PU-LEET SYLLABUS
SYLLABUS FOR PULEET .
GENERAL ENGINEERING
(a) Basic Electrical Engineering
1. DC circuits: Voltage and current sources, Kircbboffs laws and network solution, network analysis by
mesh and node analysis, superposition theorem, Thevenins theorem, Nortons theorem, delta-star
transformation and vice-versa, maximum- power transfer theorem, energy storage elements, step
response of RL, RC and RLC circuits
2. Single Phase AC Fundamentals: Alternating current systems, waveform terms and definitions,
average and r.m.s. values of alternating, quantities, phasor notation, solution and phasor diagram of
single phase ac circuits with sinusoidal source excitation.
3. Three Phase AC Fundamentals: Disadvantages of single phase system, three phase voltages and
currents, voltages and currents in star and delta connected systems, power in a three phase system,
solution of three phase balanced circuits, power and power factor measurement by two watt-meter
method.
4. Magnetic Circuit: Introduction to magnetic circuit, magneto motive force and magnetic field strength,
permeability of free space, relative permeability, reluctance, comparison of electric and magnetic
circuits,B/H curve, magnetic circuits calculations, self and mutual inductance.
5. Translormers: Introduction, Basic Principle, EMF equation, approximate equivalent circuit, phasor
diagram, losses, efficiency and condition for maximum efficiency, voltage regulation, open circuit and
short circuit tests.
6. Electric Machines: Operating principle and application of DC machine as generator and motor, EMF
and Torque equations, methods of excitation.
Operating principle and applications of 3 phase squirrel cage and slip ring induction motors, equivalent
circuit and torque speed characteristics (qualitative treatment) Operating principle of single phase
induction motor (split Phase and capacitor motors), torque-speed characteristics (qualitative treatment)
Principle of operation and applications of variable reluctance, permanent magnet and hybrid stepper motors, speed torque characteristics (qualitative approach)
(b) BASIC ELECTRONICS
1. Semiconductor Diode: PN-Junction, Junction Theory, V-I characteristics of a PNJunction Diode,
Ideal Diode, Use of Diode in Rectifiers: Half Wave Rectifiers, Full Wave Rectifiers, Zener Diode,
Varacter Diode, Light Emitting Diodes.
2. Bipolar Junction Transistor: Introduction, Junction Transistor Structure, Operation, Transistor
amplifying action, GB, CC and CE Configuration, characteristics, application of transistor as an
amplifier.
3. Field Effect Transistor: Introduction, Types of FETs, JFETs, MOSFETs, CMOS, characteristics,
working, applications.
4. Operational Arnpliliers: Block Diagram, Characteristics of an ideal OP-AMP, Application of OP-AMP
as an Inveaing amplifier, Phase Shifter, Scale Changer, Noninverting amplifier, Adder or Summing
amplifier, differential or difterence amplifier, integrator.
5. Oscillators: Block Diagram of feedback circuit used as an oscillator, Barkbausen criterion, types of
oscillators.
6. Boolean Algebra and Logic Gates: Binary and Hexadecimal number system, BCD and weighted
codes, Binary arithmetic, Logic-positive and negative logic, basic and universal logic gates. Boolean
algebra and postulates, reduction of Boolean expression.
7. Flip Flops: Concept of flip-flops, RS, D, JK and T types, triggered and clocked, master slave, Shift
Register, concept of synchronous and asynchronous counters. Half and full adder, subtractor, Seven
Segment display, Concept of Mux, deMux, decoder and encoder.
8. Test and Measuring Instruments: Block diagram, concept of digital electronic voltmeters, ammeter
and wattmeter, CR0, Signal Generators, Sensors and Transducers and their classification. Working
principle of resistive, capacitive, photosensitive and temperature transducers. Block diagram and
working principle of analog and digital data acquisition system.
