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# GATE 2019 Exam Syllabus

The syllabus for each of the papers can be found by clicking on the subject papers below. Read the section on structure of GATE to know what sections appear in each paper, especially in XE and XL.

#### Syllabus for Architecture and Planning (AR)

**Architecture and Design:** Visual composition in 2D and 3D; Principles of Art and Architecture; Organization of space; Architectural Graphics; Computer Graphics– concepts of CAD, BIM, 3D modeling and Architectural rendition; Programming languages and automation.

**Environmental Planning and Design**:Concepts of Environmental Impact Analysis; Environmental considerations in planning and design; Thermal comfort, ventilation and air movement; Principles of lighting and illumination; Climate responsive design; Solar architecture

#### Syllabus for Biotechnology (BT)

*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. Differential Equations: Linear and nonlinear first order ODEs, higher order ODEs with constant coefficients, Cauchy’s and Euler’s equations, Laplace transforms, PDE-Laplace, heat and wave equations.

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#### Syllabus for Civil Engineering (CE)

#### 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, local maxima and minima, Taylor and Maclaurin series; Evaluation of definite and indefinite integrals, application of definite integral to obtain area and volume; Partial derivatives; Total derivative; Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.

#### Syllabus for Chemical Engineering (CH)

#### ENGINEERING MATHEMATICS

**Linear Algebra:** Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.

**Calculus: **Functions of single variable, Limit, continuity and differentiability, Taylor series, 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.

#### Syllabus for Computer Science and Information Technology (CS)

*ENGINEERING MATHEMATICS*

**Discrete Mathematics: **Propositional and first order logic. Sets, relations, functions, partial orders and lattices. Groups. Graphs: connectivity, matching, coloring. Combinatorics: counting, recurrence relations, generating functions.

**Linear Algebra: **Matrices, determinants, system of linear equations, eigenvalues and eigenvectors, LU decomposition.

**Calculus: **Limits, continuity and differentiability. Maxima and minima. Mean value theorem. Integration.

**Probability: **Random variables. Uniform, normal, exponential, poisson and binomial distributions. Mean, median, mode and standard deviation. Conditional probability and Bayes theorem.

#### Syllabus for Chemistry (CY)

#### PHYSICAL CHEMISTRY

**Structure: **Postulates of quantum mechanics. Time dependent and time independent Schrödinger equations. Born interpretation. Particle in a box. Harmonic oscillator. Rigid rotor. Hydrogen atom: atomic orbitals. Multi-electron atoms: orbital approximation. Variation and first order perturbation techniques. Chemical bonding: Valence bond theory and LCAO-MO theory. Hybrid orbitals.

**Equilibrium: **Laws of thermodynamics. Standard states. Thermochemistry. Thermodynamic functions and their relationships: Gibbs-Helmholtz and Maxwell relations, van’t Hoff equation. Criteria of spontaneity and equilibrium. Absolute entropy.

#### Syllabus for Electronics and Communication (EC)

#### ENGINEERING MATHEMATICS

**Linear Algebra:**Vector space, basis, linear dependence and independence, matrix algebra, eigen values and eigen vectors, rank, solution of linear equations – existence and uniqueness.

**Calculus**: Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series.

#### Syllabus for Electrical Engineering (EE)

#### ENGINEERING MATHEMATICS

**Linear Algebra**:Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.

**Calculus**: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series, Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s theorem, Green’s theorem.

#### Syllabus for Geology and Geophysics (GG)

**PART – A : COMMON TO GEOLOGY **

Geomorphic processes and agents; development and evolution of landforms; slope and drainage; processes in deep oceanic and near-shore regions; quantitative and applied geomorphology

**PART – B : COMMON TO Geophysics **

The earth as a planet; different motions of the earth; gravity field of the earth, Clairaut’s theorem, size and shape of earth; geomagnetic field, paleomagnetism; Geothermics and heat flow; seismology and interior of the earth; variation of density, velocity, pressure, temperature, electrical and magnetic properties of the earth.

#### Syllabus for Instrumentation Engineering (IN)

#### ENGINEERING MATHEMATICS

**Linear Algebra**: Matrix algebra, systems of linear equations, Eigen values and Eigen vectors.

**Calculus**: Mean value theorems, theorems of integral calculus, partial derivatives, maxima and minima, multiple integrals, Fourier series, vector identities, line, surface and volume integrals, Stokes, Gauss and Green’s theorems.

#### Syllabus for Mathematics (MA)

**Linear Algebra:**Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization, Jordan-canonical form, Hermitian, Skew- Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators, definite forms.

