal is made up of identical structural units (atoms, molecules, or ions) that are infinitely repeated in space; each unit can be replaced by a geometrical point. The outcome is a pattern of dots with crystal-like geometrical characteristics. The crystal lattice or space lattice is this geometric arrangement. Lattice points are the name given to the geometrical points.

The regular pattern of points that describes the three-dimensional arrangement of points (atoms, molecules, or ions) in the crystal structure is called the crystal lattice or space lattice.

BASIS

The unit assembly of atoms, molecules, or ions identical in the composition, arrangement, and orientation is called basis. If we add the basis to every lattice point, then it forms a crystal structure, as shown in Figure 10.3.

Space lattice + Basis = Crystal structure.

Engineering physics plays a crucial role in providing the foundational knowledge necessary for the development of innovative technologies. It is an essential part of the curriculum for students in various streams of science and engineering at the undergraduate level.

The goal of this book is to develop a solid understanding of the basic principles of physics and highlight their relevance to engineering. The content is structured to progressively build the knowledge and skills necessary for further studies in both theoretical and applied sciences. Each chapter begins with the basic concepts and gradually moves to more advanced topics, supported by numerical examples, illustrations, and problem sets that reinforce learning. The problems included are designed to improve the problem-solving skills of students and provide practical insight into the engineering applications of physics.

The manuscript includes 14 chapters that were prepared in accordance with the syllabus taught in various Indian colleges and universities. In addition to core topics, the manuscript also covers advanced topics such as relativistic mechanics, quantum mechanics, optical fiber, lasers, semiconducting materials, superconducting materials, and nanomaterials. Students who want to pursue higher education and a career in research, as well as instructors who instruct postgraduate courses at universities, will find these topics helpful for building a solid foundational understanding and developing problem-solving abilities.

Welcome to the World of Machine Learning!

In this ever-evolving era of technology, the field of machine learning (ML) stands at the forefront of innovation, promising unprecedented insights and solutions to complex problems. This textbook provides a comprehensive understanding of the theoretical foundations of ML algorithms, coupled with practical implementation using Python, designed to be a companion for both beginners venturing into the field and seasoned practitioners seeking to deepen their understanding.

Why Machine Learning?

ML is not just a technical endeavor; it is a transformational force shaping the future of how we interact with data. From enhancing search engines and revolutionizing social media to powering self-driving cars and advancing artificial intelligence (AI), the applications of ML are boundless. ML has paved the way for developing sophisticated chatbots, generative AI models, and AI copilots. This book aims to demystify the intricate concepts of ML, making them accessible to learners of all backgrounds.

What This Book Offers

• - Foundations: We begin with the fundamentals, laying a solid groundwork to help you grasp the core concepts of ML.

• - “Learning by Doing” Approach: This book adopts a “learning by doing” approach, offering step-by-step coding instructions for various ML techniques. The aim is to empower you with the knowledge and skills to implement these principles effectively.

• - Real-World Applications: Understanding theory is essential, but applying it to real-world scenarios is where the true power of ML unfolds. This book bridges theory and application, ensuring a holistic learning experience.

For Whom This Book Is Intended

Whether you are a student exploring the realms of ML for the first time, a data professional aiming to expand your skill set, or a business leader seeking insights into how ML can elevate your organization, this book is crafted with you in mind.

How to Use This Book

Feel free to navigate the chapters based on your familiarity with the subject. If you’re a beginner, start from the beginning, and if you’re seeking advanced knowledge, dive into specific sections of interest. Explore GitHub resources that provide access to datasets, sample code, and examples used in this book for hands-on learning. For enhanced visual understanding, this book is complemented by an online video course available at learncompscience.com, allowing you to reinforce your knowledge through engaging video sessions.

DIFFRACTION

Diffraction is a phenomenon in which a light beam bends around the corner of an obstacle and spreads into the geometric shadow of that obstacle.