9. Communication: Basic Concepts, Modulation, Need for modulation, introduction to AM, FM, PM. (c) Programming Fundamentals
FUNDAMENTALS OF COMPUTER ENGG
1. Introduction: Computer Basic, Block Diagram of Computer, Memory Hierarchy, Types of RAM,
Secondary Memory Introduction to Operating Systems, Programming Languages,
Program Structure, Linux Shell Commands, Bourne Shell, C Shell, Korn Shell
2. Basic Constructs of C: Keywords, Identifiers, Variables, Symbolic Constants, Data Types
and their storage, Operands, Arithmetic Operators, Relational Operators, Logical
Operators, Bitwise Operators, Increment & Decrement Operators, Expressions, Conditional
Expressions, Assignment Operators and Expressions, Type Conversions, Precedence and
Order of Evaluation, External Variables and Scope of Variables. Basic Input Output,
Formatted I/O.
3. Program Control Flow: Statements and Blocks, Conditional Statements, IF, ELSE-I F, Switch Case
statements, Control Loops, For, While and Do-While, Go to and Labels,
4. Arrays & Functions: Pointers and Addresses, Arrays, Multi dimensional arrays, strings, pointer
arrays, Functions, Function Prototyping, Scope of functions, Arguments, Call by value and call by
references, static variables, recursion, C-Preprocessor and Macros, Command line arguments.
5. Structures: Structures, Array of Structures, pointer to structures, Typedef, Unions, Bit fields, passing
structures as an argument to functions
6. Input and Output: Standard and Formatted Input and Output, File Access & its types, Line Input and
Output, Types of Files, Binary & ASCII Files, Error handling, stderr and Exit functions
7. Introduction to Object Oriented Programming: Classes and Objects, Structures vs Classes,
Abstraction, Encapsulation, Polymorphism, Inheritance.
(d) FUNDAMENTAL OF MECHNICAL ENGG.
1. Laws 01 Thermodynamics: First law of thermodynamics, Steady flow energy equation and its
applications (nozzle, throttling device, turbine, compressor, heat exchanger). Limitations of first law,
statements of second law by Max-planck and Clausis, equivalence between the two statements.
Reversible and irreversible processes, Carnots theorem. Energy analysis of a heat engine, refrigerator
and heat pump.
2. Steam and Its Formation: P-V, P-T, T-S, H-S diagrams of water. Dryness fraction and its
measurement by calorimeter. Uses of steam tables and mollier chart (H-S chaa)
3. Power Cycles: Carnot and Rankine steam power cycles. Effect of mean temperature of heat
addition on Ranking cycle efficiency. Otto, Diesel and Dual combustion cycles for reciprocating 1.0.
engines.
4. Kinematics Of Fluid Flow: Types of flow, acceleration in fluid flow, stream lines, stream tubes,
irrotational flow, stream function, velocity potential, flow nets.
5. Fluid Dynamics: Equation of continuity, Eulers Equation, Bernoullis equation, simple applications to
one dimensional flow problems.
6. Flow Measurement: Pilot tube, Venturimeter, Orificemeter, Notches (Rectangular & Triangular) and
weirs, Rotameter.
7. Simple Stress and Strains: Concept of stress and strain. Stress and strains in bars subjected to
tension and compression, stress-strain diagrams, mechanical properties, factor of safety, Exlension of
Uniform bar under its own weight, stress produced in compound bars (two or three) due to axial loads.
8. Bending moment (B.M.) and Shear force( S. F.) : Diagrams for cantilevers, simply suppoaed beams
with or without overhang and calculation of maximum B.M. and S.F. and the point of contra flexture
under the following loads. Concentrated loads, Uniformly distributed loads over whole span or part of
span, combination of concentrated loads (two or three) and uniformly distributed loads.
9. Bending and Torsion: Stress in beams due to bending, proof of formulae Mu = fly = E/R and its
application to beams of rectangular and circular section. Application of torsion equation to hollow and
solid circular shaft.
II. PHYSICS
(a) MECHANICS
Linear kinematics and its equations of motion, projectile motion, circular motion.
Newbons laws of motion, principle of conservation of momentum applications to linear and planar
motion, concept of friction and its laws, motion on smooth and rough inclined planes, simple and
complex Atwoods machines.
Concept of work, energy and power, work-energy principle, principle of conservation of energy.
