Topics: Numerical Methods, mathematical modeling, MATLAB, mathematical operations, structured programming, errors, roundoff errors, truncation errors, total numerical errors, blunders, model errors, data uncertainty, roots, graphical methods, bracketing methods, bisection, roots, Simple Fixed-Point Iteration, Newton-Raphson, secant methods, Brent's method, MATLAB functions, optimization, linear systems, linear algebraic equations, matrices, Gauss elimination, Naive gauss elimination, tridiagonal systems, LU factorization, matrix inverse, system condition, error analysis, iterative methods, linear systems, nonlinear systems, Eugen values, power method, curve fitting, linear regression, random numbers, linear least-squares regression, polynomial regression, multiple linear regression, QR factorization, nonlinear regression, Fourier analysis, Continuous Fourier series, frequency domain, time domain, Fourier integral, Fourier transform, Discrete Fourier transform, power spectrum, polynomial interpolation, Newton interpolating polynomial, Lagrange interpolating polynomial, inverse interpolation, extrapolation, oscillations, splines, linear splines, quadratic splines, cubic spline, multidimensional interpolation, integration, differentiation, Numerical integration formulas, Newton-Cotes formulas, Trapezoidal rule, Simpson's rules, initial value problem, Runge-Kutta methods, adaptive Runge-Kutta methods, stiff systems, Boundary-value problems, shooting method, finite-difference methods, MATLAB function

Topics: real numbers, rule of algebra, limits, continuity, derivatives, differentiation formula, Taylor series, Partial derivatives, maxima, minima, Lagrange multiplier, complex numbers, ordinary differential equations, linear differential equations, operator notation, linear operators, linear dependence, Wronskians, Laplace transforms, vector analysis, vector algebra, Jacobians, Orthogonal curvilinear coordinates, Fourier series, Dirichlet conditions, orthogonal functions, Fourier integrals, Fourier transforms, Gamma function, beta function, error function, exponential integral, sine integral, cosine integral, Fresnel sine Integral, Fresnel cosine Integral, Bessel function, Legendre functions, Legendre differential equation, Hermite polynomials, Laguerre polynomial, sturm-Liouville systems, heat conduction equation, vibrating string equation, complex variables, conformal mapping, Cauchy-Riemann equations, Cauchy's theorem, Laurent's series, conformal mapping, complex inversion formula, matrices, Cramer's rule, determinants, Euler's equation, Hamilton's principle

Topics: laplace transforms, z transforms, gamma functions, beta functions, fourier series, ordinary diffrential equations, power series

Topics: Real Numbers, Mathematical Induction, Mathematical Conventions, Complex Numbers, Taylor Theorem, Maclaurin Theorem, Vectors, Vector Spaces, Matrices, linear equation, Echelon, Eigen, Differential equations, fourier series, Laplace transform, vector calculus, complex analysis, bernoulli, riccati, cauchy-euler, Gamma function, frobenieus method, bessel function, Fourier integrals, Fourier transform, Vector Differential Calculus, Vector Integral Calculus, analytic functions, complex intergration, laurent series

Topics: Integration, Laplace transform, Z-transform, power series, difference equation, Leibnitz theorem, Maclurin series, series solution, Beta function, Gamma function, total derivatives, implicit differentiation

Topics: Materials Design, Atomic Structure, Atomic Bonding, interatomic spacing, amorphous materials, lattice, basis, unit cells, crystal structure, Allotropic Transformation, Polymorphic Transformation, Crystal Structures, unit cell, Covalent Structures, diffusion, Fick’s Law, Mechanical Properties, Tensile Test, stress, strain, Nanoindentation, Fracture Mechanics, Fatigue, Fatigue Test, creep, rupture, stress corrosion, Strain Hardening, Annealing, Hot Working, Nucleation, cooling curves, cast structure, casting, Directional Solidification, Single Crystal Growth, Epitaxial Growth, Phase Diagram, Phase Equilibrium, Dispersion Strengthening, Eutectic Phase Diagrams, Eutectoid Reaction, Martensitic Reaction, Tempering, Nonferrous Alloys, Glass-Ceramics, Polymers, Polymerization, Thermoplastics, elastomers, rubbers, adhesives, Composites, Particulate Composites, Fiber-Reinforced Composites, plywood, concrete, asphalt, Electronic Materials, semiconductors, insulators, Electrostriction, Piezoelectricity, Ferroelectricity, Magnetic Materials, Magnetization

Topics: Materials Design, Atomic Structure, Atomic Bonding, interatomic spacing, amorphous materials, lattice, basis, unit cells, crystal structure, Allotropic Transformation, Polymorphic Transformation, Crystal Structures, unit cell, Covalent Structures, diffusion, Fick’s Law, Mechanical Properties, Tensile Test, stress, strain, Nanoindentation, Fracture Mechanics, Fatigue, Fatigue Test, creep, rupture, stress corrosion, Strain Hardening, Annealing, Hot Working, Nucleation, cooling curves, cast structure, casting, Directional Solidification, Single Crystal Growth, Epitaxial Growth, Phase Diagram, Phase Equilibrium, Dispersion Strengthening, Eutectic Phase Diagrams, Eutectoid Reaction, Martensitic Reaction, Tempering, Nonferrous Alloys, Glass-Ceramics, Polymers, Polymerization, Thermoplastics, elastomers, rubbers, adhesives, Composites, Particulate Composites, Fiber-Reinforced Composites, plywood, concrete, asphalt, Electronic Materials, semiconductors, insulators, Electrostriction, Piezoelectricity, Ferroelectricity, Magnetic Materials, Magnetization

Topics: Digital Communication, Communication Error Correction, Information Compression Error, Information Compression, Data Compression, data Coding, Huffman Coding Algorithm, Error Correction, Linear Block Codes, noise, convolutional coding, Viterbi decoding of convolutional codes, Systematic Code, Convolution Codes, Hamming Codes, Convolutional Codes, Convolutional Code Construction, Parity Equations, Shift-Register View, State-Machine View, Decoding Problem, Viterbi Decoder, Soft-Decision Decoding, Signal to Noise Ratio, linear Time-Invariant Systems, Baseband Signal, Modulation, Demodulation, Baseband Channel, Linear Time-Invariant Models, Baseband Channel Model, Signal Spectra, Discrete-Time Fourier Transform, Fourier Transform, Discrete-Time Fourier Series, Fourier Series, Channel Distortions, Binary Phase Shift Keying, Quadrature Phase Shift Keying, Quadrature Amplitude Modulation, Media Access Protocols, Shared Media Satellite communications, Satellite communications, Time Division Multiple Access, ALOHA, Carrier Sense Multiple Access, Circuit Switching, Packet Switching, Little’s Law, Network Routing, Routing, Broadcast routing, Routing Protocol, Reliable Data Transport Protocols

Topics: Digital Signal Processing, common filters, digital control systems, Digital-to-analog conversion, Analog-to-digital conversion, Adaptive digital systems, adaptation algorithms, median filter, artificial neural netowrks, fuzzy logic, Discrete Fourier transform, fast Fourier transform, spectral analysis, modulation, Kalman filter, data compression, source coding, Recognition techniques, channel coding, Error-correcting codes, Digital signal processors, Programming digital signal processors

Topics: Magnetism, Electromechanical energy conversion, Magnetic Flux, Magnetic Circuit, Hysteresis loses, Transformers, transformer phasor diagram, induced EMF analysis, Induction Motor, Synchronous Machine, Measurement of three Phasor power, DC generator