GATE 2015 Syllabus: Agricultural Engineering (AG)

ENGINEERING MATHEMATICS
Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.
Vector Calculus: Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes,
Gauss and Green’s theorems.

GATE 2015 Syllabus: Architecture and Planning (AR)

City planning: Evolution of cities; principles of city planning; types of cities & new towns; planning regulations and building byelaws; eco-city concept; sustainable development. Housing:Concept of housing; neighbourhood concept; site planning principles; housing typology; housing standards; housing infrastructure; housing policies, finance and management; housing programs in India; self help housing.
Landscape Design: Principles of landscape design and site planning; history of landscape styles; landscape elements and materials; plant characteristics & planting design; environmental considerations in landscape planning.

GATE 2015 Syllabus: Engineering Sciences (XE)

• Section A: Engineering Mathematics
• Section B: Fluid Mechanics
• Section C: Materials Science
• Section D: Solid Mechanics
• Section E: Thermodynamics
• Section F: Polymer Science and Engineering
• Section G: Food Technology

Section A: Engineering Mathematics (Compulsory)
Linear Algebra: Algebra of matrices, inverse, rank, system of linear equations, symmetric, skew-symmetric and orthogonal matrices. Hermitian, skew-Hermitian and unitary matrices.eigenvalues and eigenvectors, diagonalisation of matrices, Cayley-Hamilton Theorem.

GATE 2015 Syllabus: Aerospace Engineering (AE)

ENGINEERING MATHEMATICS

Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors.
Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems, evaluation of definite and improper integrals, partial derivatives, total derivative, maxima and minima, gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals. Theorems of Stokes, Gauss and Green.

GATE 2015 Syllabus: Textile Engineering and Fibre Science (TF)

ENGINEERING MATHEMATICS
Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.
Vector Calculus: Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green’s theorems.
Diferential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs –Laplace, heat and wave equations.
Probability and Statistics: Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis.
Numerical Methods: Solutions of linear and non-linear algebraic equations; integration of trapezoidal and Simpson’s rule; single and multi-step methods for differential equations.
TEXTILE ENGINEERING AND FIBRE SCIENCE

GATE 2015 Syllabus: General Aptitude (GA)

Syllabus for General Aptitude (GA) (COMMON TO ALL PAPERS)

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.

GATE 2015 Syllabus: Production and Industrial Engineering (PI)

ENGINEERING MATHEMATICS
Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.

GATE 2015 Syllabus: Physics (PH)

Mathematical Physics: Linear vector space; matrices; vector calculus; linear differential equations; elements of complex analysis; Laplace transforms, Fourier analysis, elementary ideas about tensors.
Classical Mechanics: Conservation laws; central forces, Kepler problem and planetary motion; collisions and scattering in laboratory and centre of mass frames; mechanics of system of particles; rigid body dynamics; moment of inertia tensor; noninertial frames and pseudo forces; variational principle; Lagrange’s and Hamilton’s formalisms; equation of motion, cyclic coordinates, Poisson bracket; periodic motion, small oscillations, normal modes; special theory of relativity – Lorentz transformations, relativistic kinematics, mass-energy equivalence.

GATE 2015 Syllabus: Metallurgical Engineering (MT)

ENGINEERING MATHEMATICS
Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and Eigen vectors.
Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.

GATE 2015 Syllabus: Mining Engineering (MN)

ENGINEERING MATHEMATICS
Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and Eigen vectors.
Calculus: Limit, continuity and differentiability; Partial Derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.