**Complex Analysis:**Analytic functions, conformal mappings, bilinear transformations; complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle; Zeros and singularities; Taylor and Laurent’s series; residue theorem and applications for evaluating real integrals.

#### Syllabus for Engineering Mathematics (XE-A)

**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.

**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.

#### Syllabus for Mechanical Engineering (ME)

#### ENGINEERING MATHEMATICS

**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.

#### Syllabus for Mining Engineering (MN)

**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.**More**

#### Syllabus for 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.

#### Syllabus for Physics (PH)

**Mathematical Physics:** Linear vector space: basis, orthogonality and completeness; matrices; vector calculus; linear differential equations; elements of complex analysis: Cauchy- Riemann conditions, Cauchy’s theorems, singularities, residue theorem and applications; Laplace transforms, Fourier analysis; elementary ideas about tensors: covariant and contravariant tensor, Levi-Civita and Christoffel symbols.

**Classical Mechanics:** D’Alembert’s principle, cyclic coordinates, variational principle, Lagrange’s equation of motion, central force and scattering problems, rigid body motion; small oscillations, Hamilton’s formalisms; Poisson bracket; special theory of relativity: Lorentz transformations, relativistic kinematics, mass‐energy equivalence.

#### Syllabus for Production and Industrial Engineering (PI)

**Also See**: M.Tech Admission 2018

#### 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.

#### Syllabus for Textile Engineering and Fibre Science (TF)

#### ENGINEERING MATHEMATICS

**Linear Algebra***: *Matrices and Determinants, Systems of linear equations, Eigen values and eigen vectors.

**Differential 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.

#### Syllabus for Polymer Science and Engineering (XE-F)

#### Section 1: Chemistry of high polymers

Monomers, functionality, degree of polymerizations, classification of polymers, glass transition, melting transition, criteria for rubberiness, polymerization methods: addition and condensation; their kinetics, metallocene polymers and other newer techniques of polymerization, copolymerization, monomer reactivity ratios and its significance, kinetics, different copolymers, random, alternating, azeotropic copolymerization, block and graft copolymers, techniques for copolymerization- bulk, solution, suspension, emulsion.

#### Section 2: Polymer Characterization

Solubility and swelling, concept of average molecular weight, determination of number average, weight average, viscosity average and Z-average molecular weights, polymer crystallinity, analysis of polymers using IR, XRD, thermal (DSC, DMTA, TGA), microscopic (optical and electronic) techniques.

#### Syllabus for Zoology (XL-T)

#### Section 1: Animal world

Animal diversity, distribution, systematics and classification of animals, phylogenetic relationships.

#### Section 2: Evolution

Origin and history of life on earth, theories of evolution, natural selection, adaptation, speciation.

#### Syllabus for Thermodynamics (XE-E)

#### Section 1: Basic Concepts

Continuum and macroscopic approach; thermodynamic systems (closed and open); thermodynamic properties and equilibrium; state of a system, state postulate for simple compressible substances, state diagrams, paths and processes on state diagrams; concepts of heat and work, different modes of work; zeroth law of thermodynamics; concept of temperature.

#### Section 2: First Law of Thermodynamics

Concept of energy and various forms of energy; internal energy, enthalpy; specific heats; first law applied to elementary processes, closed systems and control volumes, steady and unsteady flow analysis.

#### Syllabus for Solid Mechanics (XE-D)

Equivalent force systems; free-body diagrams; equilibrium equations; analysis of determinate trusses and frames; friction; particle kinematics and dynamics; dynamics of rigid bodies under planar motion; law of conservation of energy; law of conservation of momentum.

#### Syllabus for Petroleum Engineering (PE)

**Linear Algebra***: *Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.

**Calculus: **Functions of single variable, Limit, continuity and differentiability, Taylor series, 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.

#### Syllabus for Microbiology (XL-S)

#### Section 1: Historical Perspective

Discovery of microbial world; Landmark discoveries relevant to the field of microbiology; Controversy over spontaneous generation; Role of microorganisms in transformation of organic matter and in the causation of diseases.

#### Section 2: Methods in Microbiology

Pure culture techniques; Theory and practice of sterilization; Principles of microbial nutrition; Enrichment culture techniques for isolation of microorganisms; Light-, phase contrast- and electron-microscopy.

#### Syllabus for Materials Science (XE-C)

#### Section 1: Processing of Materials

Powder synthesis, sintering, chemical methods, crystal growth techniques, zone refining, preparation of nanoparticles and thin films

#### Section 2: Characterisation Techniques

X-ray diffraction, spectroscopic techniques like UV-vis, IR, Raman. Optical and Electron microscopy

#### Syllabus for Food Technology (XL-U)

#### Section 1: Food Chemistry and Nutrition

Carbohydrates: structure and functional properties of mono-, oligo-, & poly- saccharides including starch, cellulose, pectic substances and dietary fibre, gelatinization and retrogradation of starch. Proteins: classification and structure of proteins in food, biochemical changes in post mortem and tenderization of muscles. Lipids: classification and structure of lipids, rancidity, polymerization and polymorphism.

