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**Engineering Math Most Scoring Topic Lists for GATE Exam**

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**Engineering Mathematics Syllabus for GATE Exam:**

**Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and**

**eigenvectors.**

**Calculus: Functions of single variable, limit, continuity and differentiability, mean**

**value theorems, indeterminate forms; evaluation of definite and improper integrals;**

**double and triple integrals; partial derivatives, total derivative, Taylor series (in one**

**and two variables), maxima and minima, Fourier series; gradient, divergence and**

**curl, vector identities, directional derivatives, line, surface and volume integrals,**

**applications of Gauss, Stokes and Green’s theorems.**

**Differential equations: First order equations (linear and nonlinear); higher order linear**

**differential equations with constant coefficients; Euler-Cauchy equation; initial and**

**boundary value problems; Laplace transforms; solutions of heat, wave and**

**Laplace's equations.**

**Complex variables: Analytic functions; Cauchy-Riemann equations; Cauchy’s**

**integral theorem and integral formula; Taylor and Laurent series.**

**Probability and Statistics: Definitions of probability, sampling theorems, conditional**

**probability; mean, median, mode and standard deviation; random variables,**

**binomial, Poisson and normal distributions.**

**Numerical Methods: Numerical solutions of linear and non-linear algebraic**

**equations; integration by trapezoidal and Simpson’s rules; single and multi-step**

**methods for differential equations.**

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**List of Most Scoring Topics [Priority in decreasing Order]**

**1. Probability and Statistics**

**2. Eigen Values and Eigen Vectors**

**3. Differential Equation**

**4. Transform Theory**

**5. Numerical Method**

**6. Calculus, Gradient, Multiple integrals**

**7. Complex variables**

**8. Matrix Algebra**

**9. Fourier Series**

**10. Partial Derivatives**

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