Engineering Mathematics Important Topics for GATE 2025

Engineering Mathematics important topics for GATE include topics such as Linear Algebra, Calculus, Complex Analysis, Probability and Statistics and Topology. These topics carry high weightage in the GATE exam.

The Engineering Mathematics comprise a total of 13 marks; out of which scoring at least 10 marks is compulsory to gain top rank in GATE 2025. If aspirants comprehensively study some of the high-weighted topics achieving high scores can be a cakewalk.

This article provides important topics of Engineering Mathematics in GATE 2025. Candidates must check out these topics and strategize their GATE 2025 preparation strategy for the engineering mathematics section.

Engineering Mathematics Important Topics for GATE 2025

Engineering Mathematics is one of the important sections in the GATE 2025 syllabus. Candidates cannot afford to miss preparing for it.

The important point to remember is that effective preparation begins with the identification of the right topics to cover. This strategy can be a game changer as candidates can have a strong hold on topics with higher weightage, allowing them to bag maximum marks.

According to experts, 1 - 3 marks questions are asked from Engineering Mathematics across numerous topics. The following are some GATE 2025 important topics for Engineering Mathematics:

Numerical Method:

• Root Finding Algorithms
• Matrix Methods
• Interpolation and Integrations
• Add on: Numerical Differentiation
• Solution for Ordinary Differential Equations

Linear Algebra:

• Vector Space and Basis
• Matrix Algebra (Types of Square Matrix, Determinant)
• Eigen Values and Eigenvectors
• Linear Dependence and Independence
• Rank of Matrix
• Solution of System Linear Equations- existence and uniqueness.

Calculus:

• Limit Cont, and Differentiability
• Mean Value Theorems
• Maxima and Minima (Local Minima, Local Maxima)
• Evaluation of Definite and Improper Integrals (Gama Function, Property-Based Questions)
• Multiple Integrals
• Line, Surface and Volume Integrals
• Limit and Series Expansions
• Series and Sequence (Continuous and Divided)

Differential Equations:

• Representations and Formations
• First Order Differential Equation (Linear and Non-Linear)
• Higher Order Linear Differential Equation with Cauchy’s Differential Equation (Complementary Function and Particular Integral)
• Boundary Value Problem (Numerical Answer Type Question)
• Partial Differential Equations
• Variable Separable Method

Vector Analysis:

• Vectors Basics
• Vector Operations (Del Operations)
• Gradient, Divergent and Curl
• Vector Integration
• Gauss’s, Green’s and Stoke’s Theorem

Complex Analysis:

• Basics of Complex Analysis
• Analytical Functions
• Cauchy’s Integral Theorem and Formula
• Taylor and Laurent Series
• Residue Theorem

Probability and Statistics:

• Mean, Mode, Median
• Standard Deviation
• Basics of Probability (Conditional Probability, Product Rule)
• Probability Distribution (Binomial, Poisson, Exponential and Normal Distribution)
• Random Variables
• Properties of RV

Functional Analysis:

• The principle of Uniform Boundedness
• Riesz Representation Theorem
• Hahn-Banach Theorem
• Hilbert Spaces

Numerical Analysis:

• Systems of Linear Equations (Gaussian Elimination, LU Decomposition, and Cholseky Factorization)
• Numerical Solutions of Non-linear Equations: Bisection Method
• Numerical Integration: Trapezoidal and Simpson Rule

Topology:

• Basic Concepts of Topology
• Basic Feasible Solution
• Graphical Method
• Duality Theory (Weak Duality, and Strong Duality)
• Hungarian Method

Some other important topics in Engineering Mathematics under GATE 2025 include the following:

• Linear Programming
• Laplace Transform
• Fourier Transform Methods

Also Read: What Does it Take to Become a GATE Topper?

GAET 2025 Exam Pattern for Engineering Mathematics

While preparing for the GATE 2025 exam, one of the crucial aspects is to check the GATE 2025 exam pattern. It is a great way to understand the number of questions asked, the time limit to attempt the paper, the types of questions, and more such information.

So, to ease out the GATE Engineering Mathematics preparation for the aspirants, the Engineering Mathematics GATE 2025 exam pattern is provided in the table given below:

Also Read: Important & High Scoring Topics for GATE

Preparation Tips for GATE 2025 Engineering Mathematics

Merely knowing about the GATE 2025 important topics for Engineering Mathematics will not sail the boat, candidates must prepare well for these topics with a good preparation strategy. The following are some tips to prepare for Engineering Mathematics in GATE 2025:

• Have the basics cleared by attending the lectures from faculty members, book reading and understanding the appropriate topics.
• Understand the important topics for GATE 2025 Engineering Mathematics.
• Strategize a preparation schedule accordingly.
• Regularly practice the numerical from textbooks and other GATE 2025 previous year’s question papers.
• Appear to the GATE 2025 mock test series.
• Most importantly have a consistent study schedule for the GATE 2025 preparation.

Also Read: Last Minute Preparation Tips for GATE

Preparing for the Engineering Mathematics in GATE exam 2025 within 5 months can be challenging. However, by opting for the right strategy and being consistent with the study schedule, candidates can gain a decent rank in the GATE exam. They must focus on solving the GATE previous year's question papers and revise the GATE Engineering Mathematics important topics.