When you are looking to apply for GATE 2019, you should give an in-depth idea about the GATE 2019 Syllabus. In the following post, we would be talking about the GATE Syllabus. But first, take a look at the GATE Exam Pattern.

## GATE 2019 Syllabus – Knowing the Exam Pattern

Before, we know about the GATE 2019 Syllabus, we should take a look at the exam pattern for GATE 2019. The exam pattern changes according to the stream or the paper that you are applying for. The following table gives the details of the GATE Exam 2019

Paper Code |
Exam Pattern |

CE, CS, EC, AE, AG, BT, CH, ME, MN, MT, EE, IN, TF, XE, PE, ST and PI | · GA (General Aptitude) – 15%
· Engineering Mathematics – 15% · Subject of the Paper – 70% |

AR, CY, GG, EY, XL, PH and MA | · GA (General Aptitude) – 15%
· Subject of the Paper – 85% |

To get more information about the GATE 2019 Exam Pattern, click on the link below:

## GATE 2019 Syllabus – General Aptitude

As you can see from the table above, General Aptitude is common for all papers. General Aptitude Paper can be divided into two sections:

- Verbal Ability
- Numerical Ability

Let us take a look at the topics in the individual sections

**Verbal Ability:** English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction.

**Numerical Ability:** Numerical computation, numerical estimation, numerical reasoning and data interpretation.

To download the GATE 2019 Syllabus PDF, click on the link below:

GATE 2019 Syllabus – General Aptitude

## GATE 2019 Syllabus – Engineering Mathematics

Engineering Mathematics is another subject that is common for a majority of papers. The following topics are included in the syllabus

**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**

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).

**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.

To download the PDF for the GATE 2019 Syllabus for Engineering Mathematics, click on the link below:

GATE 2019 Syllabus – Engineering Mathematics

These were the details of the GATE 2019 Syllabus. To get complete details about GATE 2019, click on the link below:

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