Syllabus

Lecture 1 [Slides]: Meaning of research, its types, objectives, and significance.

Lecture 2 [Slides]: Research method and research methodology

Lecture 3 [Slides]: Criteria for good research, literature review, research papers

Lecture 4 [Slides]: Finding research papers, research ethics, technical writing, and Turnitin demo

Python [Notebook, PDF]: 

• Variables, data types, operations, if-else loops, lists

• Functions, classes, modules

• Control structures and scope of variables

• Miscellaneous (parts of previously covered topics):

  • Control structures: Loops: for, while; control structures: break and continue

  • Scope of variables

  • Recursion

  • Debugging and exception handling

  • Stacks & Queues

  • Dictionaries and Sets

  • File I/O Operations

Python assignments: 

• Assignment 1

• Assignment 2 

• Assignment 3

• Assignment 4

• Assignment 5: Recursion, dictionary, and queue

• Assignment 6: File I/O operations

• Practice Problems1

Lecture Plan

Lecture 1 [Notes]: System of linear equations and the Gaussian elimination method.

Lecture 2 [Notes]: Row-echelon form, pivot elements, Gaussian elimination operations

Lecture 3 [Notes]: Recap of previous lectures, invertible matrices with properties

Lecture 4 [Notes]: Gauss-Jordan method to compute matrix inverse

Lecture 5 [Notes]: Definition of a vector space with some examples

Lecture 6 [Notes]: More examples related to vector spaces, definition of vector subspaces

Lecture 7 [Notes]: Equivalent definitions of vector subspaces, examples, and definition of linear span

Lecture 8 [Notes]: Examples of linear span, linear span is a vector subspace

Lecture 9 [Notes]: Linearly independent set, examples

Lecture 10 [Notes]: Basis and dimension, examples

Lecture 11 [Notes]: Linear transformation, kernel and range, examples

Lecture 12 [Notes]: Rank-nullity theorem, examples

Lecture 13 [Notes]: Rank of a matrix, row and column spaces

Lecture 14 [Notes]: Co-ordinates of a vector, examples

Lecture 15 [Notes]: Co-ordinate transformation, invertible linear maps

Lecture 16 [Notes]: Matrix representation of linear transformation

Lecture 17 [Notes]: Examples of matrix representation of linear transformation, properties

Lecture 18 [Notes]: Eigenvalues of a linear transformation, characteristic polynomial

Lecture 19 [Notes]: Cayley-Hamilton theorem, algebraic and geometric multiplicities

Lecture 20 [Notes]: Minimal polynomial, similarity transformation, diagonalizability (part I)

Lecture 21 [Notes]: Diagonalizability (Part II)

Lecture 22 [Notes]: Orthogonal matrix and orthogonal diagonalization

Lecture 23 [Notes]: Quadratic forms and their canonical form [Part I]

Lecture 24 [Notes]: Quadratic forms and their canonical form [Part II], signature, index

Lecture 25 [Notes]: Differential equations-order and degree, formation, and its solutions

Lecture 26 [Notes]: Exact differential equations (Part I)

Lecture 27 [Notes]: Exact differential equations (Part II)

Lecture 28 [Notes]: Bernoulli equation, Verhulst equation

Lecture 29 [Notes]: Orthogonal trajectories

Lecture 30 [Notes]: Picard's existence and uniqueness theorem

Lecture 31 [Notes]: Picard's iteration method

Lecture 32 [Notes]: Fundamental solutions to second-order linear differential equation, Wronskian

Lecture 33-34 [Notes]: Abel's theorem, method of reduction of order

Lecture 35 [Notes]: Wronskian and linear independence of solutions

Lecture 36 [Notes]: Second or higher order linear ODE with constant coefficients

Lecture 37 [Notes]: Method of variation of parameters, inverse operator method

Lecture 38 [Notes]: Cauchy-Euler method

Lecture 39 [Notes]: Formation of PDEs by elimination of arbitrary constants as well as arbitrary functions

Lecture 40 [Notes]: Lagrange's method to solve quasi-linear first-order PDEs

Lecture 41 [Notes]: Particular solutions and finding orthogonal surfaces to the given surface family

Lecture 42 [Notes]: Charpit's method

Syllabus

Lecture 1 [Slides]: Meaning of research, its types, objectives, and significance.