FRESNEL AND FRAUNHOFER DIFFRACTION

Diffraction can be classified into two categories:

• 1. Fresnel diffraction

• 2. Fraunhofer diffraction

The distinction between these two categories is as follows:

• a. In Fresnel diffraction, the screen and source are at a finite distance from an obstacle. The distances are important in this class. In Fraunhofer diffraction, the source and screen are at an infinite distance from an obstacle. Therefore, inclination is important.

• b. The incident wavefront in Fresnel diffraction is either spherical or cylindrical, whereas the incident wavefront in Fraunhofer diffraction is planar.

• c. In Fresnel diffraction, the central point of the screen is either bright or dark depending on the number of zones, whereas in Fraunhofer diffraction, the central point of the screen is always bright.

FRAUNHOFER DIFFRACTION DUE TO SINGLE SLIT

Let us consider a monochromatic light source of wavelength ƛ placed at the focus of convex lens L1. The collimated rays of plane wavefront are incident on a single-slit AB of width “e.” The un-deviated rays from the slit reaches at point O, and the rays diffracted by an angle θ reach at P on the screen, as shown in Figure 12.1.

19.1 Building Image Classifier with CNN

The convolutional neural network (CNN) is the perfect choice for building an image classifier system. In this chapter, we will implement various CNN classifiers in Python by considering various case studies.

19.2 Dog–Cat Classifier

Consider an image classification problem that involves identifying photos as either containing a cat or dog. Our task is to develop a CNN model that can identify the object in the image as a dog or cat. The CNN model will be trained on a dataset of images containing a dog or cat, and then this trained model will be used for classification. Once the model is built, it can be used as a template to build other models for predicting the class of any image on the trained dataset. It means we can use the same model to classify the tumors by training them on medical images.

Preparing the Dataset

To build a dog–cat classifier, we will use 11000 manually annotated photos of dogs and cats, where 5500 photos are of dogs, and the remaining ones are of cats. This is the partial dataset that has been created from the dogs-vs-cats dataset available at Kaggle. The link for this dataset is given below.

https://www.kaggle.com/competitions/dogs-vs-cats/data

This full dataset contains 37500 images (24000 in the train and 13500 in the test folders), which must be manually segregated into dog and cat folders. Since the dataset is huge and segregation is time-consuming, we took 10000 images (5000 images of dogs and 5000 images of cats) in the train folder and 1000 images in the test folder (500 images of dogs and 500 images of cats).

12.1 Introduction to Clustering

In machine learning (ML), labeling the data is one of the crucial tasks. But sometimes, we do not have the labeled data. Even though the data is not labeled, we can still analyze it using clustering techniques. As you know, algorithms in ML are broadly classified as supervised and unsupervised techniques. In the case of supervised learning, the input data points/examples are labeled, while in unsupervised learning, the input data points/examples are not labeled. Cluster analysis, also called clustering, comes under unsupervised learning. Here, the input data points are not labeled. Clustering is the most popular technique in unsupervised learning.

Clustering is defined as grouping the input data points into various clusters/groups based on their similarity.

A cluster contains objects that are more similar to each other. In other words, during cluster analysis, the data is grouped into classes or clusters, so that records within a cluster (intra-cluster) have high similarity with one another but have high dissimilarities in comparison to objects in other clusters (inter-cluster).

The clustering algorithm aims to minimize the intra-cluster distance and maximize the inter-cluster distance, as shown in Figure 12.1.

An example of clustering is shown in Figure 12.2. Here, records in the input have different shapes. Here, we only have the input data without any label of shape. After applying the clustering algorithm, they were classified into three types of clusters. Here, the clustering algorithm considers the dimensions of the object and its color as the input features. Records whose features are highly similar are gathered to form a single cluster. In this case, we get three clusters representing three types of records, i.e., it clusters rhombus, circle, and triangle separately, as shown in Figure 12.2.

