GATE 2026 Engineering Sciences Syllabus (Out) - Download GATE XE Syllabus PDF, Important Topics/Chapters, Section Wise Weightage

Section 1: Linear Algebra

- Algebra of real matrices: Determinant, inverse and rank of a matrix

- System of linear equations (conditions for unique solution, no solution, and infinite solutions)

- Eigenvalues and eigenvectors of matrices

- Properties of eigenvalues and eigenvectors of symmetric matrices

- Diagonalization of matrices

- Cayley-Hamilton Theorem

Section 2: Calculus

Functions of Single Variable:

- Limit, indeterminate forms, and L'Hospital's rule

- Continuity and differentiability

- Mean value theorems

- Maxima and minima

- Taylor's theorem

- Fundamental theorem and mean value theorem of integral calculus

- Evaluation of definite and improper integrals

- Applications of definite integrals to evaluate areas and volumes (rotation of a curve about an axis)

Functions of Two Variables:

- Limit, continuity, and partial derivatives

- Directional derivative

- Total derivative

- Maxima, minima, and saddle points

- Method of Lagrange multipliers

- Double integrals and their applications

Sequences and Series:

- Convergence of sequences and series

- Tests of convergence of series with non-negative terms (ratio, root, and integral tests)

- Power series

- Taylor's series

- Fourier Series of functions of period 2π

Section 3: Vector Calculus

- Gradient, divergence, and curl

- Line integrals and Green's theorem

Section 4: Complex Variables

- Complex numbers

- Argand plane and polar representation of complex numbers

- De Moivre’s theorem

- Analytic functions

- Cauchy-Riemann equations

Section 5: Ordinary Differential Equations

- First-order equations (linear and nonlinear)

- Second-order linear differential equations with constant coefficients

- Cauchy-Euler equation

- Second-order linear differential equations with variable coefficients

- Wronskian

- Method of variation of parameters

- Eigenvalue problem for second-order equations with constant coefficients

- Power series solutions for ordinary points

Section 6: Partial Differential Equations

- Classification of second-order linear partial differential equations

- Method of separation of variables: One-dimensional heat equation and two-dimensional Laplace equation

Section 7: Probability and Statistics

- Axioms of probability

- Conditional probability

- Bayes' Theorem

- Mean, variance, and standard deviation of 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 method

- Lagrange and Newton's interpolations

- Solution of polynomial and transcendental equations by Newton-Raphson method

- Numerical integration by trapezoidal rule and Simpson's rule

- Numerical solutions of first-order differential equations by explicit Euler's method

Section 1: Flow and Fluid Properties

Fluid Properties

- Density, viscosity, surface tension

- Relationship between stress and strain-rate for Newtonian fluids

Classification of Flows

- Viscous vs inviscid flows

- Incompressible vs compressible flows

- Internal vs external flows

- Steady vs unsteady flows

- Laminar vs turbulent flows

- 1-D, 2-D, 3-D flows

- Newtonian vs non-Newtonian fluid flow

Hydrostatics

- Buoyancy

- Manometry

- Forces on submerged bodies

- Stability

Section 2: Kinematics of Fluid Motion

Descriptions of Fluid Motion

- Eulerian and Lagrangian descriptions

- Concept of local, convective, and material derivatives

Fluid Lines

- Streamline

- Streakline

- Pathline

- Timeline

Section 3: Integral Analysis for a Control Volume

Reynolds Transport Theorem (RTT)

- Conservation of mass

- Conservation of linear and angular momentum

Section 4: Differential Analysis

Equations of Motion

- Differential equations for incompressible flows

- Inviscid flows (Euler equations)

- Viscous flows (Navier-Stokes equations)

