Subject-Wise Syllabus of TS ECET 2025
The subject-wise TS ECET 2025 syllabus can be found in the below table. All aspirants preparing for the exam must have thorough knowledge of the syllabus.
Syllabus for B.Sc Mathematics
| Units | Topics |
|---|
| Unit 1: Partial Differentiation | 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
|
| Unit 2: Curvature and Lengths of Plane Curves | - 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)
|
| Unit 3: Differential Equations of First Order | - 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 contains x or y
- Equations Homogeneous in x and y
- Equations of the First degree in x and y
- Clairaut’s equation.
|
| Unit 4: Higher order Linear Differential Equations and PDE | - 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,
|
| Unit 5: Sequences and Series | - 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.
|
| Unit 6: Continuity, Differentiation and Riemann Integral | - 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.
|
| Unit 7: Groups | - 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
|
| Unit 8: Rings | - Rings
- Examples of Rings
- Properties of Rings
- Subrings
- Integral Domains
- Fields
- Characteristics of a Ring
- Ideals, Factor Rings, Prime Ideals and Maximal Ideals
- Ring Homomorphism’s and isomorphisms.
|
| Unit 9: Vector Spaces | - 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
|
| Unit 19: Diagonalization and Orthogonality | - 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
|
Syllabus For Analytical Ability
Data sufficiency: A question is given along with data in the form of two short statements labelled A and B. If statement A by itself is enough to provide an answer, then Answer (A) should be considered. If only statement B by itself can provide a response, then Answer (B) may apply. If both statements A and B, which together describe all relevant information needed to give a response, are insufficient by themselves , this indicates that additional information must be provided before answering the question. In such case, Answer (C) is appropriate if some other data or facts presented along with A & B are needed to arrive at an answer while Answer (D) applies if no additional data or supporting factors need to be taken into account - everything you need to know is explicitly present either in statement set A+B alone or even better is implicitly provided by the context of the situation without being specifically mentioned anywhere at all.
Sequences and Series: Analogies of numbers and letters, completion of blank spaces, following the pattern in A: B: C: D relationship, odd thing out; Missing number in a sequence or a series.
Data Analysis: In this question type, you may be provided with data in the form of Table, Graph, Bar Diagram or Pie Chart. Answer questions based upon the given data either by analyzing it and answering questions directly as they appear in the passage or by comparing and contrasting it to other data provided in the same passage.
Coding and Decoding Problems: A code pattern of the English alphabet is given. The word or group of letters given to us after the coded string of letters are to be decoded based on the given alphabet.
Date, Time and Arrangement Problems: Dates, Time, and Schedules; Arrangements of Seats, Letters and Symbols Interpretation
Communicative English (50 Marks)
Vocabulary
- Antonyms
- Synonyms
- Single word substitues
- Idioms & Phrasal words
Grammar
- Tenses
- Prepositions
- Active & Passive Voice
Correction of sentences
Reading & Spelling
Reading Comprehension
Candidates preparing for TS ECET 2025, can check the detailed syllabus Course-wise & Subject wise with downloadable PDF links which will make the preparation process more efficient
