Topics: Materials Science, materials Engineering, Rutherford model, Bohr model, atom, De- Broglie’s atomic model, Atomic bonding, ionic bonding, covalent bonding, Secondary Bonding, metallic bonding, Fluctuating Induced Dipole Bonds, Polar Molecule-Induced Dipole Bonds, Permanent Dipole Bonds, Crystallography, crystal structures, Crystal Lattice, Bravais lattices, Metallic Crystal Structures, Polycrystalline Materials, Non-Crystalline Solids, Miller Indices, Point Defects, Mechanical Properties of Metals, Stress-Strain curve, Elastic deformation, plastic deformation, Tensile Properties, Brinell Hardness Test, Micro-hardness Test, Knoop Hardness Test, Scleroscope Hardness Test, durometer, fracture, creep, dislocation, Solid-Solution Strengthening, Microstructural Exam, Grain size determination, carbon steel, cast iron, alloy, Dielectric Materials, Dielectric strength, Intrinsic dielectric strength, Magnetic Properties, Diamagnetism, Ferromagnetism, Ferrimagnetism, Hard Magnetic Materials, Extrinsic Semiconductor, semiconductor

Topics: measurement, estimating, motion, kinematics, dynamics, friction, circular motion, drag forces, gravitation, Newton's synthesis, work, energy, conservation of energy, linear momentum, rotational motion, angular momentum, static equilibrium, elasticity, fracture, fluids, oscillators, wave motion, sound, temperature, thermal expansion, ideal gas law, kinetic theory of gases, thermodynamics, electric charge, electric field, Gauss law, electric potential, capacitance, dielectrics, electric energy storage, electric currents, resistance, DC circuits, magnetism, magnetic field sources, electromagnetic induction, inductance, electromagnetic oscillations, AC circuits, Maxwell's equations, electromagnetic waves, light, reflection, refraction, lenses, optical instruments, wave nature of light, diffraction, polarization, quantum theory, quantum mechanics, molecules, solids, nuclear physics, radioactivity, nuclear energy, elementary particles

Topics: self-adjoint operators, Eigen function expansion, simple model system, linear algebra, BRA-Ket notation, formal developments, harmonic oscillators, coherent state, quantum mechanics, angular momentum, stationary perturbations, perturbation theory, scattering off potentials, density of state, time-independent perturbation, perturbation, path integrals, polarizability tensor, electromagnetic coupling, Lagrangian field theory, Non-relativistic Quantum Field Theory, Maxwell field, relativistic quantum fields, spinor QED

Topics: discrete mathematics, mathematical logic, functions, proofs, set theory, set operations, axiomatic set theory, real numbers, arithmetic, induction, recursion, summation notation, Asymptotic notation, number theory, graphs, multiplication, exponentiation, binomial coefficients, generating functions, probability theory, random variables, Markov's inequality, probability generating functions, linear algebra, abstract vector spaces, finite fields

Topics: Limits, Continuity, Calculus, differentiation, Transcendental Functions, Integration, Integration techniques, conics, parametric curves, polar curves, sequence, series, power series, vectors, Coordinate Geometry, vector functions, vector curves, partial differentiation, partial derivatives, multiple integration, vector fields, vector calculus, Differential Forms, Exterior Calculus, Ordinary Differential Equations

Topics: Calculus, limits, continuity, transcendental function, differentiation, integration, conics, parametric curvess, polar curves, sequence, series, power series, vectors, coordinate geometry, vector functions, curves, partial differentiation, multiple integration, vector fields, vector calculus, differential forms, exterior calculus, ordinary differential equations

Topics: functions, combining functions, trigonometric functions, exponential functions, inverse functions, logarithms, limit, continuity, derivatives, differentiation rules, chain rule, implicit differentiation, inverse trigonometric functions, related rates, linearization, differentials, mean value theorem, monotonic functions, applied optimization, integrals, transcendental functions, hyperbolic functions, integration, trigonometric integrals, trigonometric substitution, numerical integration, improper integrals, infinite sequences, infinite series, integral test, comparison test, absolute convergence, power series, Taylor series, Maclurin series, parametric equations, polar coordinates, vectors, dot product, cross product, vector-valued functions, partial derivatives, saddle points, multiple integrals, vector fields, Euler equations

Topics: Advanced engineering mathematics, numerical solution, Newton-Raphson iterative method, numerical methods, linear interpolation, graphical interpolation, Lagrange interpolation, Laplace transform, convolution theorem, periodic functions, Z transform, difference equations, Invariant linear systems, Differential equations, Fourier series, harmonics, Dirichlet conditions, Gibbs’ phenomenon, Complex Fourier series, complex spectra, Fourier’s integral theorem, Leibnitz-Maclaurin method, power series, Cauchy-Euler equi-dimensional equations, Leibnitz theorem, Bessel’s equation, Gamma functions, Bessel functions, Legendre’s equation, Legendre polynomials, Rodrigue’s formula, Sturm-Liouville systems, Orthogonality, Taylor’s series, First-order differential equations, Euler's method, Runge-Kutta method, Matrix algebra, Matrix transformation, Eigenvalues, direction fields, phase plane analysis, nonlinear systems, dynamical systems, Bifurcation, partial differentiation, Elliptic equations, Hyperbolic equations, Parabolic equations, multiple integration, Green’s theorem, integral functions, error function, elliptic functions, vector analysis, Curvilinear coordinates, complex analysis, complex mapping, Maclaurin series, optimization, linear programming, Linear inequalities

Topics: Abstract Algebra, Binary Operations, sets, logic, Switching Algebras, Orders, Lattice, Boolean Algebra, Mapping, Groups, Homomorphism, Rings, Fields, Mathematical Induction, Divisibility, Euclid’s Algorithm, Congruence, Polynomials, Remainder Theorem, factor theorem, Rational Functions

Topics: Semantics, ambiguity, predication, verbs, logic, language comparison, cognition, formal semantics, sentence meaning, compositionality, descriptive meaning, connotations, lexemes, lexical ambiguity, compositional ambiguity, contextual ambiguity, deixis, determination, presuppositions, predication, verbs, nouns, adjectives, predicate logic notation, thematic roles, verbs, argument structure diatheses, aspect tense, logical basis, logical relations, sentential logic, meaning relations, synonymy, hyponymy, oppositions, lexical fields, meaning components, semantic features, semantic formulae, semantic primes, Barsalou frames, Japanese numerals