Frabjous said:
Physics heavy and physics are not the same thing.
We are already at post 28 and I cannot believe that you are going to make us ask for the specific curricula that you are evaluating. You are going to burn people out.
Ok sorry im just going post the math and physics related parts of each program its going to be long but here :
prep year ( shared by both ) :
Math 1:
Differential Calculus (Differentiation)
Transcendental functions – Inverse function of transcendental functions –Derivative of
transcendental functions – Leibniz’s rule –L’hopital’s rule – Mean value theorem – Taylor and
Maclaurin series –Functions of several variables – Partial derivatives – Applications of partial
derivatives.
Algebra
Binomial theorem – Partial fractions – Mathematical induction – Theory of equations –Matrices and
determinants –System of linear algebraic equations (Gauss methods)– Applications of system of
linear algebraic equations – Eigenvalues and Eigenvectors – Vector space.
Math 2:
Integral Calculus (Integration)
Integration techniques – Reduction formula – Definite integral and its properties – Improper integral
– Applications of integration (area, volume, and arc length) – First order ordinary differential
equations (separable, homogeneous, exact, linear and Bernoulli) and their applications– Infinite
series.
Analytic Geometry
Two-variable quadratic equations – Conic sections (circle, parabola, ellipse and hyperbola) –
Parametric equations of conic sections –Coordinates systems in plane and space – Line and plane in
space – Quadratic surfaces (cylinder, sphere, ellipsoid, hyperboloid, cone and paraboloid).
Mechanics 1:
Statics: Force vectors in three dimensions - Equilibrium of a particle in three dimension – System of
forces and moments – Moment of a force about point and line - Moment of a couple – Equivalent
systems of forces and couples – Reduction of systems of forces and couples - Equilibrium of Rigid
body in two dimension - Equilibrium of Rigid body in three dimension - Center of gravity and
centroid– Frames and Machines: Analysis of frames – Dismembering connected parts of the frame -
Analysis of Machines.
Mechanics 2:
Statics: Distributed forces– Fluid statics: Hydrostatic forces – Horizontal, Vertical and Inclined flat
plate, curved plate of constant width –Trusses: Internal and external redundancy, Assumptions of
design, Method of joints and Methods of sections. – Friction: Types of friction, Theory of dry
friction – Static friction and Impending motion – Kinetic friction – Types of problems involving dry
friction – Wedges – Power screws.
Dynamics: Introduction to dynamics – Kinematics of a particle: curvilinear Motion – Rectangular
components – Motion of projectiles – Normal and Tangential components – cylindrical components
Physics 1:
Mechanical Properties of matter:
Units and dimensional analysis - Mechanical Properties of metals - Oscillations- The waves and
superposition principle -The Sound Waves – Doppler effect.
Heat and thermodynamics:
Temperature and thermometers – Quantity of heat - Thermal expansion- Heat Transfer- The first law
of thermodynamics- the entropy and the second law of thermodynamics.
Physics 2:
Electricity and Magnetism:
The Charge and matter - The electric field – Coulomb's law- The electric flux Gauss's law - The
electric Potential - the capacitors and dielectrics- The magnetic field -Boit- Savart's law- The
magnetic flux Gauss's Law – Faraday's Law- Magnetic Induction.
Optics and atomic physics:
Nature of light -Interference - Diffraction - Polarization - Early quantum theory - Special Relativity.
ECE:
Math 3:
Ordinary Differential Equations (ODE)
Homogeneous higher order ODE – Nonhomogeneous higher order ODE with constant coefficients
(undesemesterined coefficients method and variation of parameters method for finding the particular
solution) – Cauchy-Euler ODE (homogeneous and nonhomogeneous) – System of ODE– Laplace transform
– Inverse Laplace transform –Applications of Laplace transform – Series solution of ODE.
Functions of Several Variables
Differentiation of integration – Vector calculus –Multiple integrals double and triple) and their applications
–Line integral – Green’s theorem – Surface integral – Divergence (Gauss) and Stokes’ theorems –
Mathematical modeling using partial differential equations
Math 4:
Partial Differential Equations (PDE)
Special functions (Gamma, Beta, Bessel and Legendre) – Fourier series – Fourier integral – Fourier
transform – Partial differential equations (PDE) – Separation of variables method (heat equation, wave
equation and Laplace equation) – Traveling wave solutions to PDE.
