📘 Mathematics Syllabus Complete Guide with Topics, Concepts & FAQs
.jpg "Gate 2026 Mathematics Engineering Exam Syllabus Breakdown") |
| Gate 2026 Mathematics Engineering Exam Syllabus Breakdown |
🧮 Calculus
Study functions with multiple variables including continuity, partial and total derivatives, directional derivatives, and optimization using Lagrange multipliers. Applications include double/triple integrals to calculate area, volume, and surface area. Vector calculus topics include gradient, divergence, curl, line/surface integrals, and theorems like Green’s, Stokes’, and Gauss divergence.
🔢 Linear Algebra
Learn about vector spaces, matrices, linear transformations, rank, nullity, eigenvalues/eigenvectors, and diagonalization. Topics include orthonormalization (Gram-Schmidt), Hermitian and unitary matrices, Jordan form, bilinear and quadratic forms, and matrix factorizations.
📐 Real Analysis
Dive into metric spaces, compactness, convergence of function sequences, uniform convergence, and theorems like Ascoli-Arzela and Weierstrass. Topics also include differentiation of multivariable functions, inverse and implicit function theorems, and Lebesgue integration theory.
🌀 Complex Analysis
Study analytic and harmonic functions, complex integration using Cauchy’s theorems, and Laurent/Taylor series. Includes residue theorem for real integrals, conformal mappings, Mobius transformations, and key theorems like Liouville’s, Rouche’s, and Schwarz Lemma.
📊 Ordinary Differential Equations (ODEs)
Focus on first and second-order ODEs, existence and uniqueness, Laplace transform method, and power series solutions. Learn about Bessel and Legendre functions, systems of ODEs, Sturm-Liouville problems, and stability analysis using Lyapunov’s method.
➗ Algebra
Understand group theory, homomorphisms, Sylow’s theorems, ring theory, polynomial rings, fields, and field extensions. Topics also cover unique factorization, Euclidean domains, and Eisenstein’s criterion.
📚 Functional Analysis
Learn about Banach and Hilbert spaces, inner-product spaces, orthonormal sets, projection theorems, Hahn-Banach theorem, uniform boundedness principle, and the spectral theorem for compact self-adjoint operators.
📉 Numerical Analysis
Covers solving linear systems using Gaussian elimination, LU decomposition, iterative methods, root-finding algorithms (Newton-Raphson, bisection), interpolation (Lagrange, Newton), numerical differentiation and integration, and solving ODEs using Euler and Runge-Kutta methods.
🧩 Partial Differential Equations (PDEs)
Study PDEs using methods like characteristics and separation of variables. Learn about heat, wave, and Laplace equations, Cauchy problems, and transform methods (Laplace and Fourier) for solutions.
🔗 Topology
Get introduced to open and closed sets, bases, subspace and product topologies, metric spaces, compactness, connectedness, countability, separation axioms, and Urysohn’s Lemma.
📈 Linear Programming
Learn about LP models, convexity, graphical and simplex methods, duality, and solutions to transportation and assignment problems using Hungarian and MODI methods. Covers two-phase and revised simplex methods.
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❓ Frequently Asked Questions (FAQs)
What are the most important topics in the mathematics syllabus?
Key topics include Calculus, Linear Algebra, Real and Complex Analysis, Differential Equations, and Linear Programming. These are crucial for competitive exams and higher studies.
Is this syllabus suitable for engineering students?
Yes, this is ideal for B.Tech, M.Tech, B.Sc, and M.Sc students, especially in engineering, computer science, and applied mathematics programs.
Can I use this for GATE or NET preparation?
Absolutely! This syllabus aligns closely with the GATE and CSIR-NET Mathematics exams.
Where should beginners start?
Start with Calculus and Linear Algebra. They form the foundation for most other advanced topics like Differential Equations and Functional Analysis.