Fluid Concepts

- Fluid rotation

- Vorticity

- Stream function

- Circulation

Exact Solutions

- Navier-Stokes solutions for Couette flow

- Poiseuille flow

- Thin film flow

Section 5: Dimensional Analysis

Similarity Concepts

- Geometric, kinematic, and dynamic similarity

Buckingham Pi Theorem

- Applications of Buckingham Pi theorem

Non-dimensional Parameters

- Reynolds number

- Froude number

- Mach number

Section 6: Internal Flows

Pipe Flow

- Fully developed pipe flow

Empirical Relations

- Laminar and turbulent flows

- Friction factor

- Darcy-Weisbach relation

- Moody’s chart

- Major and minor losses

Section 7: Bernoulli’s Equation and its Applications, Potential Flows

Bernoulli’s Equation

- Assumptions

- Applications

Flow Measurements

- Venturi meter

- Pitot-static tube

- Orifice meter

Potential Flows

- Velocity potential function

- Uniform flow

- Source

- Sink

- Vortex

- Superposition of flow past simple geometries

Section 8: External Flows

Prandtl Boundary Layer Equations

- Concept and assumptions

Boundary Layer Characteristics

- Boundary layer thickness

- Displacement thickness

- Momentum thickness

- Boundary layer separation

Forces on Bodies

- Streamlined and bluff bodies

- Drag and lift forces

1: Classification and Structure of Materials

Classification of Materials

- Metals

- Ceramics

- Polymers

- Composites

Nature of Bonding in Materials

- Metallic, ionic, covalent, and mixed bonding

Structure of Materials

- Fundamentals of crystallography

- Symmetry operations

- Crystal systems

- Bravais lattices

- Unit cells

- Primitive cells

- Crystallographic planes and directions

- Structures of metals, ceramics, polymers, amorphous materials, and glasses

Defects in Crystalline Materials

- 0-D, 1-D, and 2-D defects

- Vacancies

- Interstitials

- Solid solutions in metals and ceramics

- Frenkel and Schottky defects

- Dislocations

- Grain boundaries

- Twins

- Stacking faults

- Surfaces and interfaces

2: Thermodynamics, Kinetics and Phase Transformations

Thermodynamics

- Extensive and intensive thermodynamic properties

- Laws of thermodynamics

Phase Equilibria

- Phase rule

- Phase diagrams (unary and binary)

Basic Electrochemistry

- Fundamental electrochemical principles

Reaction Kinetics

- Fundamentals of diffusion

- Fick’s laws, solutions, and applications

Phase Transformations

- Solidification of pure metals and alloys

- Nucleation and growth

- Diffusional solid-state phase transformations (precipitation and eutectoid)

- Martensitic transformation

3: Properties and Applications of Materials

Mechanical Properties

- Stress-strain response (elastic, anelastic, and plastic deformation)

Electronic Properties

- Free electron theory

- Fermi energy

- Density of states

- Elements of band theory

- Semiconductors

- Hall effect

- Dielectric, piezoelectric, and ferroelectric behaviour

Magnetic Properties

- Origin of magnetism

- Para-, dia-, ferro-, and ferri-magnetism

Thermal Properties

- Specific heat

- Heat conduction

- Thermal diffusivity

- Thermal expansion

- Thermoelectricity

Optical Properties

- Refractive index

- Absorption and transmission of electromagnetic radiation

Applications

- Examples of materials exhibiting mechanical, electronic, magnetic, thermal, and optical properties, and their common applications

4: Characterization and Measurements of Properties

Characterization Techniques

- X-ray diffraction

- Spectroscopic techniques: UV-Vis, IR, Raman

- Optical and electron microscopy

Measurements

- Composition analysis in electron microscopes

- Tensile test

- Hardness measurement

- Electrical conductivity, carrier mobility and concentrations

- Thermal analysis: thermogravimetry and calorimetry

5: Processing of Materials

Heat Treatment and Processing

- Heat treatment of ferrous and aluminium alloys

- Preparation of ceramic powders

- Sintering

Thin Film Deposition

- Evaporation and sputtering techniques

- Chemical vapour deposition

- Thin film growth phenomena

6: Degradation of Materials

Material Degradation

- Corrosion and its prevention

- Embrittlement of metals

- Polymer degradation

1: Mechanics of Rigid Bodies

Equivalent Force Systems

- Free-body diagrams

- Equilibrium equations

Analysis of Structures

- Determinate trusses

- Frames

- Friction

- Principle of minimum potential energy

Dynamics of Rigid Bodies

- Particle kinematics and dynamics

- Planar motion of rigid bodies

- Law of conservation of energy

- Law of conservation of momentum

2: Mechanics of Deformable Bodies

Stresses and Strains

- Transformation of stresses and strains

- Principal stresses and strains

- Mohr’s circle for plane stress and plane strain

Material Behavior

- Generalized Hooke’s Law

- Elastic constants

- Thermal stresses

- Theories of failure

Structural Analysis

- Axial force

- Shear force

- Bending moment diagrams

- Axial, shear, and bending stresses

- Combined stresses

- Deflection (for symmetric bending)