Complex Analysis
Complex Numbers – Functions of complex variable – Complex derivative – Analytic functions – Harmonic
functions and their applications – Elementary functions – Complex integration – Cauchy theorems and
their applications – Taylor and Laurent series – Residue theorem and its applications – Conformal mapping.
Math 5:
Numerical Methods
Curve fitting – Interpolation – Numerical integration – Numerical solution of algebraic and transcendental
equations – Iterative methods for solving system of linear algebraic equations – Numerical differentiation –
Numerical solution of ordinary differential equations – Numerical solution of partial differential equations–
Finite difference method.
Applied Probability and Statistics
Introduction to probability – Discrete random variables – Special discrete distributions – Continuous
random variables – Special continuous distributions – Multiple random variables – Sampling distribution
and estimation theory – Test of hypotheses – Correlation theory – Analysis of time series.
Solid state and electronics devices:
Crystals in solids, properties; Quantum theory of solid; Electron and hole properties in semiconductors,
doping of semiconductors, Fermi Dirac; Semiconductors in equilibrium. Doping, electric conductivity, PN
Junction: Operation, forward bias, reverse bias; Metal-Semiconductor Junction. Diodes Characteristics –
Zener and Schottky Barrier Diode - Diode SPICE Model. Diode Circuits Analysis. Field-Effect Transistors
MOS Characteristics.The NMOS Transistor Characteristics- Mode MOSFETS – MOSFET Circuit Symbols –
MOSFET Modeling in SPICE. The Junction Field-Effect Transistor – Bipolar Junction Transistors – Physical
Structure – the NPN Transistor model – The Complete Transport Model Equations for Arbitrary Bias
Equivalent Circuit Representations, The Operating Regions of the BJT, Biasing, PNP and other Devices.
Engineering thermodynamics:
Fundamental Concepts; First Law of Thermodynamics; Second Law of Thermodynamics; General
Thermodynamic relations (Maxwell), Application of thermodynamic principles to simple engine cycles;
Properties of vapours with specific reference to the use of the steam tables; Application to simple Rankine and
refrigeration cycles; Properties of mixtures with specific reference to the measurement of humidity;
Dimensional Analysis; Buckingham's theorem and derivation of some basic dimensional groups; Heat Transfer:
use of the basic laws for simple problems in conduction, convection and radiation
Electromagnetic fields:
Review of Vector Algebra and Calculus, Coulomb’s Law and the Electric Field Intensity, Electric Flux and
Flux Density Gauss’s Law, Electrostatic potential, Conductors, Dielectrics, and Capacitance, Boundary
conditions for electrostatic fields, Uniqueness, Method of Images, Simple Boundary value problems,
Conformal Mapping Technique, Electrostatic Energy, The Steady Magnetic Field, Biot-Savart law, The
Vector magnetic potential, Magnetic materials, Boundary Conditions, Inductance, Magnetic energy,
Magnetic Forces, and Torque: Lorentz force, Time Varying Fields and Maxwell's Equations: Introduction.
Microwave electronics:
Introduction; O type tubes; Two cavity Klystron; Reflex Klystron; M-type tubes-bMagnetron: Construction
and Principle of operation of 8 cavity cylindrical travelling wave magnetron, o/p characteristics,
Applications; Slow wave devices: Advantages of slow wave devices, Helix TWT: Construction and principle
of operation, Applications; Microwave Solid State Devices: Microwave bipolar transistor, FET, MESFET,
Varactor Diode, PIN Diode, Shottky Barrier Diode, Tunnel Diode, Gunn Diodes, IMPATT diode and TRAPATT
diode. Principle of operation, various modes, specifications, and applications of all these devices; Theory of
lasers Oscillator.
Discrete math:
Logic and logical equivalence- Methods of proofs- Mathematical induction- Algorithms- Basic counting
techniques- Advanced counting techniques- Recurrence relations- Binary relations- Graphs - Shortest path
algorithm- Trees- Minimum spanning trees.
