Mathematics for Electrical and Physical Science 3
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Questions and Answers

What is the primary focus of fluid statics in this course?

  • Understanding the behavior of fluids at rest (correct)
  • Calculating fluid viscosity under varying temperatures
  • Fluid dynamics at high velocities
  • Methods of flow measurement in open channels

Which type of manometer is specifically used for measuring pressure differences?

  • Inverted U tube manometer
  • Simple manometer
  • U tube differential manometer (correct)
  • Mechanical gauges

What determines the stability of a floating body according to the course content?

  • The condition of the center of buoyancy and meta-centric height (correct)
  • The density of the fluid only
  • The speed of fluid currents around the body
  • The shape of the floating body only

What method is utilized to describe fluid motion in the course content?

<p>Lagrangian and Eulerian methods (A)</p> Signup and view all the answers

Which equation relates to the measurement of fluid pressure in this course?

<p>Pascal’s Law (C)</p> Signup and view all the answers

What is the primary focus of Course Outcome 1 (CO1)?

<p>Determining Fourier transforms of functions (A)</p> Signup and view all the answers

Which knowledge level is associated with Course Outcome 2 (CO2)?

<p>K3 - Apply (C)</p> Signup and view all the answers

Which Course Outcome focuses on computing complex integrals using specific theorems?

<p>CO3 (C)</p> Signup and view all the answers

Which outcome applies to understanding the series expansion of complex functions about a singularity?

<p>CO4 (B)</p> Signup and view all the answers

What is the mapping rating for CO1 in terms of PO1?

<p>3 (A)</p> Signup and view all the answers

Which Course Outcome has the same mapping rating in both PO1 and PO2?

<p>CO2 (C)</p> Signup and view all the answers

Which knowledge level is NOT represented in the Course Outcomes?

<p>K6 - Create (A)</p> Signup and view all the answers

What method is used with CO4 to compute real integrals?

<p>Residue theorem (D)</p> Signup and view all the answers

What is the primary focus of the Fourier Transform as introduced in this course?

<p>Applications in various engineering fields (B)</p> Signup and view all the answers

Which of the following equations is not a part of the Cauchy-Riemann Equations?

<p>$ rac{ ext{∂}u}{ ext{∂}x} + rac{ ext{∂}v}{ ext{∂}y} = 0$ (D)</p> Signup and view all the answers

What is a key attribute of functions that satisfy Laplace’s Equations?

<p>They are harmonic functions (A)</p> Signup and view all the answers

What is the purpose of conformal mapping?

<p>To preserve angles and shapes in a neighborhood (B)</p> Signup and view all the answers

Which of the following best describes a complex integral?

<p>An integral over a path in the complex plane (D)</p> Signup and view all the answers

In Fourier Transforms, what does linearity refer to?

<p>The ability to distribute the transform over addition and scaling (B)</p> Signup and view all the answers

What is the significance of Cauchy's Integral Formula in complex analysis?

<p>It simplifies the computation of contour integrals (B)</p> Signup and view all the answers

What is the relationship between harmonic functions and their harmonic conjugates?

<p>Harmonic conjugates are derived from harmonic functions and relate through Cauchy-Riemann conditions (C)</p> Signup and view all the answers

Which programming languages can be utilized for Machine Learning implementations?

<p>Python, R, and MATLAB (B)</p> Signup and view all the answers

What is the total mark distribution for Continuous Internal Evaluation (CIE)?

<p>40 marks (A)</p> Signup and view all the answers

In the End Semester Examination (ESE), how many total questions are provided in Part A?

<p>8 Questions (A)</p> Signup and view all the answers

What is the maximum number of marks a student can earn from Part B of the ESE?

<p>36 marks (B)</p> Signup and view all the answers

What is the course outcome related to applying machine learning algorithms?

<p>Understanding machine learning algorithms including neural networks (A)</p> Signup and view all the answers

Which statistical methods are mentioned for analyzing and interpreting data?

<p>Descriptive statistics, correlation, and regression analysis (B)</p> Signup and view all the answers

What mathematical concepts are applied to analyze engineering problems?

<p>Matrix operations, singular values, and PCA (B)</p> Signup and view all the answers

What is the Bloom's Knowledge Level (KL) for the course outcomes stated?

<p>K3 (D)</p> Signup and view all the answers

What is one of the components included in the portfolio for Continuous Internal Evaluation?

<p>Project reports (A)</p> Signup and view all the answers

How many marks are allocated for the Continuous Internal Evaluation?

<p>50 marks (C)</p> Signup and view all the answers

What is the maximum group size for the activities during the semester?

