Engineering Mathematics Books For Gate Exam Pdf

IIT Kharagpur has released GATE Mathematics (MA) Syllabus 2022 on the official website. No changes have been made to the syllabus this year. GATE 2022 Mathematics Paper will have a total of 65 questions. Out of these total questions, 55 questions will be based on Mathematics and the remaining questions will be based on the General Aptitude section. The candidates who opted for Mathematics as their first paper in GATE 2022 can appear for Computer Science and Information Technology (CS), Geomatics Engineering (GE), Physics (PH), or (ST) as their second paper. Check GATE 2022 Exam Pattern

Major topics that are covered in GATE Mathematics Syllabus 2022 include Calculus, Linear Algebra, Real Analysis, Algebra, Functional Analysis, Numerical Analysis, etc. The students are advised to attempt as many previous year question papers as possible and analyze their mistakes. This would enable them to gain confidence and form a better judgment regarding GATE Mathematics Syllabus 2022. Check GATE Paper Analysis .

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GATE MA Syllabus

GATE Mathematics Syllabus 2022

There are 11 chapters in the GATE Mathematics Syllabus. Each chapter has many subtopics. The complete syllabus of Mathematics paper is given below.

Section 1: Calculus

Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange's multipliers;
Double and Triple integrals and their applications to area, volume and surface area; Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green's theorem, Stokes' theorem, and Gauss divergence theorem.

Section 2: Linear Algebra

Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank and nullity; systems of linear equations, characteristic polynomial, eigenvalues and eigenvectors, diagonalization, minimal polynomial
Cayley-Hamilton Theorem, Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, symmetric, skew-symmetric
Hermitian, skew-Hermitian, normal, orthogonal and unitary matrices; diagonalization by a unitary matrix, Jordan canonical form; bilinear and quadratic forms.

Section 3: Real Analysis

Metric spaces, connectedness, compactness, completeness; Sequences and series of functions, uniform convergence, Ascoli-Arzela theorem;Weierstrass approximation theorem; contraction mapping principle
Power series; Differentiation of functions of several variables, Inverse and Implicit function theorems; Lebesgue measure on the real line, measurable functions; Lebesgue integral, Fatou's lemma, monotone convergence theorem, dominated convergence theorem.

Section 4: Complex Analysis

Functions of a complex variable: continuity, differentiability, analytic functions, harmonic functions; Complex integration: Cauchy's integral theorem and formula
Liouville's theorem, maximum modulus principle, Morera's theorem; zeros and singularities; Power series, radius of convergence
Taylor's series and Laurent's series; Residue theorem and applications for evaluating real integrals; Rouche's theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius transformations.

Section 5: Ordinary Differential equations

First order ordinary differential equations, existence and uniqueness theorems for initial value problems, linear ordinary differential equations of higher order with constant coefficients
Second order linear ordinary differential equations with variable coefficients; Cauchy-Euler equation, method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties; Systems of linear first order ordinary differential equations
Sturm's oscillation and separation theorems, Sturm-Liouville eigenvalue problems, Planar autonomous systems of ordinary differential equations: Stability of stationary points for linear systems with constant coefficients, Linearized stability, Lyapunov functions.

Section 6: Algebra

Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups,Group action,Sylow's theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains
Principal ideal domains, Euclidean domains, polynomial rings, Eisenstein's irreducibility criterion; Fields, finite fields, field extensions,algebraic extensions, algebraically closed fields.

Section 7: Functional Analysis

Normed linear spaces, Banach spaces, Hahn-Banach theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner-product spaces
Hilbert spaces, orthonormal bases, projection theorem,Riesz representation theorem, spectral theorem for compact self-adjoint operators.

Section 8: Numerical Analysis

Systems of linear equations: Direct methods (Gaussian elimination, LU decomposition, Cholesky factorization), Iterative methods (Gauss-Seidel and Jacobi) and their convergence for diagonally dominant coefficient matrices; Numerical solutions of nonlinear equations: bisection method, secant method, Newton-Raphson method, fixed point iteration; Interpolation
Lagrange and Newton forms of interpolating polynomial, Error in polynomial interpolation of a function; Numerical differentiation and error.
Numerical integration: Trapezoidal and Simpson rules, Newton-Cotes integration formulas, composite rules, mathematical errors involved in numerical integration formulae; Numerical solution of initial value problems for ordinary differential equations: Methods of Euler, Runge-Kutta method of order 2.

Section 9: Partial Differential Equations

Method of characteristics for first order linear and quasilinear partial differential equations; Second order partial differential equations in two independent variables: classification and canonical forms, method of separation of variables for Laplace equation in Cartesian and polar coordinates, heat and wave equations in one space variable
Wave equation: Cauchy problem and d'Alembert formula, domains of dependence and influence, non-homogeneous wave equation; Heat equation: Cauchy problem; Laplace and Fourier transform methods.

Section 10: Topology

Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, quotient topology, metric topology, connectedness, compactness, countability and separation axioms, Urysohn's Lemma.

Section 11: Linear Programming

Linear programming models, convex sets, extreme points;Basic feasible solution,graphical method, simplex method, two phase methods, revised simplex method ; Infeasible and unbounded linear programming models, alternate optima; Duality theory, weak duality and strong duality; Balanced and unbalanced transportation problems
Initial basic feasible solution of balanced transportation problems (least cost method, north-west corner rule, Vogel's approximation method); Optimal solution, modified distribution method; Solving assignment problems, Hungarian method.

Direct link to download GATE Mathematics (MA) Syllabus PDF

GATE MA Exam Pattern

GATE 2022 Exam Pattern of Mathematics

GATE 2022 Exam Pattern varies for different disciplines. Given below is the examination pattern for GATE Mathematics.