Rotational motion, equations of rotational kinematics, moment of inerbia and radius of gyration of a
rotating body: torque and angular momentum: work, power and energy in rotational motion,
conservation of angular momentum.
Simple harmonic motion and its characteristics, energetics of simple harmonic motion, idea of damped
and forced oscillations, resonance and its applications.
Wave motion and its characteristics, theory of sound propagation, velocity of sound and factors
influencing the velocity of sound, Doppler effect in sound, superposition of sound in space (stationary
waves) and time (beats), vibrations of air columns and stretched strings.
(b) OPTICS Geometrical optics, reflection and refraction of light, reflections by spherical mirrors, refraction through
lenses, spherical and chromatic aberrations, dispersion and deviation of light through prism, optical
microscopes and telescopes.
Wave nature of light: interference, Youngs double slit experiment, Lloyds mirror and Fresenels biprism
techniques for producing interference pattern, interference through thin film, colouring of thin films :
diffraction of light through a single slit, Rayleighs criteria of
resolution, resolving power of optical instruments concept of polarization, methods of producing
polarized light, analysis of polarized light, Doppler effect in light.
Laser, its principle, characteristics and applications.
(c)HEAT
Thermometry, idea of specific heat and heat capacity, latent heats of fusion and vaporization, variation
of specific heats of solids, liquids and gases with temperature, concept of degree of freedom, law of
equiparfition of energy.
Modes of heat transfer (conduction, convection and radiation): linear, surface and volume expansion
of matter on heating.
(d) ELECTROSTATICS Electric field and electric potential, electric dipole and its field, Gauss law and its applications: concept
of capacitance, energy stored in a capacitor, effect of introducing dielectric and conducting slabs
between plates of a capacitor, dielectric constant of material.
Current electricity, Kirchoffs laws and applications, thermal and chemical effects of current, slide wire
bridge, potentiometer, ammeter and voltmeter.
Magnetic effects of current, Biot-Savert law and its applications, Lorentz force, moving coil
galvanometers : laws of electromagnetic induction, eddy currents and its applications, self and mutual
inductance.
(e) MODERN PHYSICS
Black body radiation distribution, photoelectric effect, idea of x-ray production, wave-mailer duality and
de-Broglie waves, position-momentum uncertainty principle.
Crystalline and amorphous solids, basic idea of crystal structures (simple cubic, body- centered cubic,
face-centered cubic) and their characteristics, close packing morphologies, Scbottkey and Frenkel
defects in crystals.
Rutherford scailering experiment, Bohrs model and hydrogen spectrum.
Nucleus and its properties (mass, size, binding energy, magnetic and quadruple moments), nuclear
forces and its properties, phenomenon of radioactivity and its laws, modes of radioactive decays (cx,
and y), nuclear fission and fusion.
Ill MATHEMATICS
(a) Algebra:
Quadratic Equations, equations reducible to quadratic form, relation between roots and coefficients,
Arithmetic Progression, Geometric Progression, AritbmeticoGeometric Progression, Harmonic
Progression, Series of Natural Numbers.
(b) Matrices:
Concept of linear independence and dependence, Rank of a matrix: Row — Echelon form, System of
linear equations: Condition for consistency of system of linear equations, Inverse of a matrix.
(c ) Trigonometry:
Trigonometric ratios and their relations, ratios of some standard angles, solution of trigonometric
equations, sum and difference formulae, product formulae, multiple and sub-multiple angles, solution
of triangles.
(d) Coordinate Geometry:
Cartesian coordinates, equations of straight line in various forms, intersection of two straight lines,
angle between two lines, distance formula. Equation of circle in various forms, tangent and normal to
circle.
(e) Differential Calculus ol Functions ol one variable:
Successive Differentiation, Leibnitz Theorem, Expansions of functions: Taylors and Maclaurins Series,
Formulae for remainder term in Taylor and Maclaurin series, Angle of contingence, Curvature, Radius
of curvature, Centre of curvature for curves in Caaesian form. Curvature at the origin: Newlons
formulas.