Opto-electronics:
Optoelectronics: Wave Nature of Light, Dielectric Waveguides and Optical Fibers, Light-Emitting Diodes,
Stimulated Emission Devices: Optical Amplifiers and Lasers, Photodetectors and Image Sensors,
Polarization and Modulation of Light.
Electromagnetic waves:
Review of Maxwell's equations; Uniform Plane waves, Waves in unbounded lossless media , Polarization of
plane waves, Phase velocity and group velocity, Waves in Lossy media; Reflection, Refraction, and
Diffraction; Electromagnetic Theorems; Wave propagation on a transmission line; Smith Chart, impedance
mismatches and reflections; TEM, TE and TM electromagnetic waves, parallel-plate waveguide;
Rectangular waveguide and cylindrical waveguide; Planar transmission lines; Microwave Network Analysis;
Impedance Matching and Tuning; Microwave Resonators; Microwave Passive Components.
Nano-photonics:
Introduction: Photonics and Optoelectronics: why nano? – Nano-photonics overview; Materials for Nano
photonics: Quantum effect for electronic confinement: quantum dots, Nano-particles – from
semiconductor to organic, Microcavity effect for photonic confinement: photonic crystals; Building Blocks
for Nano-photonics: Nano-lasers, Nano-detectors, Nano-sensors, Nano-channels; System Integration for
Nano-photonics: Photonic crystal Nano-PIC, Silicon PIC, Other approaches.
Nuclear engineering:
MP 113 Mathematics – 3
Methods of Integration, some special techniques, successive reduction method, improper integrals,
mean value theorem special function: the error, gamma and beta functions of several variables,
limits and continuity, partial derivatives, chain rule directional derivatives, Taylor expansions of
functions of several variables, extreme, differentiation under integral sign.
Sequences, series, convergence and convergence tests, uniform convergence. Fourier series
expansions of general periodic functions, expansions of even and odd functions, convergence and
remarks.
MP x14 Mathematics-4
Multiple Integral, Regions in plane and space, Double and triple integrals, Change of variables
technique and the Jacobeans, Line integrals and green theorem, ordinary differential equations of
the second order and higher. Elle’s homogeneous equations and simultaneous differential equation.
Calculus of finite differences, Vector algebra, Scalar and cross product. Identifies, Application.
Line and planes in space, Spherical and cylindrical coordinate systems, Quadratic surfaces. Line,
Surface and volume integral, green’s and stock’s and divergence theorems.
MP 215 Mathematics-5
Ordinary and Prtial differential equation: Solution of ordinary differential equations with variable
Coefficients, system of linear differential equations, heat wave and Iapilace equation in two and
three dimensions. Separation of variable technique, some boundary value problems and
applications. Numerical solutions of differential equation.
Complex analysis: Function of complex variables, differentiation and integration, analytic
functions, cache theorem and cache formula. Contour integration, power, series expansion,
conformal mapping vector analysis: Scalar and vector fields, vector, operator, application to
geometry, line, surface and volume integral, divergence theorem of gauss stock’s and Green
theorem. Curvilinear and orthogonal coordinates.
MP x16 Mathematics-6
Numerical analysis (Gauss elimination method, numerical solution of nonlinear algebraic equations,
numerical integration, interpolation, numerical solution of differential equations, error analysis),linear algebra (vector spaces, independence, bases, subspaces, dimensions, linear transformations
and matrices, eigen values and eigen vectors, inner product), special functions (beta and gamma
functions, Legendre functions, Bessel functions, Chebyshev functions), Z-transform.
MP 317 Mathematics-7
Numerical analysis (Gauss elimination method, numerical solution of nonlinear algebraic equations,
numerical integration, interpolation, numerical solution of differential equations, error analysis),
introduction to probability theory (sample space, conditional probability and Bayes' theorem,
discrete and continuous random variables, distribution functions, expectation and variance, some
special distributions, moments and moment generating function, central limit theorem and law of
large numbers, Chebyshev's inequality).