Lecture 2 [Slides]: Research method vs. Research methodology

Lecture 3 [Slides]: Criteria for good research, literature review, research papers

Lecture 4 [Slides]: Reviewing literature, sources for articles--Google Scholar, Scopus, arXiv

Lecture 5 [Slides]: Journal rankings and research ethics

Lecture 6 [Slides]: Technical writing

Lecture 7 [Slides]: Turnitin plagiarism checking tool

Lecture 8 [Slides]: LaTeX - document classes, packages,  text formatting

Lecture 9 [Slides]: LaTeX - Lists, figures, tables, followed by practice

Lecture 10 [Slides]: LaTeX - Bibliography (adding them manually and with .bib file), demonstration

Lecture 11 [Slides]: LaTeX - document customization (geometry, fancyhdr, newcommand/renewcommand, theorems) followed by practice

Lecture 12 [Slides]: Presentation tools -- keynote, ppt, beamer; demonstrations

Lecture 13 [Slides]: MATLAB: Basics, arrays, and operations on them

Lecture 14 [Slides]: MATLAB: Symbolic calculations with matrices

Lecture 15 [Slides]: MATLAB: Plotting 2D graphs

Lecture 16 [Slides]: MATLAB: Plotting 3D graphs

Tutorial 1: MATLAB Plotting

Lecture 17 [Slides]: MATLAB: Plotting bars and histograms

Lecture 18 [Slides]: PowerBI: Basic functionalities, data importing, and data cleaning

Tutorial 2: PowerBI practice [employees-10000, people-10000]

Lecture 19 [Slides]: PowerBI: Basic visualizations (stacked and 100% stacked bar charts, line chart, pie chart, cards, tables) and customizations

Tutorial 3: Questions/tasks, StockMarket

Lecture 1 [Slides]: Meaning of research, its types, objectives, and significance.

Lecture 2 [Slides]: Research methodology, writing research documents

Lecture 3 [Slides]: Reviewing the literature: how, where, what

Lecture 4 [Slides]: Research article search tools, journal rankings, and sources to evaluate journals

Lecture 5 [Slides]: Research ethics, presentation tools

Lecture 6 [Slides]: MATLAB: Basics, arrays and operations on them

Lecture 7 [Slides]: MATLAB: Symbolic calculations

Lecture 8 [Slides]: MATLAB: Plotting 2D graphs

Lecture 9 [Slides]: MATLAB: Plotting 3D graphs

Lecture 10 [Slides]: Technical writing (part I)

Quiz-1 solutions: [Click here]

Lecture 11 [Slides]: Technical writing (part II)

Lecture 12 [Slides]: Plagiarism checking, Turnitin demo

Lecture 13 [Slides]: Power BI Module 1 - Introduction to Power BI

Lecture 14 [Slides]: Power BI Module 2 - Data importing and cleaning

Tutorial 1 [Tutorial 1, people-10000.csv, employees-10000.csv]

Lecture 15 [Slides]: Power BI Module 3 - Basic visuals (Part I)

Lecture 16 [Slides]: Power BI Module 3 - Basic visuals (Part II)

Lecture 17 [Slides]: Using DAX for basic calculations

Lecture 18 [Slides]: Data relationships and data modeling

Lecture 19 [Slides]: Advanced visualizations: Funnel chart, scatter chart, waterfall chart

Lecture 20 [Slides]: Interactive reports and dashboard (Slicers and filters)

Lecture 21 [Slides]: Interactive reports and dashboard (Cross-filtering, drill-down, drill-through)

Tutorial 2 [Questions/tasks, StockMarket]

Tutorial 3 [Questions/tasks, Customer_1000]

Lecture 1 [Notes]: Solving system of linear equations using the Gaussian elimination method.