(I) Differential Calculus ol Functions ol two variables:
Concept of limit and continuity of a function of two variables, Partial derivatives, total differential,
differentiation of an implicit function, chain rule, change of variables, Jacobian, Taylors and Maclaurins
series. Maxima and minima of a function of two variables: Lagranges method of multipliers.
(g) Ordinary Ditlerential Equations:
Review of geometrical meaning of the differential equation[çí . directional fields, Exact differential
equations, Integrating factors.
(N Integral Calculus:
Reduction formula for fsi n sdx, fcos sdx,
fsin xcos sax.fx ç]ogxY dx. fx dx.fx sil] nudx.fx cosnudx. Areas of curves, Length of curves, Volume and
surface areas of revolution, Double integrals, Change of order of integration, Areas enclosed by plane
curves.
Vector Ditlerential Calculus:
Vectors and scalar functions and fields, derivatives. Curves, tangents, arc lengths,
Curvature and torsion of a curve, Gradient of a Scalar field, Directional Derivative,
Divergence of a vector field, Curl of a vector field.
Ii) Vector Integral Calculus: Line integrals, Line integrals independent of path, Greens theorem in the plane, Surface Integrals, Triple integrals, Gauss Divergence Theorem, Stokes Theorem.
IV ENVIRONMENT EDUCATION
Ecology and Ecosystems
Structure and functions of Ecosystems, producers, consumers & Decomposers, ecological
succession, food chains, food webs & ecological pyramids.
Biodiversity and its conservation
Genetics, species, and ecosystem diversity, Biodiversity at global, National and
Local levels, Threats to diversity.
Natural Resources
Air resources, composition, air quality management
Forest resources, deforestation, case studies, timber edractions, mining, dams and their effects on
forests.
Water Resources: Use and over utilization of surface and water, floods, draught, water quality
management.
Food Resources: World food problems, effects of modern Agriculture, water logging.
Energy Resources: Growing energy needs, renewable and non renewable energy sources.
Land Resources: Land degradation, soil erosion & deseaification
Environmental Pollution
Air pollution, water pollution, thermal pollution, soil pollution, noise pollution, their causes, effects &
control measures.
GENERAL ENGINEERING
(a) Basic Electrical Engineering
1. DC circuits: Voltage and current sources, Kircbboffs laws and network solution, network analysis by
mesh and node analysis, superposition theorem, Thevenins theorem, Nortons theorem, delta-star
transformation and vice-versa, maximum- power transfer theorem, energy storage elements, step
response of RL, RC and RLC circuits
2. Single Phase AC Fundamentals: Alternating current systems, waveform terms and definitions,
average and r.m.s. values of alternating, quantities, phasor notation, solution and phasor diagram of
single phase ac circuits with sinusoidal source excitation.
3. Three Phase AC Fundamentals: Disadvantages of single phase system, three phase voltages and
currents, voltages and currents in star and delta connected systems, power in a three phase system,
solution of three phase balanced circuits, power and power factor measurement by two watt-meter
method.
4. Magnetic Circuit: Introduction to magnetic circuit, magneto motive force and magnetic field strength,
permeability of free space, relative permeability, reluctance, comparison of electric and magnetic
circuits,B/H curve, magnetic circuits calculations, self and mutual inductance.
5. Translormers: Introduction, Basic Principle, EMF equation, approximate equivalent circuit, phasor
diagram, losses, efficiency and condition for maximum efficiency, voltage regulation, open circuit and
short circuit tests.
6. Electric Machines: Operating principle and application of DC machine as generator and motor, EMF
and Torque equations, methods of excitation.
Operating principle and applications of 3 phase squirrel cage and slip ring induction motors, equivalent
circuit and torque speed characteristics (qualitative treatment) Operating principle of single phase
induction motor (split Phase and capacitor motors), torque-speed characteristics (qualitative treatment)
Principle of operation and applications of variable reluctance, permanent magnet and hybrid stepper motors, speed torque characteristics (qualitative approach)
(b) BASIC ELECTRONICS
1. Semiconductor Diode: PN-Junction, Junction Theory, V-I characteristics of a PNJunction Diode,
Ideal Diode, Use of Diode in Rectifiers: Half Wave Rectifiers, Full Wave Rectifiers, Zener Diode,
Varacter Diode, Light Emitting Diodes.