- Torsion in circular shafts

- Thin walled pressure vessels

- Energy methods (Castigliano’s theorems)

- Euler buckling

3: Vibrations

Free Vibrations

- Undamped single degree of freedom systems

1: Basic Concepts

Fundamental Concepts

- Continuum and macroscopic approach

- Thermodynamic systems (closed and open)

- Thermodynamic properties and equilibrium

State and Processes

- State of a system

- State postulate for simple compressible substances

- State diagrams

- Paths and processes on state diagrams

Heat and Work

- Concepts of heat and work

- Different modes of work

- Zeroth law of thermodynamics

- Concept of temperature

2: First Law of Thermodynamics

Energy Concepts

- Concept of energy and various forms of energy

- Internal energy

- Enthalpy

- Specific heats

Application

- First law applied to elementary processes

- Closed systems

- Control volumes

- Steady and unsteady flow analysis

3: Second Law of Thermodynamics

Basic Principles

- Limitations of the first law

- Concepts of heat engines and heat pumps/refrigerators

- Kelvin-Planck and Clausius statements and their equivalence

Processes and Cycles

- Reversible and irreversible processes

- Carnot cycle and Carnot principles/theorems

- Thermodynamic temperature scale

- Clausius inequality and entropy

Entropy

- Microscopic interpretation of entropy

- Principle of increase of entropy

- T-s diagrams

- Second law analysis of control volume

- Availability and irreversibility

- Third law of thermodynamics

4: Properties of Pure Substances

Phase Behavior

- Thermodynamic properties in solid, liquid, and vapor phases

- PvT behavior of simple compressible substances

- Phase rule

Equations of State

- Thermodynamic property tables and charts

- Ideal and real gases

- Ideal gas equation of state

- Van der Waals equation of state

- Law of corresponding states

- Compressibility factor and generalized compressibility chart

5: Thermodynamic Relations

Thermodynamic Functions

- TdS relations

- Helmholtz and Gibbs functions

- Gibbs relations

- Maxwell relations

- Joule-Thomson coefficient

- Coefficient of volume expansion

Relations and Equations

- Adiabatic and isothermal compressibilities

- Clapeyron and Clapeyron-Clausius equations

6: Thermodynamic Cycles

Cycles and Processes

- Carnot vapor cycle

- Ideal Rankine cycle

- Rankine reheat cycle

- Air-standard Otto cycle

- Air-standard Diesel cycle

- Air standard Brayton cycle

- Vapor-compression refrigeration cycle

7: Ideal Gas Mixtures

Mixing Laws and Properties

- Dalton’s and Amagat’s laws

- Properties of ideal gas mixtures

- Air-water vapor mixtures

- Simple thermodynamic processes involving them

Humidity and Temperature

- Specific and relative humidities

- Dew point and wet bulb temperature

- Adiabatic saturation temperature

- Psychrometric chart

1: Chemistry of High Polymers

Basic Concepts

- Monomers

- Functionality

- Degree of polymerizations

- Classification of polymers

- Glass transition

- Melting transition

- Criteria for rubberiness

Polymerization Methods

- Addition and condensation

- Kinetics

- Metallocene polymers

- Newer methods of polymerization

- Copolymerization

- Monomer reactivity ratios and significance

Copolymerization Types

- Random, alternating, azeotropic

- Block and graft copolymers

- Techniques: bulk, solution, suspension, emulsion

Morphology

- Concept of intermolecular order

- Amorphous, crystalline, orientation states

- Factors affecting crystallinity

- Crystalline transition

- Effect on polymer properties

2: Polymer Characterization

Molecular Weight

- Solubility and swelling

- Molecular weight distribution

- Average molecular weight: number, weight, viscosity, Z-average

- Polymer crystallinity

Analytical Techniques

- IR, XRD

- Thermal: DSC, DMTA, TGA

- Microscopic: optical, electronic

- GPC

- Mooney viscosity

3: Synthesis, Manufacturing and Properties

Types of Polymers

- Commodity and general-purpose thermoplastics: PE, PP, PS, PVC, Polyesters, Acrylic, PU polymers

- Engineering Plastics: Nylon, PC, PBT, PSU, PPO, ABS, Fluoropolymers

- Thermosetting polymers: Polyurethane, PF, MF, UF, Epoxy, Unsaturated polyester, Alkyds