Lecture 2 [Notes]: Breakdown of the Gaussian elimination method and remedies

Lecture 3 [Notes]: Gauss-Jordan method for finding matrix inverse

Lecture 4 [Notes]: Worked out examples of the Gauss-Jordan method

Lecture 5 [Notes]: Definition of a vector space with examples

Lecture 6 [Notes]: More examples of vector spaces, vector subspace definition, examples

Lecture 7 [Notes]: Linear span, examples

Lecture 8 [Notes]: Linear independence, examples

Lecture 9 [Notes]: Basis, dimension, examples

Lecture 10 [Notes]: Linear transformation, kernel, range, and examples

Lecture 11 [Notes]: Rank nullity theorem, examples

Lecture 12 [Notes]: Subspaces associated with a matrix, its rank, and nullity

Lecture 13 [Notes]: Coordinates of a vector relative to an ordered basis

Lecture 14 [Notes]: The coordinate transformation, invertible linear transformation

Lecture 15 [Notes]: Matrix representation of general linear transformation

Lecture 16 [Notes]: Solved examples for matrix representation of linear transformation

Lecture 17 [Notes]: Eigenvalues and eigenvectors for linear transformation

Lecture 18 [Notes]: Examples to find eigenvalues and eigenvectors

Lecture 19 [Notes]: Characteristic polynomial, Cayley-Hamilton theorem, minimal polynomial

Lecture 20 [Notes]: Algebraic and geometric multiplicities

Lecture 21 [Notes]: Diagonalizability of a matrix (Part I)

Lecture 22 [Notes]: Diagonalizability of a matrix (Part II)

Lecture 23 [Notes]: Diagonalizability of a matrix (Part III) and quadratic forms

Lecture 24 [Notes]: Diagonalization of quadratic forms, positive-definite quadratic forms

Lecture 25 [Notes]: Exact differential equations (Part I) - checking exactness and solving

Lecture 26 [Notes]: Exact differential equations (Part II) - Integrating factors

Lecture 27 [Notes]: Bernoulli equation (reduction to linear form), Verhulst equation (logistic equation)

Lecture 28 [Notes]: Orthogonal trajectories, Initial Value Problem: Picard's existence theorem

Lecture 29 [Notes]: Picard's existence and uniqueness theorems with examples

Lecture 30 [Notes]: Picard's iteration method

Lecture 31 [Notes]: Homogenous second-order linear DE, linear dependence of two solutions, Wronskian, general solution theorem

Lecture 32 [Notes]: Method of reduction of order

Lecture 33 [Notes]: Second or higher order linear ODEs with constant coefficients

Lecture 34 [Notes]: Higher-order linear ODEs: C.F., P.I., Wronskian

Lecture 35 [Notes]: Method of variation of parameters

Lecture 36 [Notes]: Inverse operator method (Part I)

Lecture 37 [Notes]: Inverse operator method (Part II)

Lecture 38 [Notes]: First-order PDE formation

Lecture 39 [Notes]: Useful techniques in inverse power method

Lecture 40 [Notes]: Lagrange's method to solve first-order quasi-linear PDEs

Lecture 41 [Notes]: Euler-Cauchy method

Approximating and computing area [Notes]

The definite integral [Notes]

The indefinite integral [Notes]

I prepared tutorials (assignments) based on each lecture, graded them, and discussed them in class

The tutorial sheets can be found here

Priyanka Dutta [LinkedIn] and I helped the professors conduct online lectures during COVID-19 

We uploaded their lectures to YouTube and shared the lecture links on Moodle for the students to access them (5 days a week, 2 to 3 lectures a day)