2. Bipolar Junction Transistor: Introduction, Junction Transistor Structure, Operation, Transistor
amplifying action, GB, CC and CE Configuration, characteristics, application of transistor as an
amplifier.
3. Field Effect Transistor: Introduction, Types of FETs, JFETs, MOSFETs, CMOS, characteristics,
working, applications.
4. Operational Arnpliliers: Block Diagram, Characteristics of an ideal OP-AMP, Application of OP-AMP
as an Inveaing amplifier, Phase Shifter, Scale Changer, Noninverting amplifier, Adder or Summing
amplifier, differential or difterence amplifier, integrator.
5. Oscillators: Block Diagram of feedback circuit used as an oscillator, Barkbausen criterion, types of
oscillators.
6. Boolean Algebra and Logic Gates: Binary and Hexadecimal number system, BCD and weighted
codes, Binary arithmetic, Logic-positive and negative logic, basic and universal logic gates. Boolean
algebra and postulates, reduction of Boolean expression.
7. Flip Flops: Concept of flip-flops, RS, D, JK and T types, triggered and clocked, master slave, Shift
Register, concept of synchronous and asynchronous counters. Half and full adder, subtractor, Seven
Segment display, Concept of Mux, deMux, decoder and encoder.
8. Test and Measuring Instruments: Block diagram, concept of digital electronic voltmeters, ammeter
and wattmeter, CR0, Signal Generators, Sensors and Transducers and their classification. Working
principle of resistive, capacitive, photosensitive and temperature transducers. Block diagram and
working principle of analog and digital data acquisition system.
9. Communication: Basic Concepts, Modulation, Need for modulation, introduction to AM, FM, PM. (c) Programming Fundamentals
FUNDAMENTALS OF COMPUTER ENGG
1. Introduction: Computer Basic, Block Diagram of Computer, Memory Hierarchy, Types of RAM,
Secondary Memory Introduction to Operating Systems, Programming Languages,
Program Structure, Linux Shell Commands, Bourne Shell, C Shell, Korn Shell
2. Basic Constructs of C: Keywords, Identifiers, Variables, Symbolic Constants, Data Types
and their storage, Operands, Arithmetic Operators, Relational Operators, Logical
Operators, Bitwise Operators, Increment & Decrement Operators, Expressions, Conditional
Expressions, Assignment Operators and Expressions, Type Conversions, Precedence and
Order of Evaluation, External Variables and Scope of Variables. Basic Input Output,
Formatted I/O.
3. Program Control Flow: Statements and Blocks, Conditional Statements, IF, ELSE-I F, Switch Case
statements, Control Loops, For, While and Do-While, Go to and Labels,
4. Arrays & Functions: Pointers and Addresses, Arrays, Multi dimensional arrays, strings, pointer
arrays, Functions, Function Prototyping, Scope of functions, Arguments, Call by value and call by
references, static variables, recursion, C-Preprocessor and Macros, Command line arguments.
5. Structures: Structures, Array of Structures, pointer to structures, Typedef, Unions, Bit fields, passing
structures as an argument to functions
6. Input and Output: Standard and Formatted Input and Output, File Access & its types, Line Input and
Output, Types of Files, Binary & ASCII Files, Error handling, stderr and Exit functions
7. Introduction to Object Oriented Programming: Classes and Objects, Structures vs Classes,
Abstraction, Encapsulation, Polymorphism, Inheritance.
(d) FUNDAMENTAL OF MECHNICAL ENGG.
1. Laws 01 Thermodynamics: First law of thermodynamics, Steady flow energy equation and its
applications (nozzle, throttling device, turbine, compressor, heat exchanger). Limitations of first law,
statements of second law by Max-planck and Clausis, equivalence between the two statements.
Reversible and irreversible processes, Carnots theorem. Energy analysis of a heat engine, refrigerator
and heat pump.