Learning Outcomes

After reading this chapter, the reader will be able to

• Understand the distribution of energy density in a black body radiation as a function of wavelength and temperature

• Derive classical laws of black body radiation such as Wien distribution law and Rayleigh–Jeans law

• Get an idea about the development of quantum theory of radiation

• Understand Planck's quanta postulates and explain the black body radiation spectrum

• Derive Planck's law of black body radiation

• Verify Planck's law of black body radiation experimentally

• Derive Wien distribution law and Rayleigh–Jeans law and explain ultraviolet catastrophe from Planck's law of black body radiation

• Determine the temperature of cosmic microwave background radiation using Planck's law of black body radiation

• Solve numerical problems and multiple choice questions on black body Radiation

11.1 Introduction

Figure 11.1 The whole electromagnetic spectrum. Thermal radiation ranges in frequency from the shortest infrared rays through the visible-light spectrum to the longest ultraviolet rays.

Radiation emitted from the surface of a heated source is known as thermal radiation. In this process, thermal energy is spread out in all directions in the form of electromagnetic radiation and travels directly to its point of absorption at the speed of light. It does not require an intervening medium for its propagation. The wavelength of thermal radiation ranges from the longest infrared rays through the visible-light spectrum to the shortest ultraviolet rays. Such electromagnetic spectrum is shown in Figure 11.1 as a function of frequency. The distribution of radiant energy with their corresponding intensities within various ranges of wavelengths is governed by the temperature of the emitting surface .

18.1 Image Recognition

Using a convolutional neural network (CNN), technological development in image recognition has revolutionized far beyond our imagination. Let us consider the comic scene shown in Figure 18.1, as it provides interesting insights into the development of image recognition and depicts a decade-back possible scenario. Here, a manager asks his computer programmer to “Develop an app which can check whether the user is in a national park or not, when he clicks some photo!” Being an easy and feasible task, the computer programmer responds that the task is merely of few hours. But, the manager's curiosity goes up, and he asks the programmer further to check whether the image is of a bird or not? Surprisingly, the programmer responds, “I need a research team and five years for this task.”

This surprised the manager as he expected it to be an easy task. But the programmer who has a knack in the field knows that it is one of the complex problems to be addressed in computer science.

In the last decade, we have provided solutions to many complex problems in the field of computers. But, for the last 50 years, we have been struggling to solve the problems in image recognition. However, thanks to the efforts of researchers and computer scientists across the globe, we can solve these problems now. Even a three-year-old child can identify a bird's photo, but identifying a way by which computers can do the same task was not a cake-walk; hence, it took almost 50 years!

We have finally found a promising approach for object recognition using deep CNN in recent years. In this chapter, we will discuss the working principle and concepts of CNN, a deep neural network approach to solving the problem of image recognition.

4A Chemical Potential

Very often, the term “chemical potential” is not well understood by the students. After studying thermal physics and statistical mechanics for several times, students are still in a lot of confusion about the meaning of the term “chemical potential”. This quantity is represented by the letter 𝜇. Typically, students learn the definition of 𝜇, its properties, its derivation in some simple cases, and its consequences, and work out numerical problems on it. Still, students ask the question: “What is the chemical potential?” and “What does it actually mean?” Attempts are made in this appendix to clarify the meaning of this physical quantity 𝜇 with some simple examples.

The concept of chemical potential has appeared first in the classical works of J. W. Gibbs. Since then, it has become actually a subtle concept in thermodynamics and statistical mechanics. It is not easy to grasp the meaning and significance of chemical potential 𝜇, like thermodynamic concepts such as temperature 𝑇 , internal energy 𝐸, or even entropy 𝑆. In fact, chemical potential 𝜇 has acquired a reputation as a concept not easy to grasp even for the experienced physicist. Chemical potential was introduced by Gibbs within the context of an extensive exposition on the foundations of statistical mechanics. In his exposition, Gibbs considered a grand canonical ensemble of systems in which the exchange of particles occurs with the surroundings. In this description, the chemical potential 𝜇 appears as a constant required for a necessary closure to the corresponding set of equations. Thus, a fundamental connection with thermodynamics is achieved by observing that the unknown constant 𝜇 is indeed related to standard thermodynamic functions like the Helmholtz free energy 𝐹 = 𝑈 − 𝑇 𝑆 or the Gibbs thermodynamic potential 𝐺 = 𝐹 + 𝑃 𝑉 through their first derivatives. 𝜇, in fact, appeared as a conjugate variable to volume V. 4A.1 Comments about chemical potential

