### GATE 2019 Syllabus for Engineering Mathematics (EM)

GATE 2019 Syllabus for Engineering Mathematics (EM)

About GATE 2019 – To test the performance and understanding capability of students in their graduate fields, Graduate Aptitude Test in Engineering (GATE) which is a national level exam is being conducted. In M.E/M-Tech and other NITs throughout India, this test is useful for the admissions. On behalf of the National Coordination Board, GATE exam is jointly conducted by the seven IITs (Indian Institute of Technology) and IISc (Indian Institute of Science) – GATE, Department of Higher Education, Ministry of Human Resource Development (MHRD), Government of India. In many of the government and private organizations, GATE score is important for the recruitment. GATE score is compulsory for many private organizations

**About Engineering Mathematics**

** **Engineering mathematics combines mathematical theory, practical engineering, and scientific computing. It is a creative and exciting discipline, spanning traditional boundaries.

**Syllabus of Engineering Mathematics – GATE 2019**

**Linear Algebra**

Algebra of matrices; System of linear equations; Determinants; Eigenvalues and eigenvectors; Diagonalisation of matrices; Cayley-Hamilton Theorem; Inverse and rank of a matrix; Symmetric, skew-symmetric and orthogonal matrices;

**Calculus**

Functions of a single variable: Maxima and minima; Taylor’s theorem; Mean value theorems; Indeterminate forms and L’Hospital’s rule; Fundamental theorem and mean value-theorems of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes; Limit, continuity and differentiability;

Functions of two variables: Directional derivative; Total derivative; Limit, continuity and partial derivatives; Tangent plane and normal line; Maxima, minima and saddle points; Method of Lagrange multipliers; Double and triple integrals, and their applications;

Sequence and series: Power series; Taylor’s series; Fourier Series; Half range sine and cosine series; Tests for convergence; Convergence of sequence and series;

Vector Calculus

Line and surface integrals; Gradient, divergence and curl; Green’s theorem, Stokes theorem and Gauss divergence theorem (without proofs);

**Complex variables**

Taylor’s series and Laurent series; Analytic functions; Line integral, Cauchy’s integral theorem and integral formula (without proof); Residue theorem (without proof) and its applications; Cauchy-Riemann equations;

**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; Legendre polynomials, Bessel functions of the first kind and their properties; Method of variation of parameters; Cauchy-Euler equation; Power series solutions;

**Partial Differential Equations**

Classification of second-order linear partial differential equations; Laplace equation; Solutions of one-dimensional heat and wave equations; Method of separation of variables;

**Probability and Statistics**

Discrete and continuous random variables: Axioms of probability; Conditional probability; Bayes’ Theorem; Binomial, Poisson and normal distributions; Correlation and linear regression;

**Numerical Methods**

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; Solution of systems of linear equations using LU decomposition, Solution of polynomial and transcendental equations by Newton-Raphson method; Gauss elimination and Gauss-Seidel methods; Lagrange and Newton’s interpolations;

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**Exam Pattern for GATE 2019**

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Exam Pattern for GATE 2019 |
||||

Section |
Question No |
No of Questions |
Marks per Question |
Total Marks |

General Aptitude | 1 to 5 | 5 | 1 | 5 |

6 to 10 | 5 | 2 | 10 | |

Technical & Engineering | 1 to 25 | 25 | 1 | 25 |

Mathematics | 26 to 55 | 30 | 2 | 60 |

Total Questions: 65

Total Marks: 100

Total Duration : 3 hours

Technical Section: 70 marks

General Aptitude: 15 marks

Engineering Mathematics: 15 marks

25 marks to 40 marks will be allotted to Numerical Answer Type Questions

**Reference Books for Engineering Mathematics- GATE 2019**

- Advanced Engineering Mathematics by RK Jain, SRK Iyengar
- Advanced Engineering Mathematics by HK Dass
- Advanced Engineering Mathematics by Erwin Kreyszig
- Engineering Mathematics solved papers by Made easy publications
- Engineering and Mathematics general aptitude by G.K Publications
- GATE Engineering and Mathematics by Nodia and company
- Higher Engineering Mathematics by Bandaru Ramana
- Higher Engineering Mathematics by B.S. Grewal

**Other GATE 2019 Syllabus and Information**

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