TS ECET 2026 Syllabus PDF - Download Latest TS ECET Syllabus for All Subjects

Unit 1: Matrices

Unit 2: Trigonometry  

Unit 3: Analytical Geometry 

Unit 4: Differentiation/Integration and its Applications

Unit 5: Integration and its Applications

Unit 6: Differential Equations

Unit 7: Laplace Transforms and Fourier Series

Unit 8: Probability and Statistics

Unit 1: Units and dimensions

Unit 2:  Elements of vectors

Unit 3: Kinematics and Friction

Unit 4: Work, Power, and Energy

Unit 5: Simple Harmonic Motion and Sound

Unit 6: Heat and Thermodynamics

Unit 6: Modern physics

Unit 1 Fundamentals of chemistry, Atomic structure, Chemical Bonding

Unit 2: Solutions

Unit 3: Acids and Bases

Unit 4: Principles of Metallurgy

Unit 5: Electrochemistry

Unit 6: Corrosion

Unit 7: Water Technology

Unit 8: Polymers

Unit 9: Fuels

Material Technology

 Material & Energy Balances

Organic Chemical Technology

Inorganic Chemical Technology

Fluid Mechanicals

Heat Transfer

Mechanical Unit Operations

Thermodynamics and Reaction Engineering

Mass Transfer Operations

Instrumentation & Process control

Digital Electronics

Microprocessors

Computer Organization

C Programming and Data Structures

Computer Hardware & Networking

Operating Systems

RDBMS:

Object Oriented Programming Through C++

Java Programming:

Internet Programming:

Basic electrical engineering

Electrical & Electronic measuring instruments

D.C Machines

A.C Circuits

A.C Machines

A.C. Motors

Electrical power systems

Protection of power systems

Electrical estimation and utilisation

Basic electronics

Digital electronics

Power electronics

PLC & C Language

Workshop technology

Production technology & metrology

Machine drawing & production drawing

CAD/CAM

Thermodynamics

Heat power engineering

Solid mechanics

Design of machine elements

Fluid mechanics & hydraulic machinery

Engineering materials

Industrial management

Elements of mining

Mining geology

Methods of working coals

Opencast mining

Rock mechanics & Strata control

Mine surveying

Mining machinery

Mine management & entrepreneurship

Electronics devices & circuits

Circuit theory

Industrial electronics

Communication systems

Digital electronics

Microcontrollers, Programming, Interfacing & applications

Consumer electronics

Data communications & computer networks

Electrical engineering, Electrostatic & Batteries

Electronics & amplifiers

Digital electronics

Process instrumentation

Control engineering

Linear IC applications

Microcontroller

Elementary principles of Mettalurgical

Fuels & Refractories

Mettalurgical thermodynamics

Physical mettalurgy

Heat treatment technology

Ferrous extractive mettalurgy

Material testing

Mechanical mettalurgy

Foundry technology

Welding technology

Engineering mechanics

Strength of materials

Reinforced concrete structures

Surveying

Hydraulics

Irrigation engineering

Transformation engineering

Water supply & sanitary engineering

Building material & construction practice

Functions of two variables

Neighborhood of a point(a, b)

Continuity of a Function of two
variables

Continuity at a point

Limit of a Function of two variables

Partial Derivatives - Geometrical representation of a Function of two Variables - Homogeneous Function

Theorem on Total Differentials

Composite Functions

Differentiation of Composite Functions

Implicit Functions

Equality of fxy(a,b) and fyz(a,b)

Taylor’s theorem for function of two variables

Maxima and Minima of functions of two variables

Lagrange’s Method of undetermined
multipliers

Definition of Curvature

Radius of Curvature

Length of Arc as a Function

Derivative of arc

Radius of Curvature

Cartesian Equations

Cartesian Equations

Newtonian Method

Centre of Curvature

Chord of Curvature

Evolutes and Involutes

Properties of the evolutes

One Parameter Family of Curves,

Consider the family of straight lines.

Determination of Envelope.

Lengths of Plane Curves: Expression for the lengths of curves y = f (x),

Expressions for the length of arcs x =
f(y); x = f(t), y = φ(t); r=f(θ)

Variables and Separable method

Homogeneous Differential Equations

DifferentialmEquations Reducible to Homogeneous Form

Linear Differential Equations

Differential Equations Reducible to Linear Form

Exact differential equations

Integrating Factors

Change in variables.

Differential Equations of first order but not first degree: Equations Solvable for p

Equations solvable for y

Equations Solvable for x Equations that do not contain x or y

Equations Homogeneous in x and y

Equations of the First degree in x and y

Clairaut’s equation.

Higher order Linear Differential Equations: Solution of homogeneous linear

Differential equations with constant coefficients

Solution of non-homogeneous differential equations P (D)y = Q(x) with constant coefficients by means of polynomial operators when Q(x) = eୟ୶, b sin ax, b cos ax, bx୩, Veୟ୶

Method of undetermined coefficients

Method of variation of parameters

Linear differential equations with non-constant coefficients

the Cauchy-Euler Equation

Legendre’s Linear EquationsPartial Differential Equations: Formation and solution,

Sequences: Limits of Sequences

Limit Theorems for Sequences

Monotone Sequences and Cauchy Sequences

Subsequences, Lim sup and Lim infimum, Series,

Alternating Series and Integral Tests.

Continuity: Continuous Functions

Properties of Continuous Functions

Uniform Continuity

Limits of Functions

Basic properties of the derivative

The mean value theorem

L-Hospital Rule

Taylor’s theorem.

The Riemann Integral,

Properties of Riemann Integral,

Fundamental Theorem of Calculus.

Definition and Examples of Groups

Elementary Properties of Groups

Finite Groups, Subgroups, Subgroup Tests, Cosets and Lagrange’s Theorem Properties of Cosets,

Cyclic Groups

Properties of Cyclic Groups

Normal Subgroups and Factor Groups

Group Homomorphism’s

Properties of Homomorphism’s

The First Isomorphism Theorem, Automorphisms

Permutation Groups: Definition and Properties of Permutations

Isomorphisms, Cayley’s Theorem

Rings

Examples of Rings

Properties of Rings

Subrings

Integral Domains

Fields

Characteristics of a Ring

Ideals, Factor Rings, Prime Ideals and Maximal Ideals

Ring Homomorphisms and Isomorphisms.

Vector Spaces and Subspaces -Null Spaces, Column Spaces,, and Linear Transformations

Linearly Independent Sets, Bases, Coordinate Systems

The Dimension of a Vector spaces

Rank

Change of Basis

Eigen values and Eigenvectors

The Characteristic Equation

Diagonalization, Eigenvectors of Linear Transformations

Inner Product spaces

Length, and Orthogonality

Orthogonal Sets

Orthogonal Projections

The Gram-Schmidt Process