We are familiar with the term potential used in mechanical and electrical system. A capacity factor is associated with each potential term. For example, in a mechanical system, mass is the capacity factor associated with the gravitational potential 𝑔(ℎ2 − ℎ1), where ℎ1 and ℎ2 are the corresponding heights, and the gravitational work done is given by 𝑚𝑔(ℎ2 − ℎ1).

12.1 INTRODUCTION [LO1]

There are in general two approaches to solving equilibrium problems in solid mechanics: Eulerian and Lagrangian. The first approach deals with vectors such as force and moments, and considers the static equilibrium and compatibility equations to solve the problems. In the second approach, scalars such as work and energy are used, and here solutions to problems are based on the principle of conservation of energy. There are many situations where the second approach is more advantageous, and here some powerful methods, such as the method of virtual work, based on this approach, are used.

Eulerian and Lagrangian approaches to solving solid mechanics problems are much more involved. However, here we have chosen to describe these in a simplified manner, which is suitable as a prologue to the present discussion on energy methods.

In mechanics, energy is defined as the capacity to do work, and this may exist in different forms. We are concerned here with elastic strain energy, which is a form of potential energy stored in a body on which some work is done by externally applied forces. Here it is assumed that the material remains elastic when work has been done so that all the energy is recoverable and no permanent deformation occurs. This means that strain energy U = work done. If the load is applied gradually in straining, the material load–extension graph is as shown in Figure 12.1, and we may write U = ½ Pδ.

The hatched portion of the load–extension graph represents the strain energy and the unhatched portion ABD represents the complementary energy that is utilized in some advanced energy methods of solution.

List of Experiments

• 1. Determine the energy band gap of N-type Germanium (Ge) semiconductor using the four-probe method.

• 2. Verify Stefan's fourth power law for black body radiation and determine the exponent of temperature.

• 3. Study of thermoelectricity: Determine thermopower of copper-constantan thermocouple.

• 4. Study the variation of magnetic field with distance along the axis of current-carrying coil and then estimate the radius of the coil.

• 5. Study of Carrey Foster bridge: Determine resistance per unit length of the bridge wire and of a given unknown resistance.

• 6. Determine specific charge (charge to mass ratio; e/m) for electron.

• 7. Study of tangent galvanometer: Determine reduction factor and horizontal component of the earth's magnetic field.

• 8. Determine the wavelength of sodium light using Newton's rings method.

• 9. Determine the concentration of sugar solution using half-shade polarimeter.

• 10. Determine the wavelength of spectral lines of mercury (for violet, green, yellow-1, and yellow-2) using plane transmission grating.

• 11. Determine the charge sensitivity and ballistic constant of a ballistic galvanometer.

• 12. Determine the wavelength of spectral lines of hydrogen and hence the value of Rydberg constant.

• 13. Draw the V-I characteristic of light-emitting diode (LED) and determine the value of Planck's constant.

Experiment 1: Band Gap of Semiconductor

Objective: To determine the energy band gap of n-type Ge-semiconductor using four-probe method.

Apparatus Used: The following apparatus are used in this experiment:

• 1. Probe arrangement (shown in Figure 14.1).

• 2. n-type Ge-crystal chip with nonconducting base.

• 3. Oven with temperature up to 200°C.

• 4. A constant current generator power supply.

• 5. Power source for the oven.

• 6. Thermometer.