Mode of Examination: Online
Duration of Exam: 3 hours
Types of Questions: MCQs and NAT
Sections: 2 sections – General Aptitude and Subject-based
Total Questions: 65 questions
Total Marks: 100 marks
Negative Marking: For MCQs only

Weightage of Sections in GATE Mathematics 2022

GATE Mathematics Syllabus 2022 is divided into two sections. The below table describes the distribution of marks in each section.

Section	Distribution of Marks	Total Marks	Types of questions
GA	5 questions of 1 mark each 5 questions of 2 marks each	15 marks	MCQs
MA- Subject-Based	25 questions of 1 mark each 30 questions of 2 marks each	85 marks	MCQs and NATs

GATE Mathematics Marking Scheme 2022

Type of question	Negative marking for wrong answer
MCQs	1/3 for 1 mark questions 2/3 for 2 marks questions
NATs	No negative marking

GATE MA Weightage

GATE Mathematics Syllabus 2022: Weightage of Topics

The students are advised to commence their GATE Preparation after going through the weightage of each topic mentioned. This will save them a lot of trouble and effort.

Important Topics	Weightage of Topics (In %)
Linear Algebra	10%
Complex Variables	10%
Vector Calculus	20%
Calculus	10%
Differential Equation	10%
Probability & Statistics	20%
Numerical Methods	20%

Check GATE Paper Analysis

GATE MA Preparation

GATE Preparation 2022 for Mathematics

To assist in the GATE Mathematics Preparation 2022, the following sections have been curated. The students are advised to check out the following and avail of the benefits.

Best Books for GATE Mathematics (MA) 2022

Given below are the recommended books for GATE Mathematics 2022 that would be beneficial for the students.

Books	Author/Publisher
Chapterwise Solved Papers Mathematics GATE	Suraj Singh, Arihant Publication
GATE Engineering Mathematics for All Streams	Abhinav Goel, Arihant Publication
GATE: Engineering Mathematics	ME Team, Made Easy Publications
Wiley Acing the Gate: Engineering Mathematics and General Aptitude	Anil K. Maini, Wiley
Higher Engineering Mathematics	B.S. Grewal, Khanna Publishers

Also Check: GATE Recommended Books

GATE MA Previous Year Question Paper

Given below are the links for GATE MA Previous Year Question Papers along with their answer key.

GATE MA Question Paper

GATE Mathematics Sample Questions

Sample Question 1:

Sample Question 2:

GATE Syllabus 2022 of Other Subjects

Other than Mathematics there are other 24 subjects for which GATE 2022 will be conducted. Candidates can check the syllabus of their respective subjects from the links provided below in the table:

Frequently Asked Questions

GATE Mathematics Syllabus 2022 FAQs

Ques. What will be the subjects or sections that one needs to cover in the GATE 2022 Mathematics paper?

Ans: GATE 2022 Mathematics syllabus includes General Aptitude and core subject i.e. Mathematics. The engineering mathematics sections which are there in various subjects of GATE will not be the part of mathematics. The major sections from mathematics are:

Chapter 1 – Linear Algebra
Chapter 2 – Complex Analysis
Chapter 3 – Real Analysis
Chapter 4 – Ordinary Differential Equations
Chapter 5 – Algebra
Chapter 6 – Functional Analysis
Chapter 7 – Numerical Analysis
Chapter 8 – Partial Differential Equations
Chapter 9 – Topology
Chapter 10 – Calculus
Chapter 11 – Linear Programming

Ques. What will be the weightage of topics and marking scheme in GATE Mathematics 2022?

Ans: The weightage and marking scheme is provided below in the table:

Section	Distribution of Marks	Total Marks	Types of questions
GA	5 questions of 1 mark each 5 questions of 2 marks each	15 marks	MCQs
MA- Subject-Based	25 questions of 1 mark each 30 questions of 2 marks each	85 marks	MCQs and NATs

Ques. Will there be any negative marking in GATE Mathematics 2022?

Ans: Yes. For every wrong answer, marks will be deducted depending on the total marks of those questions. Moreover, for attempting wrong NAT questions no marks will be deducted.

Type of question	Negative marking for wrong answer
MCQs	1/3 for 1 mark questions 2/3 for 2 marks questions
NATs	No negative marking

Ques. What are the best books for GATE Mathematics preparation 2022?

Ans: Candidates can refer to the following books:

Chapterwise Solved Papers Mathematics GATE – By Suraj Singh, Arihant Publication
GATE Engineering Mathematics for All Streams – By Abhinav Goel, Arihant Publication

Ques. What is the paper code for GATE Mathematics Syllabus 2022?

Ans. The paper code for GATE Mathematics is MA. The students are advised to check the eligibility criteria before appearing for GATE 2022. Check GATE Eligibility

Ques. Which is the most important topic for GATE Mathematics Syllabus 2022?

Ans. The most important topics for GATE Mathematics Syllabus 2022 are Probability and Statistics, Numerical Methods, and Vector Calculus. However, the students are advised to go through every topic mentioned in the syllabus to score the desired marks.

Ques. What will be the difficulty level of GATE Mathematics Syllabus 2022?

Ans. The difficulty level of GATE Mathematics 2022 can be estimated by checking out GATE Paper Analysis. The candidates are advised to practice daily and try to solve every difficult question. In this case, they won't find GATE 2022 difficult.

Ques. What is the syllabus for calculus in GATE Mathematics Syllabus 2022?

Ans. The syllabus for calculus in GATE Mathematics Syllabus 2022 consists of:

Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange's multipliers;
Double and Triple integrals and their applications to area, volume and surface area; Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green's theorem, Stokes' theorem, and Gauss divergence theorem.

*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College.