- Natural and synthetic rubbers: NR, SBR, Nitrile, CR, CSM, EPDM, IIR, BR, Silicone, TPE

- Speciality plastics: PEK, PEEK, PPS, PSU, PES

- Biopolymers: PLA, PHA/PHB

4: Polymer Blends and Composites

Blends and Composites

- Difference between blends and composites

- Significance

- Choice of polymers for blending

- Miscibility: miscible and immiscible blends

- Thermodynamics

- Phase morphology

- Polymer alloys, polymer eutectics

- Plastic-plastic, rubber-plastic, and rubber-rubber blends

- FRP, particulate, long and short fibre reinforced composites

- Polymer reinforcement, reinforcing fibres (natural and synthetic)

- Base polymer for reinforcement

- Ingredients/recipes for reinforced polymer composite

5: Polymer Technology

Compounding and Ingredients

- Need and significance of polymer compounding

- Compounding ingredients: antioxidants, light stabilizers, UV stabilizers, lubricants, processing aids, impact modifiers, flame retardants, antistatic agents

- PVC stabilizers and plasticizers

- Function of each ingredient

Processing Techniques

- Cross-linking and vulcanization

- Vulcanization kinetics

6: Polymer Rheology

Flow Properties

- Flow of Newtonian and non-Newtonian fluids

- Flow equations

- Dependence of shear modulus on temperature

- Molecular/segmental deformations

Rheological Measurements

- Measurements: capillary, rotating, parallel plate, cone-plate rheometer

- Visco-elasticity: creep and stress relaxation

- Mechanical models

- Control of rheological characteristics

7: Polymer Processing

Molding and Shaping

- Compression molding

- Transfer molding

- Injection molding

- Blow molding

- Reaction injection molding

- Filament winding

- SMC, BMC, DMC

- Extrusion

- Pultrusion

- Calendaring

- Rotational molding

- Thermoforming

- Powder coating

- Rubber processing: two-roll mill, internal mixer, twin screw extruder

8: Polymer Testing

Mechanical Properties

- Static and dynamic tensile

- Flexural, compressive, abrasion

- Endurance, fatigue, hardness

- Tear, resilience, impact, toughness

Conductivity and Thermal Properties

- Thermal and electrical conductivity

- Dielectric constant, dissipation factor, power factor

- Electric resistance

- Surface resistivity, volume resistivity

- Swelling, ageing resistance

- Environmental stress cracking resistance

- Limiting oxygen index

Thermal Properties

- Heat deflection temperature

- Vicat softening temperature

- Brittleness temperature

- Glass transition temperature

- Coefficient of thermal expansion

- Shrinkage

Optical Properties

- Refractive index

- Luminous transmittance and haze

- Melt flow index

9: Polymer Recycling and Waste Management

Recycling Techniques

- Polymer waste and environmental impact

- Sources

- Identification and separation techniques

- Recycling classification

- Recycling thermoplastics, thermosets, and rubbers

- Applications of recycled materials

- Life cycle assessment of polymer products (e.g., PET bottles, packaging bags)

1: Food Chemistry and Nutrition

Carbohydrates

- Structure and functional properties

- Mono-, oligo-, & poly- saccharides

- Starch, cellulose, pectic substances, dietary fiber

- Gelatinization, retrogradation

Proteins

- Classification and structure

- Biochemical changes in post mortem

- Tenderization of muscles

Lipids

- Classification and structure

- Rancidity

- Polymerization, polymorphism

Pigments

- Carotenoids

- Chlorophylls

- Anthocyanins

- Tannins

- Myoglobin

Food Flavours

- Terpenes

- Esters

- Aldehydes

- Ketones

- Quinines

Enzymes

- Specificity

- Simple and inhibition kinetics

- Coenzymes

- Enzymatic and non-enzymatic browning

Nutrition

- Balanced diet

- Essential amino acids, fatty acids

- Protein efficiency ratio

- Vitamins: water soluble, fat soluble

- Role of minerals

- Co-factors

- Anti-nutrients

- Nutraceuticals

- Nutrient deficiency diseases

Chemical and Biochemical Changes

- Changes occurring in foods during processing

2: Food Microbiology

Characteristics of Microorganisms

- Morphology of bacteria, yeast, mold, actinomycetes

- Spores and vegetative cells

Microbial Growth

- Growth and death kinetics

- Serial dilution technique

- Gram-staining

Food Spoilage

- Spoilage microorganisms in milk, fish, meat, egg, cereals, and their products

Toxins from Microbes

- Pathogens and non-pathogens: Staphylococcus, Salmonella, Shigella, Escherichia, Bacillus, Clostridium, Aspergillus genera