Learning Outcomes

After reading this chapter, the reader will be able to

• Demonstrate the meaning of reversible, irreversible, and quasi-static processes used in thermodynamics

• Explain heat engines, and their efficiency and indicator diagram

• Formulate the second law of thermodynamics and apply it to various thermodynamic processes

• Demonstrate an idea about entropy and its variation in various thermodynamic processes

• State and compare various statements of the second law of thermodynamics

• Elucidate the thermodynamic scale of temperature and its equivalence to the perfect gas scale

• Explain the principle of increase of entropy

• Understand the third law of thermodynamics and explain the significance of unattainability of absolute zero

• Solve numerical problems and multiple choice questions on the second law of thermodynamics

9.1 Introduction

The first law of thermodynamics states that only those processes can occur in nature in which the law of conservation of energy holds good. But our daily experience shows that this cannot be the only restriction imposed by nature, because there are many possible thermodynamic processes that conserve energy but do not occur in nature. For example, when two objects are in thermal contact with each other, the heat never flows from the colder object to the warmer one, even though this is not forbidden by the first law of thermodynamics. This simple example indicates that there are some other basic principles in thermodynamics that must be responsible for controlling the behavior of natural processes. One such basic principle is contained in the formulation of the second law of thermodynamics.

This principle limits the use of energy within a source and elucidates that energy cannot be arbitrarily passed from one object to another, just as heat cannot be transferred from a colder object to a hotter one without doing any external work. Similarly, cream cannot be separated from coffee without a chemical process that changes the physical characteristics of the system or its surroundings. Further, the internal energy stored in the air cannot be used to propel a car, or the energy of the ocean cannot be used to run a ship without disturbing something (surroundings) around that object.

7.1 Introduction to Multiple Linear Regression

In simple linear regression, we have one dependent variable and only one independent variable. As we discussed in the previous chapter, the stipend of a research scholar is dependent on his years of research experience.

But most of the time, the dependent variable is influenced by more than one independent variable. When the dependent variable depends on more than one independent variable, it is known as multiple linear regression.

Figure 7.1 indicates the difference between simple and multiple regressions mathematically.

In Figure 7.1(b), b0 is the constant while x1, x2, and xn are independent variables on which the dependent variable y depends. You can point out that mathematically multiple linear regression is derived similarly to simple linear regression. The major difference is that in multiple linear regression, we have multiple independent variables, as it is from x1 to xn instead of only one independent variable, x1, in the case of simple linear regression. It is also important to note that we have b1 to bn as the coefficients of these independent variables, respectively.

The price prediction of a house can be viewed as a multiple linear regression problem, where factors such as plot size, number of bedrooms, and location play a significant role in determining the price. Unlike simple linear regression, which relies solely on plot size, multiple linear regression considers various features to accurately estimate the house price.

Let us understand this concept further with a real-life example. Consider a case where a venture capitalist has hired a data scientist to analyze different companies’ data to predict their profit. Identifying the company having maximum profit will help the venture capitalist to select the company he could invest in the near future to earn maximum profit.

NANO

The term “nano” is derived from a Greek word that means “dwarf” (small) and is represented by the symbol “n.” As a unit prefix, it signifies “one billionth,” denoting a factor of 10-9 or 0.000000001. It is primarily used with the metric system, as illustrated in Figures 8.1 and 8.2. For example, one nanometer is equal to 1 × 10-9 m, and one nanosecond is equal to

1 × 10-9 sec. It is frequently encountered in science and electronics, particularly for prefixing units of time and length.

HISTORY OF NANOTECHNOLOGY

The origin of nanotechnology is often attributed to American physicist Richard Feynman's speech, “There's Plenty of Room at the Bottom,” which he gave on December 29, 1959, at an American Physical Society conference at Caltech. A 1959 lecture by Richard Feynman served as the intellectual inspiration for the field of nanotechnology. The term “nanotechnology” was initially used in a conference in 1974 by a Japanese scientist by the name of Norio Taniguchi from Tokyo University of Science to describe semiconductor techniques with characteristic control on the order of a nanometer, such as thin film deposition and ion beam milling. According to his definition, “nanotechnology” is primarily the processing, separation, consolidation, and deformation of materials by a single atom or molecule.