<p>4 to 6 members (A)</p> Signup and view all the answers

What type of analysis is a part of the micro project?

<p>Engineering Ethics Case Study analysis (C)</p> Signup and view all the answers

What reflects the personal insights and application of learned concepts in the course?

<p>Reflective Journal (C)</p> Signup and view all the answers

What is included in the group activities conducted throughout the course?

<p>Collective group reports (A)</p> Signup and view all the answers

What is the focus of the literature survey for one of the micro projects?

<p>Code of Ethics for Engineers (D)</p> Signup and view all the answers

During which seminar are the portfolios expected to be displayed?

<p>7th Semester Seminar (D)</p> Signup and view all the answers

Which of the following books focuses on the concepts and practice of data science?

<p>Data Science: Concepts and Practice (A)</p> Signup and view all the answers

What is the publication year of 'Foundations of Data Science'?

<p>2020 (B)</p> Signup and view all the answers

Who are the authors of 'Probability and Statistics for Data Science'?

<p>Fernandez-Granda and Rosenthal (C)</p> Signup and view all the answers

Which publisher released 'Statistics For Data Science'?

<p>Packt Publishing (D)</p> Signup and view all the answers

What edition of 'The Science of Uncertainty' was published in 2009?

<p>1st edition (A)</p> Signup and view all the answers

Which book is authored by Arno Meysman?

<p>Introducing data science: big data, machine learning, and more, using Python tools (A)</p> Signup and view all the answers

Which of the following books was published by Morgan Kaufmann?

<p>Data Science: Concepts and Practice (C)</p> Signup and view all the answers

What is the correct order of publishing years for 'Foundations of Data Science' and 'Statistics For Data Science'?

<p>2020, 2019 (B)</p> Signup and view all the answers

Flashcards

Fluid Statics

Study of fluids at rest and the forces acting within them.

Pascal's Law

Pressure applied to a fluid in a closed container is transmitted equally in all directions.

Manometers

Devices used for measuring fluid pressure, usually involving liquids.

Buoyancy

Upward force exerted by a fluid that opposes the weight of an immersed object.

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Metacentric Height

Measure of the stability of a floating body.

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Course Outcomes (COs)

Specific skills and knowledge students should gain after completing a course.

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CO1

Determining Fourier transforms and applying them in engineering problems.

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CO2

Understanding analyticity of complex functions and using it in conformal mapping.

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CO3

Calculating complex integrals using Cauchy's theorems.

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CO4

Understanding series expansions of complex functions around singularities and applying residue theorem to real integrals.

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Bloom's Knowledge Level (KL)

Classifies the cognitive skills expected, from remembering to creating.

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K3

Applying knowledge to solve problems.

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Fourier Transform

A mathematical transformation that decomposes a function into its constituent frequencies.

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Complex Function

A function that maps complex numbers to complex numbers.

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Analytic Function

A complex function that satisfies the Cauchy-Riemann equations.

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Cauchy-Riemann Equations

Necessary conditions for a complex function to be analytic.

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Contour Integrals

Integrals over a path (curve) in the complex plane.

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Cauchy's Integral Theorem

States that the integral of an analytic function around a closed contour is zero under certain conditions.

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Simply Connected Domain

A domain where any closed curve can be continuously shrunk to a point without leaving the domain.

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Conformal Mapping

A transformation that preserves angles between curves.

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Machine Learning Implementation Languages

Python, MATLAB, and R can be used to implement machine learning.

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Course Assessment Weightage

Continuous Internal Evaluation (CIE) accounts for 40 marks and End Semester Examination (ESE) accounts for 60 marks.

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CIE Components

CIE includes attendance, assignments, micro-project, and internal examinations (two).

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ESE Structure

ESE is divided into Part A (all questions required) and Part B (one question from two provided).

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ESE Part A Questions

Part A has 2 questions from each module, each carrying 3 marks (8x3 = 24 marks).

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ESE Part B Questions

Part B has a choice of one question per module; each question is worth 9 marks (4x9 = 36 marks) and has a maximum of 3 sub-divisions.

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Data Science Books

Books that introduce or explain concepts in data science areas, including big data, machine learning, data science practice, probability and statistics and the foundations and fundamentals of data science.

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Kapoor 2020

A 2020 book that introduces data science, big data, and machine learning using Python tools.

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Kotu 2018

2018 book about data science, covering concepts and practical applications; likely covers different frameworks.

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Fernandez-Granda 2017

2017 book on Probability & statistics needed for data science.

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Blum, Hopcroft, and Kannan 2020

A data science foundations book published in 2020.