2. Steam and Its Formation: P-V, P-T, T-S, H-S diagrams of water. Dryness fraction and its
measurement by calorimeter. Uses of steam tables and mollier chart (H-S chaa)
3. Power Cycles: Carnot and Rankine steam power cycles. Effect of mean temperature of heat
addition on Ranking cycle efficiency. Otto, Diesel and Dual combustion cycles for reciprocating 1.0.
engines.
4. Kinematics Of Fluid Flow: Types of flow, acceleration in fluid flow, stream lines, stream tubes,
irrotational flow, stream function, velocity potential, flow nets.
5. Fluid Dynamics: Equation of continuity, Eulers Equation, Bernoullis equation, simple applications to
one dimensional flow problems.
6. Flow Measurement: Pilot tube, Venturimeter, Orificemeter, Notches (Rectangular & Triangular) and
weirs, Rotameter.
7. Simple Stress and Strains: Concept of stress and strain. Stress and strains in bars subjected to
tension and compression, stress-strain diagrams, mechanical properties, factor of safety, Exlension of
Uniform bar under its own weight, stress produced in compound bars (two or three) due to axial loads.
8. Bending moment (B.M.) and Shear force( S. F.) : Diagrams for cantilevers, simply suppoaed beams
with or without overhang and calculation of maximum B.M. and S.F. and the point of contra flexture
under the following loads. Concentrated loads, Uniformly distributed loads over whole span or part of
span, combination of concentrated loads (two or three) and uniformly distributed loads.
9. Bending and Torsion: Stress in beams due to bending, proof of formulae Mu = fly = E/R and its
application to beams of rectangular and circular section. Application of torsion equation to hollow and
solid circular shaft.
II. PHYSICS
(a) MECHANICS
Linear kinematics and its equations of motion, projectile motion, circular motion.
Newbons laws of motion, principle of conservation of momentum applications to linear and planar
motion, concept of friction and its laws, motion on smooth and rough inclined planes, simple and
complex Atwoods machines.
Concept of work, energy and power, work-energy principle, principle of conservation of energy.
Rotational motion, equations of rotational kinematics, moment of inerbia and radius of gyration of a
rotating body: torque and angular momentum: work, power and energy in rotational motion,
conservation of angular momentum.
Simple harmonic motion and its characteristics, energetics of simple harmonic motion, idea of damped
and forced oscillations, resonance and its applications.
Wave motion and its characteristics, theory of sound propagation, velocity of sound and factors
influencing the velocity of sound, Doppler effect in sound, superposition of sound in space (stationary
waves) and time (beats), vibrations of air columns and stretched strings.
(b) OPTICS Geometrical optics, reflection and refraction of light, reflections by spherical mirrors, refraction through
lenses, spherical and chromatic aberrations, dispersion and deviation of light through prism, optical
microscopes and telescopes.
Wave nature of light: interference, Youngs double slit experiment, Lloyds mirror and Fresenels biprism
techniques for producing interference pattern, interference through thin film, colouring of thin films :
diffraction of light through a single slit, Rayleighs criteria of
resolution, resolving power of optical instruments concept of polarization, methods of producing
polarized light, analysis of polarized light, Doppler effect in light.
Laser, its principle, characteristics and applications.
(c)HEAT
Thermometry, idea of specific heat and heat capacity, latent heats of fusion and vaporization, variation
of specific heats of solids, liquids and gases with temperature, concept of degree of freedom, law of
equiparfition of energy.
Modes of heat transfer (conduction, convection and radiation): linear, surface and volume expansion
of matter on heating.
(d) ELECTROSTATICS Electric field and electric potential, electric dipole and its field, Gauss law and its applications: concept
of capacitance, energy stored in a capacitor, effect of introducing dielectric and conducting slabs
between plates of a capacitor, dielectric constant of material.
Current electricity, Kirchoffs laws and applications, thermal and chemical effects of current, slide wire
bridge, potentiometer, ammeter and voltmeter.
Magnetic effects of current, Biot-Savert law and its applications, Lorentz force, moving coil
galvanometers : laws of electromagnetic induction, eddy currents and its applications, self and mutual
inductance.
