Calculus, Linear Algebra, Complex variables, Ordinary Differential Equations, Probability, and Statistics are some topics covered in the GATE Engineering Mathematics syllabus 2024.
GATE Engineering Mathematics syllabus 2024 includes topics from Calculus, Linear Algebra, Complex variables, Ordinary Differential Equations, Probability & Statistics, and Numerical Methods. This section constitutes 15% of the total weightage in the exam. It is a common paper, and everyone has to attend it.
GATE 2024 is one of the toughest exams in India, and is a highly competitive exam. The cutoffs for admissions are on the higher side of the graph.
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GATE Engineering Mathematics Syllabus 2024
GATE engineering mathematics syllabus 2024 is compulsory and comes under the XE paper section. Further, it is a compulsory subject and carries 15 marks.
Section 1: Linear Algebra
- Algebra of matrices
- Inverse and rank of a matrix
- System of linear equations
- Symmetric, skew-symmetric and orthogonal matrices
- Determinants
- Eigenvalues and eigenvectors
- Diagonalisation of matrices
- Cayley-Hamilton Theorem
Section 2: Calculus
- Calculus Functions of single variable: Limit, continuity and differentiability
- Mean value theorems
- Indeterminate forms and L'Hospital's rule
- Maxima and minima
- Taylor's theorem
- Fundamental theorem and mean value-theorems of integral calculus
- Evaluation of definite and improper integrals
- Applications of definite integrals to evaluate areas and volumes
- Functions of two variables: Limit, continuity and partial derivatives
- Directional derivative
- Total derivative
- Tangent plane and normal line
- Maxima, minima and saddle points
- Method of Lagrange multipliers
- Double and triple integrals, and their applications
- Sequence and series: Convergence of sequence and series
- Tests for convergence
- Power series
- Taylor's series
- Fourier Series
- Half range sine and cosine series
Section 3: Vector Calculus
- Gradient, divergence and curl
- Line and surface integrals
- Green's theorem, Stokes theorem and Gauss divergence theorem (without proofs)
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Section 4: Complex Variables
- Analytic functions
- Cauchy-Riemann equations
- Line integral, Cauchy's integral theorem and integral formula (without proof)
- Taylor's series and Laurent series
- Residue theorem (without proof) and its applications
Section 5: Ordinary Differential Equations
- First order equations (linear and nonlinear)
- Higher order linear differential equations with constant coefficients
- Second order linear differential equations with variable coefficients
- Method of variation of parameters
- Cauchy-Euler equation
- Power series solutions
- Legendre polynomials, Bessel functions of the first kind and their properties
Section 6: Partial Differential Equations
- Classification of second order linear partial differential equations
- Method of separation of variables
- Laplace equation
- Solutions of one dimensional heat and wave equations
Section 7: Probability and Statistics
- Axioms of probability
- Conditional probability
- Bayes' Theorem
- Discrete and continuous random variables
- Binomial, Poisson and normal distributions
- Correlation and linear regression
Section 8: Numerical Methods
- Solution of systems of linear equations using LU decomposition, Gauss elimination and Gauss-Seidel methods
- Lagrange and Newton's interpolations, Solution of polynomial and transcendental equations by Newton-Raphson method
- Numerical integration by trapezoidal rule, Simpson's rule and Gaussian quadrature rule
- Numerical solutions of first order differential equations by Euler's method and 4th order Runge-Kutta method.
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GATE Engineering Mathematics Syllabus 2024 Best Books
Only some selected books covers the GATE engineering mathematics syllabus 2024. Toppers who opted for this subject suggested the following books to be the best.
You will find these GATE books both online and offline.
| Best Books | Authors |
| Higher Engineering Mathematics | B. S. Grewal |
| Essential Engineering Mathematics | Erwin Kreyszig |
| Advanced Engineering Mathematics | H K Dass |
GATE Engineering Mathematics Syllabus 2024 Important Topics
The GATE engineering mathematics syllabus 2024 is quite elaborate; thus, focusing on each chapter becomes difficult. Therefore, we have added important topics for GATE engineering mathematics to ease preparation.
| Name of Chapter | Important Topics in Engineering Mathematics |
| Linear Algebra |
Eigenvalues and Vectors Rank and Determinant of Matrices Systems of Linear Equations |
| Calculus |
Maxima and Minima in single variable calculus Vector calculus Gradient, Divergence, and Curls Vector Integral Theorems |
| Differential Equations |
First-order equations Bernoulli's Equation, Euler's Differential Equation |
| Probability and Statistics |
Bayes' Theorem, Random Variables like Poisson's Distribution Statistics, mean, median, mode Coefficient of correlation |
| Complex Analysis | Cauchy-Riemann EquationsResidue Method of Integration and the Taylor series |
| Numerical Methods |
Trapezoidal Rule and Simpson’s Rule Newton-Raphson and Bisection method Numerical integration techniques |
| Transform Theory | Laplace and inverse Laplace transforms |
| Discrete Mathematics |
Mathematical Logic, Relations, and Functions Finding tautology, satisfiability, and equivalences of given propositional statements Graph connectivity and colouring Finding the number of edges, vertices, or components graph Checking isomorphism Euler circuit, Hamiltonian cycle Complete graph, bipartite graph, regular graph, cycle graph, and line graph |
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GATE Engineering Mathematics Syllabus 2024 Preparation Tips
While you start preparing for the GATE exam, there will be various sources of information. It is important that you set your focus on one thing at a time.
Here are some tips to cover GATE engineering mathematics syllabus 2024:
- Start your preparation by assessing the entire GATE engineering mathematics syllabus 2024 and marking the important points.
- Next, check the exam pattern, and ensure you know what to choose and what to avoid.
- If you want to ace your game, get help from the best books available.
- Practice, practice, and practice; this is what will return your best results.
- Arrive for mock tests and remember that revision is the key to success.
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