Fermented Foods and Beverages

- Curd, yoghurt, cheese, pickles, soya-sauce, sauerkraut, idli, dosa, vinegar, alcoholic beverages, sausage

3: Food Products Technology

Processing Principles

- Thermal processing

- Chilling, freezing

- Dehydration

- Preservatives and food additives

- Irradiation

- Fermentation

- Hurdle technology

- Intermediate moisture foods

Food Packaging and Storage

- Packaging materials

- Aseptic packaging

- Controlled and modified atmosphere storage

Cereal Processing

- Milling of rice, wheat, maize

- Parboiling of paddy

- Bread, biscuits, extruded products, ready-to-eat breakfast cereals

Oil Processing

- Expelling

- Solvent extraction

- Refining

- Hydrogenation

Fruits and Vegetables Processing

- Extraction, clarification

- Concentration and packaging of fruit juice, jam, jelly, marmalade, squash

- Candies, tomato sauce, ketchup, puree, potato chips, pickles

Plantation Crops Processing

- Tea, coffee, cocoa

- Spice processing

- Extraction of essential oils and oleoresins from spices

Milk and Milk Products Processing

- Pasteurization, sterilization

- Cream, butter, ghee, ice cream, cheese, milk powder

Processing of Animal Products

- Drying, canning, freezing of fish and meat

- Production of egg powder

Waste Utilization

- Pectin from fruit wastes

- Uses of by-products from rice milling

Food Standards and Quality

- FPO, PFA, A-Mark, ISI

- HACCP

- Food plant sanitation

- Cleaning in Place (CIP)