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Miller 2019

2019 Statistics for Data Science book.

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Rosenthal 2009

2009 book on Probability and Statistics, essential for data science.

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Big Data

The technique of analyzing and mining large volumes of data.

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Portfolio

Collection of work showcasing learning progress, including reflections, reports, case studies, and other materials.

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Reflective Journal

Regular entries reflecting on what was learned, personal insights, and applying knowledge to local contexts.

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Engineering Ethics Case Study

Analyzing real-world scenarios involving ethical dilemmas in engineering practices.

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Code of Ethics for Engineers

Set of principles guiding ethical conduct of engineers, outlining responsibilities and values.

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Gender-Related Topic

Issues related to gender equality, representation, and social impact in engineering.

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Kerala Context

Analyzing a specific issue or topic in the context of Kerala, a state in India.

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TED Talk

Short, inspiring talk on a specific topic, usually delivered at a TED conference.

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Literature Survey

Reviewing existing research papers and articles on a specific topic.

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Study Notes

MATHEMATICS FOR ELECTRICAL AND PHYSICAL SCIENCE - 3 (GYMAT301)

  • Course Code: GYMAT301
  • CIE Marks: 40
  • ESE Marks: 60
  • Teaching Hours/Week: 3 (L) : 0 (T) : 0 (P) : 0 (R)
  • Credits: 3
  • Exam Hours: 2 hours 30 minutes
  • Course Type: Theory
  • Prerequisites: Basic knowledge in complex numbers
  • Course Objectives: Introduce Fourier transforms, complex variable theory (residue integration, conformal transformation), and their applications.

Syllabus (Module Breakdown)

  • Module 1 (9 hours): Fourier Integral – Fourier series to Fourier Integral, Fourier Cosine and Sine integrals, Fourier Cosine and Sine Transform, Linearity, Transforms of Derivatives, Fourier Transform and its inverse, Linearity, Transforms of Derivatives (textbook sections 11.7, 11.8, 11.9).
  • Module 2 (9 hours): Complex Functions - Limit, continuity, derivative, analytic functions, Cauchy-Riemann Equations (without proof), Laplace’s Equations, Harmonic functions, finding harmonic conjugate, conformal mapping, transformations of w = z, w = ez, w = sin z (textbook sections 13.3, 13.4, 17.1, 17.2, 17.4).
  • Module 3 (9 hours): Complex Integration – Line integrals in the complex plane (definition & basic properties), First & second evaluation methods, Cauchy’s integral theorem (without proof) on simply connected domains, independence of path, Cauchy integral theorem on multiply connected domains (without proof), Cauchy integral formula (without proof).

Course Outcomes (COs)

  • CO1: Apply Fourier transforms and solve engineering problems. (Bloom's Level: K3)
  • CO2: Understand analyticity of complex functions and apply in conformal mapping. (Bloom's Level: K3)
  • CO3: Compute complex integrals using Cauchy's theorems and formulas. (Bloom's Level: K3)
  • CO4: Understand series expansions of complex functions around singularities and apply the residue theorem to compute real integrals. (Bloom's Level: K3)

Course Assessment (GYMAT301)

  • CIE (40 marks): Includes assignment/attendance (5 marks), internal examination 1 (15 marks), internal examination 2 (10 marks), micro project(10 marks).
  • ESE (60 marks): Part A (8 questions, 3 marks each) covering all modules, Part B (4 questions, 9 marks each), with choice from two options in each module.

FLUID MECHANICS AND HYDRAULICS (Course Code not explicitly mentioned)

  • Course Objectives: Introduce fundamental concepts of fluid mechanics and hydraulics in pipes & open channels; pressure measurement and flow measurement systems.

  • Syllabus (Module Breakdown): Fluid properties, fluid statics (pressure, Pascal's Law, manometers, pressure measurement gauges), determination of pressure/centre of pressure on surfaces, buoyancy & floatation (centre of buoyancy, meta-centre), fluid kinematics (Lagrangian & Eulerian methods).

  • Course Assessment: Continuous Internal Evaluation (CIE: 50 marks), End Semester Examination (ESE: 50 marks)

  • CIE Details: Reflective journal (5 marks), Micro project(1 part details analysis(8marks), part 2 literature search ( 5 marks))

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Description

This quiz covers key concepts from the 'Mathematics for Electrical and Physical Science - 3' course, focusing on Fourier transforms and complex variable theory. Students will explore Fourier integrals, series, and foundational properties of complex functions. A solid grasp of complex numbers is essential for tackling the questions.

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