Click here for the notes

• • • 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)