MP128 Mechanics-8
Central Force Motion: Polar Coordinates – Properties of central Force Motion – Equation of
Motion – Applications to Space Mechanics –Kinetics of System of Particles: Equations of Motion-
Motion of the Mass Center of System of Particles – Systems Gaining or Losing Mass: Motion of
Rockets – Motion of Chains and Cables- Plane Kinematics of Rigid Bodies: Translational,
Rotational and General plane motion- Instantaneous center of rotation in plane motion – Rolling
without sliding – Gears – Mechanisms - Kinetics of Plane Motion of Rigid Bodies : Angular
Momentum – Kinetic Energy – Equations of Motion – Moment of Inertia – Applications- Initial
Motion –Impulse and Momentum of Plane motion of Rigid Bodies : Principle of Impulse and
Momentum for a rigid Body and for a System of Rigid Bodies – Collision of Rigid Bodies –
Mechanical Vibrations: Free Vibrations – Damped Free Vibrations – Forced Vibrations –
Analytical Mechanics: Generalized Coordinates - Energy and Work – Canonical Transformations –
Lagrange’s Equations – The Hamiltonian – Hamiltonian form of the Equation of motion –
Applications – Wave Mechanics.
NE111 Modern Physics
Special Theory of Relativity, Photoelectric Ionization, X-Rays, Compton Scattering, Waves and
Particles, Atomic Structure, Atomic Models, Uncertainty Principle, Pauli Exclusion Principle.
NE121 Introduction to Engineering Materials Science
Atomic Structure and Atomic Bonding, Crystalline Structure of Solids, Defects in Solids, Diffusion,
Phase Diagrams, Characterization of Materials.
NE211 Nuclear Physics
Nuclear Radii, Nuclear Charge and Mass, Bonding Energy and Nuclear Stability, Natural and
Artificial Radioactivity, Nuclear Transmutations: Alpha, Beta, and Gamma Transmutations,
Nuclear Reactions, Nuclear Forces and Models.
NE251 Thermodynamics and Kinetic Theory of Gases
Basics and Definitions, Properties of Pure Materials, Heat and Work, The First Law of
Thermodynamics, The Second Law of Thermodynamics, The Entropy, Introduction to the Kinetic
Theory of Gases, Maxwell-Boltzmann Distribution, Deduction of the Properties of Gases.
NE311 Quantum Mechanics
Schrödinger Wave Equation, Synchronized Oscillator, Multi Particles Systems, Potential Wells,
Angular Momentum, The Scattering Problem.
NE312 Plasma and Electromagnetic Theory
Vector Algebra (Revision), Electric Potential and Field, Gauss' Law, Magnetic Field, Ampere's
Law, Faraday's Law for Induction, Maxwell's Equations and the Limits Conditions, Introduction to
Plasma, Single Particle Motion, Fluidized Plasma, Waves in the Plasma, Diffusion and Resistance,
Equilibrium and Stability, The Kinetic Theory, Introduction to Fusion Reactors and Devices,
Fabrication of Semiconductors Using the Plasma, Polymers, Plasma Spray Coating.
NE331 Nuclear Reactors Physics
Nuclear Physics (Revision), Reactions Cross Sections, Nuclear Fission, Reaction Rates and Energy
Threshold, Fission Products, Neutrons from Fission, Energy Released from Fission, Nuclear Fission
Theory, Neutrons Diffusion, Fick's Law for Diffusion, Methods for Solving the Diffusion Equations
with Different Boundary Conditions, Neutrons Moderation without Absorption in Hydrogenous
Media, Neutrons Moderation using Non Hydrogenous Moderators, Equation of Neutron Moderation
and Diffusion, Neutrons Moderation and Diffusion with Absorption, Numerical Methods for
Solving Diffusion Equations in Homogeneous Media.
NE351 Heat Transfer
Fundamental Laws for Heat Transfer, Steady State Conduction in One and Multiple Dimensions,
Variable Conduction, Heat Transfer by Natural and Forced Convection, Condensation and Boiling,
Heat Exchangers, Heat Transfer by Radiation
ME 232 Fluid Mechanics and Flow Engineering
Fluid properties – Fluid statics and kinematics – Flow in pipes – Pumps – Valves – Dimensionless
analysis and similitude
NE343 Introduction to Simulation of Radiation Transport
Analytical Methods used to Analyze Radiation Transport Described by Different Differential and
Integral Equations, Numerical Methods: Finite Difference, Finite Elements, Finite Orthogonal
Coordinates, Monte Carlo Method