#### Section 2: Food Microbiology

**Characteristics of microorganisms: **morphology of bacteria, yeast, mold and actinomycetes, spores and vegetative cells, gram-staining. **Microbial growt h: **growth and death kinetics, serial dilution technique.

#### Syllabus for Fluid Mechanics (XE-B)

#### Section 1: Flow and Fluid Properties

viscosity*, *relationship between stress and strain-rate for Newtonian fluids, incompressible and compressible flows, differences between laminar and turbulent flows*. ***Hydrostatics: **Buoyancy, manometry, forces on submerged bodies.

#### Section 2: Kinematics

Eulerian and Lagrangian description of fluids motion, concept of local and convective accelerations, steady and unsteady flows*.*

#### Syllabus for Ecology and Evolution (EY)

#### Section 1: Ecology

Population ecology; metapopulation dynamics; growth rates; density independent growth; density dependent growth; niche concept

#### Section 2: Evolution

Origin, evolution and diversification of life; natural selection; levels of selection.

Types of selection (stabilizing, directional etc.); sexual selection; genetic drift; gene flow; adaptation; convergence; species concepts

#### Syllabus for Chemistry (XL-P)

#### Section 1: Atomic Structure and Periodicity

Planck’s quantum theory, wave particle duality, uncertainty principle, quantum mechanical model of hydrogen atom, electronic configuration of atoms and ions. Periodic table and periodic properties: ionization energy, electron affinity, electronegativity and atomic size.

#### Section 2: Structure and Bonding

Ionic and covalent bonding, MO and VB approaches for diatomic molecules, VSEPR theory and shape of molecules, hybridization, resonance, dipole moment, structure parameters such as bond length, bond angle and bond energy, hydrogen bonding and van der Waals interactions. Ionic solids, ionic radii and lattice energy (Born‐Haber cycle). HSAB principle.

#### Syllabus for Botany (XL-R)

#### Section 1:Plant Systematics

Major systems of classification, plant groups, phylogenetic relationships and molecular systematics.

#### Section 2: Plant Anatomy

Plant cell structure and its components; cell wall and membranes; organization, organelles, cytoskeleton, anatomy of root, stem and leaves, floral parts, embryo and young seedlings, meristems, vascular system, their ontogeny, structure and functions, secondary growth in plants and stellar organization.

#### Syllabus for Atmospheric & Ocean Science (XE-H)

#### Section A: Atmospheric Science

Fundamental of Meteorology, Thermal structure of the atmosphere and its composition, Radiation Balance and Laws, Wind Belts, Monsoon, Climate. Atmospheric Thermodynamics. Hydrostatic equilibrium and: Hydrostatic equation, variation of pressure with height, geopotential, Tropical convection. Atmospheric Electricity. Cloud Physics. Observation Techniques of the Atmosepheric Properties.

#### Section B: Ocean Sciences

Seawater Properties, T-S diagrams, Ocean Observations, Ocean Tide and Waves and their properties. Coastal processes and Estuary Dynamics. coastal zone management. Wind Driven Circulation: Ekman, Sverdrup, Stommel and Munk theories, Inertial currents; geostrophic motion; barotropic and baroclinic conditions; Oceanic eddies. Global conveyor belt circulation. Subtropical gyres; Western boundary currents; equatorial current systems; Current System in the Indian Ocean.

#### Syllabus for Biochemistry (XL-Q)

#### Section 1:

Organization of life; Importance of water; Structure and function of biomolecules: Amino acids, Carbohydrates, Lipids, Proteins and Nucleic acids; Protein structure, folding and function: Myoglobin, Hemoglobin, Lysozyme, Ribonuclease A, Carboxypeptidase and Chymotrypsin.

#### Section 2:

Enzyme kinetics including its regulation and inhibition, Vitamins and Coenzymes ; Metabolism and bioenergetics; Generation and utilization of ATP; Metabolic pathways and their regulation: glycolysis, TCA cycle, pentose phosphate pathway, oxidative phosphorylation,gluconeogenesis, glycogen and fatty acid metabolism; Metabolism of Nitrogen containing compounds: nitrogen fixation, amino acids and nucleotides. Photosynthesis: Calvin cycle.

**Also See**: Engineering Entrance Exam 2018