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# Engineering Mathematics Topic wise Priority List for GATE Exam

## Engineering Math Most Scoring Topic Lists for GATE Exam

### Engineering Mathematics Syllabus for GATE Exam:

Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.
Calculus: Functions of a 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.

#### 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