(e) MODERN PHYSICS
Black body radiation distribution, photoelectric effect, idea of x-ray production, wave-mailer duality and
de-Broglie waves, position-momentum uncertainty principle.
Crystalline and amorphous solids, basic idea of crystal structures (simple cubic, body- centered cubic,
face-centered cubic) and their characteristics, close packing morphologies, Scbottkey and Frenkel
defects in crystals.
Rutherford scailering experiment, Bohrs model and hydrogen spectrum.
Nucleus and its properties (mass, size, binding energy, magnetic and quadruple moments), nuclear
forces and its properties, phenomenon of radioactivity and its laws, modes of radioactive decays (cx,
and y), nuclear fission and fusion.
Ill MATHEMATICS
(a) Algebra:
Quadratic Equations, equations reducible to quadratic form, relation between roots and coefficients,
Arithmetic Progression, Geometric Progression, AritbmeticoGeometric Progression, Harmonic
Progression, Series of Natural Numbers.
(b) Matrices:
Concept of linear independence and dependence, Rank of a matrix: Row — Echelon form, System of
linear equations: Condition for consistency of system of linear equations, Inverse of a matrix.
(c ) Trigonometry:
Trigonometric ratios and their relations, ratios of some standard angles, solution of trigonometric
equations, sum and difference formulae, product formulae, multiple and sub-multiple angles, solution
of triangles.
(d) Coordinate Geometry:
Cartesian coordinates, equations of straight line in various forms, intersection of two straight lines,
angle between two lines, distance formula. Equation of circle in various forms, tangent and normal to
circle.
(e) Differential Calculus ol Functions ol one variable:
Successive Differentiation, Leibnitz Theorem, Expansions of functions: Taylors and Maclaurins Series,
Formulae for remainder term in Taylor and Maclaurin series, Angle of contingence, Curvature, Radius
of curvature, Centre of curvature for curves in Caaesian form. Curvature at the origin: Newlons
formulas.
(I) Differential Calculus ol Functions ol two variables:
Concept of limit and continuity of a function of two variables, Partial derivatives, total differential,
differentiation of an implicit function, chain rule, change of variables, Jacobian, Taylors and Maclaurins
series. Maxima and minima of a function of two variables: Lagranges method of multipliers.
(g) Ordinary Ditlerential Equations:
Review of geometrical meaning of the differential equation[çí . directional fields, Exact differential
equations, Integrating factors.
(N Integral Calculus:
Reduction formula for fsi n sdx, fcos sdx,
fsin xcos sax.fx ç]ogxY dx. fx dx.fx sil] nudx.fx cosnudx. Areas of curves, Length of curves, Volume and
surface areas of revolution, Double integrals, Change of order of integration, Areas enclosed by plane
curves.
Vector Ditlerential Calculus:
Vectors and scalar functions and fields, derivatives. Curves, tangents, arc lengths,
Curvature and torsion of a curve, Gradient of a Scalar field, Directional Derivative,
Divergence of a vector field, Curl of a vector field.
Ii) Vector Integral Calculus: Line integrals, Line integrals independent of path, Greens theorem in the plane, Surface Integrals, Triple integrals, Gauss Divergence Theorem, Stokes Theorem.
IV ENVIRONMENT EDUCATION
Ecology and Ecosystems
Structure and functions of Ecosystems, producers, consumers & Decomposers, ecological
succession, food chains, food webs & ecological pyramids.
Biodiversity and its conservation
Genetics, species, and ecosystem diversity, Biodiversity at global, National and
Local levels, Threats to diversity.
Natural Resources
Air resources, composition, air quality management
Forest resources, deforestation, case studies, timber edractions, mining, dams and their effects on
forests.
Water Resources: Use and over utilization of surface and water, floods, draught, water quality
management.
Food Resources: World food problems, effects of modern Agriculture, water logging.
Energy Resources: Growing energy needs, renewable and non renewable energy sources.
Land Resources: Land degradation, soil erosion & deseaification
Environmental Pollution
Air pollution, water pollution, thermal pollution, soil pollution, noise pollution, their causes, effects &
control measures.
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