4: Food Engineering

Mass and Energy Balance

- Mass and energy balance principles

Momentum Transfer

- Flow rate and pressure drop relationships for Newtonian fluids

- Reynolds number

Heat Transfer

- Conduction

- Convection

- Radiation

- Heat exchangers

Mass Transfer

- Molecular diffusion

- Fick's law

- Conduction and convective mass transfer

- Permeability through single and multilayer films

Mechanical Operations

- Size reduction of solids

- High pressure homogenization

- Filtration

- Centrifugation

- Settling

- Sieving

- Mixing & agitation of liquid

Thermal Operations

- Thermal sterilization

- Evaporation of liquid foods

- Hot air drying of solids

- Spray and freeze-drying

- Freezing and crystallization

Mass Transfer Operations

- Psychometric

- Humidification

- Dehumidification

A: Atmospheric Science

Vertical Structure and Composition

- Layers of the atmosphere

- Composition of atmospheric gases

Blackbody Radiation and Radiation Balance

- Blackbody radiation principles

- Radiation balance in the atmosphere

Modes of Heat Transfer

- Conduction

- Convection

- Radiation

Greenhouse Effect

- Mechanism

- Impact on climate

Cloud Types

- Classification

- Formation processes

Laws of Thermodynamics

- First law

- Second law

- Third law

Gas Laws

- Boyle’s Law

- Charles’s Law

- Ideal Gas Law

Hydrostatic Equation

- Hydrostatic equilibrium

- Application in atmospheric science

Clausius-Clapeyron Equation

- Derivation

- Application to phase changes

Adiabatic Processes

- Adiabatic cooling and heating

- Dry and moist adiabatic lapse rates

Humidity in the Atmosphere

- Measurement

- Types: absolute, relative, specific humidity

Atmospheric Stability

- Stability criteria

- Types of atmospheric stability

Weather and Climate

- Distinction between weather and climate

- Factors influencing weather and climate

Navier-Stokes and Continuity Equations

- Fundamental equations

- Applications in atmospheric dynamics

Compressible and Incompressible Fluids

- Characteristics

- Differences and applications

Pressure Gradient, Centripetal, Centrifugal, and Coriolis Forces

- Pressure gradient force

- Centripetal force

- Centrifugal force

- Coriolis effect

Geostrophic, Gradient, and Cyclostrophic Balances

- Geostrophic balance

- Gradient balance

- Cyclostrophic balance

Circulations and Vorticity

- Atmospheric circulation patterns

- Vorticity and its significance

General Circulation of the Atmosphere

- Large-scale circulation patterns

- Zonal and meridional circulations

Broad Features of Indian Monsoons

- Seasonal variations

- Monsoon onset and withdrawal

Monsoon Depressions

- Formation

- Impact on weather

Tropical Convergence Zones

- Definition

- Role in global circulation

Tropical Cyclones

- Formation

- Structure

- Impacts and forecasting

B: Ocean Sciences

Vertical Profiles of Temperature and Salinity

- Measurement

- Effects on ocean circulation

Stability and Double Diffusion

- Stability in the ocean

- Double diffusion processes

Equation of State

- Thermodynamic equation of state for seawater

Equations for Conservation of Mass, Momentum, Heat, and Salt

- Fundamental equations

- Applications in oceanography

Inertial Currents

- Generation and characteristics

- Impact on ocean circulation

Geostrophic Motion

- Mechanism

- Relation to ocean currents

Air-Sea Surface Fluxes

- Heat fluxes

- Momentum fluxes

- Impact on climate

Wind-Driven Circulation

- Mechanism

- Ekman and Sverdrup transports

Storm Surges, Tides, Tsunamis, and Wind Waves

- Characteristics

- Formation

- Impact on coastal areas

Eddies and Gyres

- Types of eddies

- Major gyres in the ocean

Eastern and Western Boundary Currents

- Characteristics

- Examples: Gulf Stream, Kuroshio Current

Equatorial Currents

- Characteristics

- Importance for climate

Indian Ocean Current Systems

- Major currents

- Seasonal variations

Thermohaline Circulation

- Mechanism

- Role in global climate

Chemical Properties of Seawater

- Major and minor elements

- Ocean acidification

Biochemical Cycling of Nutrients

- Nutrient cycles

- Role in marine ecosystems

Trace Metals and Organic Matter

- Presence and significance

- Impact on marine life

Biological Pump

- Mechanism

- Impact on carbon sequestration

Primary and Secondary Biological Productivity

- Measurement

- Factors affecting productivity

Air-Sea Exchange of Biogenic Dissolved Gases

- Types of gases

- Exchange processes

Marine Ecology

- Marine ecosystems

- Interactions between organisms

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Spatial Aptitude

- Transformation of Shapes: Translation, Rotation, Scaling, Mirroring

- Paper Folding and Cutting: Patterns in 2 and 3 Dimensions

- Assembling and Grouping

Analytical Aptitude

- Logic: Deduction and Induction

- Analogy

- Numerical Relations and Reasoning

Quantitative Aptitude

- Data Interpretation: Data Graphs (Bar Graphs, Pie Charts, 2D and 3D Plots, Maps, Tables)

- Numerical Computation and Estimation: Ratios, Percentages, Powers, Exponents, Logarithms, Permutations, Combinations, Series

- Mensuration and Geometry

- Elementary Statistics and Probability

Verbal Aptitude

- Basic English Grammar: Tenses, Articles, Adjectives, Prepositions, Conjunctions, Verb-Noun Agreement, and Other Parts of Speech

- Basic Vocabulary: Words, Idioms, Phrases in Context

- Reading and Comprehension

- Narrative Sequencing

XE-A: Engineering Mathematics

- Calculus: Differentiation, Integration, Differential Equations, Multiple Integrals

- Linear Algebra: Matrix Theory, Vector Spaces, Systems of Linear Equations

- Probability and Statistics: Probability Distributions, Statistical Inference, Regression and Correlation Analysis

- Numerical Methods: Numerical Solutions, Root Finding Algorithms, Numerical Integration

XE-B: Fluid Mechanics

- Fluid Properties: Viscosity, Density, Surface Tension

- Hydrostatics: Buoyancy, Manometry

- Fluid Flow Analysis: Reynolds Transport Theorem, Navier-Stokes and Euler Equations

- Dimensional Analysis: Buckingham Pi Theorem, Non-Dimensional Numbers

- Internal and External Flows: Pipe Flow, Bernoulli’s Equation Applications

XE-C: Materials Science

- Material Classification and Structure: Metals, Ceramics, Polymers, Composites, Crystallography

- Thermodynamics and Phase Transformations: Phase Diagrams, Diffusion, Solidification

- Properties of Materials: Mechanical, Thermal, Magnetic, Optical Properties

- Characterization Techniques: X-ray Diffraction, Spectroscopy, Mechanical Testing

