Welcome to the B.Tech Computer Engineering (B.Tech-CE) repository — a curated, modular, and scalable digital workspace developed by Jagdev Singh Dosanjh to power next-generation AI-enabled learning environments under the SmartSchoolAI initiative.
This repository is designed to serve as the backbone for organizing course materials, quizzes, and AI-assisted teaching tools for B.Tech Computer Engineering students. It aligns with the vision of SmartSchoolAI: delivering adaptive, interactive, and personalized learning experiences across technical disciplines.
- 📚 Organized by Subjects – Categorized modules for Mathematics, Computer Science, Engineering Physics, and more.
- 🧩 Smart Content Blocks – Includes JSON-based quizzes, theory outlines, and concept explainers ready to power AI workflows.
- 🤖 AI Integration Ready – Designed to work seamlessly with tools like Streamlit, FastAPI, and OpenAI APIs.
- 📈 Scalable Modules – Can be expanded to include new semesters, subjects, and adaptive feedback mechanisms.
- 💡 Reference Aligned – Content is crafted with academic relevance to B.Tech syllabi (especially for Indian institutions).
B.Tech-CE/ ├── Mathematics/ │ ├── Matrices/ │ └── Rank-Nullity/ ├── Computer-Programming/ │ └── C_Basics/ ├── Quizzes/ │ ├── matrices_quiz.json │ └── rank_nullity_quiz_set.json ├── README.md
This repository feeds into the larger SmartSchoolAI mission:
“To empower educators with AI-ready tools and modular digital resources that scale accessibility, personalization, and impact.”
You can read more about connected tools like:
- BioEd Tutor – interactive biology explanations via LLMs
- Virtual Chemistry Lab – simulation-driven learning
- Streamlit Dashboards – personalized portals for students and teachers
- Python
- Streamlit
- OpenAI API
- FastAPI
- JSON, Markdown, and good ol’ pedagogy!
You're welcome to suggest improvements, raise issues, or collaborate. This is a growing knowledge base — help us make it better for learners everywhere.
Maintained by Jagdev Singh Dosanjh
Faculty, Computer Science — Government School (India)
Passionate about AI in education | Interdisciplinary learning | Student success
“True education is not about remembering facts — it’s about building minds that can think, question, and create.”
— SmartSchoolAI Philosophy
This module forms the mathematical foundation for first-semester students of Computer Engineering, blending linear algebra, calculus, and vector analysis into a toolkit essential for engineering problem solving. The course is divided into four major sections:
📊 Total Lectures: 10
📚 Tags: Rank, Inverse, Eigenvalues, Diagonalization, Cayley-Hamilton
- Introduction to Matrices – Basic operations, types of matrices, notation.
- Inverse and Rank of a Matrix – Elementary transformations, row-echelon form, Gauss-Jordan method.
- Rank-Nullity Theorem – Relationship between rank and solution space for homogeneous systems.
- Symmetric, Skew-Symmetric and Orthogonal Matrices – Definitions and algebraic properties.
- Hermitian and Skew-Hermitian Matrices – Matrices equal to their conjugate transpose (or its negative).
- Unitary Matrix – Complex analog to orthogonal matrices.
- Determinants – Properties, cofactor expansion, effect of row operations.
- System of Linear Equations – Matrix representation and solution methods (Cramer's rule, matrix inverse, row operations).
- Eigenvalues and Eigenvectors – Characteristic polynomial, algebraic and geometric multiplicities.
- Diagonalization – Conditions, process, and applications.
- Cayley-Hamilton Theorem – A matrix satisfies its own characteristic equation; applied to find matrix inverse.
📊 Total Lectures: 10
📚 Tags: Convergence, Power Series, Tests, Alternating Series
- Convergence and Divergence – Criteria and understanding divergence behavior.
- Geometric Series Test – Closed form and convergence criterion.
- Positive Term Series – Fundamental behavior and convergence nature.
- p-Series Test – Series of the form Σ(1/nᵖ) and its thresholds.
- Comparison Test – Direct and limit comparisons with known convergent/divergent series.
- D’Alembert’s Ratio Test – Useful for factorial and exponential growth.
- Cauchy’s Root Test – Based on nth roots, powerful for power series.
- Integral Test – Continuous analog using improper integrals.
- Raabe’s Test, Logarithmic Test, Gauss’s Test – More nuanced series evaluations (proofs excluded).
- Alternating Series & Leibnitz’s Rule – Alternating convergence and error bounds.
- Power Series – Form, manipulation, and function approximation.
- Radius and Interval of Convergence – Determining valid input ranges.
📊 Total Lectures: 12
📚 Tags: Partial Derivatives, Taylor Expansion, Maxima-Minima
- Partial Derivatives – Functions of multiple variables, mixed derivatives.
- Euler’s Theorem – Homogeneous functions and identity relation.
- Maclaurin’s and Taylor’s Series – Expansion of single and multivariable functions.
- Maxima and Minima of Multivariable Functions – First and second derivative tests.
- Lagrange Multiplier Method – Optimization with constraints.
- Multiple Integrals – Double and triple integrals with change of order and limits.
- Applications – Surface area and volume calculations using integrals.
📊 Total Lectures: 12
📚 Tags: Gradient, Divergence, Curl, Theorems of Vector Integration
- Scalar and Vector Fields – Definitions and field representation.
- Vector Differentiation – Limit, derivative, chain rules.
- Gradient – Directional rate of change of scalar fields.
- Divergence and Curl – Measuring flux density and rotational tendency.
- Line Integral – Work done by a vector field along a path.
- Surface and Volume Integrals – Generalization of scalar area and volume.
- Green’s Theorem – Conversion of line integral to double integral.
- Stokes’ Theorem – Relating surface integral of curl to boundary line integral.
- Gauss’ Divergence Theorem – Conversion of volume integral of divergence into surface integral (no proofs included).
By the end of this module, students will:
- Compute the rank, eigenvalues, and inverse of matrices using the Cayley-Hamilton Theorem.
- Analyze and determine the convergence of series using multiple standard tests.
- Apply multivariate calculus to solve optimization problems and compute geometric quantities.
- Understand and apply vector field analysis using gradient, divergence, and curl alongside the major vector integral theorems.
- Louis A. Pipes — Applied Mathematics for Engineers and Physicists
- Erwin Kreyszig — Engineering Mathematics
- B.S. Grewal — Higher Engineering Mathematics
🧩 For AI-powered quizzes and topic-wise flashcards based on these sections, check the /Quizzes/ directory in this repository.