Matrices, Linear equations, and solvability:
Vector spaces
Basis and dimension
Linear transforms
Similarity of matrices

Rank-Nullity theorem and its applications:
Eigenvalues and eigenvectors
Cayley-Hamilton theorem and diagonalization
Inner-product spaces
Gram-Schmidt process

Optimization:
Unconstrained optimization: Gradient descent and Stochastic gradient descent methods.
Constrained optimization: Lagrange multiplier, Linear and dynamic programming, Bellman's principle of optimality.

Module 1: Audience analysis and adaptation.

Module 2: Technical writing formats and styles (e.g., reports, minutes, posters, proposals, manuals, instructions), Writing style and tone, Clarity, conciseness, and coherence, Introduction to Technical Writing: Document planning and organization.

Module 3: Reading and appreciating stories, poems, essays, Comprehensive questions and answers, Listening and note taking video lectures.

Module 4: short plays, individual presentations, group discussions, debates
 

Introduction to different paradigms of programming: Imperative - Object Oriented - Functional- Logic Imperative and Object-oriented Programming - Role of Types - Static and Dynamic Type Checking - Scope rules ; Grouping Data and operations, Information Hiding and Abstract Data Types, Objects, Inheritance, Polymorphism, Templates. Functional Programming - Expressions, Evaluation, types, type systems, values and operations, function declarations, lexical scope, lists and programming with lists, polymorphic functions, higher order functions, Data abstraction.

Concept of Mathematical Proof, Logic, Proof by contradiction, Mathematical Induction, Constructive Proofs, Sets, Relations, Illustration of Proof Techniques in various mathematical topics.

Combinatorics: Basic Counting Principles, Inclusion-Exclusion Principle, Binomial/Multinomial Coefficients, Bijections, Double Counting, Pigeon-Hole Principle, Recurrence Relations.
Introduction to Graphs: Basic terminology/Definitions, Isomorphism, Connectivity, Trees, Planarity.
Introduction to abstract algebra: Basics of Groups, Rings, Field, Polynomial Rings.

Mechanics:

Introduction to vectors: linear independence – completeness – basis – dimensionality– inner product – orthogonality – displacement – derivatives of a vector – velocity– acceleration – plane polar coordinates.

Electricity and Magnetism:

Electricity: Electrostatic potential and field due to discrete and continuous charge distributions, energy density in an electric field.

Magnetism:

Big-O notation, Basic data types - Lists, Stacks, Queues, Trees, Abstract data types. 

Advanced data types: Dictionaries, Binary search trees, Balanced search trees, B Trees, Hash tables - Chaining and Open Addressing, Heaps, Priority queues.

Graphs: Basic representation of Graphs, Breadth First search, Disjoint Set Data Structure and application to Minimum Spanning Tree.
Lab Implementation of some of the above data structures, Applications of data structures in solving computational problems.

DC Circuit Analysis: Network Theorems - Thevenin’s theorem, Norton’s theorem, Superposition theorem, Maximum power transfer theorem.
AC Circuit Analysis: Basic concepts of AC circuits – RMS value and average value – Behavior of resistor, capacitor and inductor in AC circuits – Sinusoidal steady state analysis of AC circuits – Power – Power factor - Resonance in AC circuits.

Introduction To Magnetic Theory

• Determination of total hardness of water

• The Nernst equation 

• Potentiometry

 • Conductometry

 • Determination of phosphoric acid content in soft drink

 • Determination of chloride content in water

 • Validation of Ostwald’s dilution law and solubility product

 • Kinetics of acid hydrolysis of ester

 • Kinetics of sucrose inversion

 • Preparation of polymers

 • Determination of molecular weight of polymers

 • Metallography of steels