XE-D: Solid Mechanics

- Mechanics of Rigid Bodies: Equilibrium, Free-Body Diagrams, Analysis of Trusses and Frames

- Mechanics of Deformable Bodies: Stress and Strain Analysis, Mohr’s Circle, Generalized Hooke’s Law

- Vibrations: Free Vibration of Single Degree of Freedom Systems

XE-E: Thermodynamics

- Basic Concepts: Thermodynamic Systems, Properties, Laws of Thermodynamics

- First Law of Thermodynamics: Energy, Internal Energy, Enthalpy, Steady and Unsteady Flow Analysis

- Second Law of Thermodynamics: Entropy, Carnot Cycle, Reversible and Irreversible Processes

- Thermodynamic Cycles: Carnot, Rankine, Otto, Diesel, Brayton Cycles

XE-F: Polymer Science and Engineering

- Chemistry of High Polymers: Polymerization Methods, Copolymerization, Morphology

- Polymer Characterization: Molecular Weight Distribution, Techniques (IR, XRD, DSC)

- Polymer Properties and Processing: Thermoplastics, Thermosets, Processing Techniques

- Polymer Testing and Recycling: Mechanical and Thermal Properties, Recycling

XE-G: Food Technology

- Food Chemistry and Nutrition: Carbohydrates, Proteins, Lipids, Vitamins, Minerals

- Food Microbiology: Microbial Growth, Spoilage, Toxins, Fermented Foods

- Food Products Technology: Processing Techniques, Packaging, Storage

- Food Engineering: Mass and Energy Balances, Heat and Mass Transfer Operations

XE-H: Atmospheric and Oceanic Sciences

- Atmospheric Science: Vertical Structure, Composition, Thermodynamics, Cloud Types, Monsoons

- Ocean Sciences: Temperature and Salinity Profiles, Ocean Circulation, Chemical Properties of Seawater

XE-A

Engineering Mathematics

Linear Algebra

15%

Calculus

20%

Vector Calculus

10%

Complex Variables

10%

Ordinary Differential Equations

10%

Partial Differential Equations

10%

Probability and Statistics

15%

Numerical Methods

10%

XE-B

Fluid Mechanics

Flow and Fluid Properties

15%

Kinematics of Fluid Motion

10%

Integral Analysis for a Control Volume

15%

Differential Analysis

15%

Dimensional Analysis

10%

Internal Flows

10%

Bernoulli’s Equation and its Applications, Potential Flows

15%

External Flows

10%

XE-C

Materials Science

Classification and Structure of Materials

15%

Thermodynamics, Kinetics and Phase Transformations

20%

Properties and Applications of Materials

20%

Characterization and Measurements of Properties

15%

Processing of Materials

15%

Degradation of Materials

15%

XE-D

Solid Mechanics

Mechanics of Rigid Bodies

30%

Mechanics of Deformable Bodies

40%

Vibrations

30%

XE-E

Thermodynamics

Basic Concepts

15%

First Law of Thermodynamics

15%

Second Law of Thermodynamics

20%

Properties of Pure Substances

15%

Thermodynamic Relations

15%

Thermodynamic Cycles

10%

Ideal Gas Mixtures

10%

XE-F

Polymer Science and Engineering

Chemistry of High Polymers

20%

Polymer Characterization

15%

Synthesis, Manufacturing and Properties

20%

Polymer Blends and Composites

15%

Polymer Technology

10%

Polymer Rheology

10%

Polymer Processing

15%

Polymer Testing

15%

Polymer Recycling and Waste Management

10%

XE-G

Food Technology

Food Chemistry and Nutrition

25%

Food Microbiology

20%

Food Products Technology

25%

Food Engineering

30%

XE-H

Atmospheric and Oceanic Science

Atmospheric Science

55%

Ocean Science

45%

Higher Engineering Mathematics

B.V. Ramana

McGraw Hill

Advanced Engineering Mathematics

R.K. Jain & S.R.K. Iyengar

Narosa Publishing

Engineering Mathematics

K.A. Stroud

Palgrave Macmillan

Fluid Mechanics

Frank M. White

McGraw Hill

Materials Science and Engineering: An Introduction

William D. Callister Jr.

Wiley

Mechanics of Materials

Ferdinand P. Beer & E. Russell

McGraw Hill

Thermodynamics: An Engineering Approach

Yunus Çengel & Michael Boles

McGraw Hill