Topics: algebraic structures, matrix, echelon form, Gaussian elimination, linear system, vector space, linear map, linear form, bilinear form, Euclidean vector space, unitary vector space, eigenvalue, endomorphism, polynomials, theory of algebra, cyclic subspace, duality, Jordan canonical form, matrix function, singular value decomposition, Kronecker product, linear matrix

Topics: Endocardial tubes, heart tube position, Cardiac folding, heart chambers, Sinus venosus, Heart wall, Ventricles, Septum formation, atrioventricular canal, Atrioventricular valves, Truncus septum formation, arterial cone, Heart Layers, pericardium, myocardium, endocardium, Cardiac Abnormalities, congenital heart disease, patent foramen ovale, heart murmur, tricuspid atresia, Atrial Septal Defects, Double Outlet Right Ventricle, Hypoplastic Left Heart, Patent Ductus Arteriosus, Tetralogy of Fallot, Great Vessel, Ventricular Septal Defects, Pulmonary Atresia, Partial Anomalous Pulmonary Venous Drainage, Aortic Stenosis, Pulmonary Stenosis, Hypertrophic Cardiomyopathy, Blood Vessel Development, Endothelial Progenitors, Vasculogenesis, Angiogenesis, vascular development, Vascular endothelial growth factor, Vascular anomaly, Vascular tumors, Infantile Hemangioma, Congenital Hemangioma, Kaposiform Hemangioendothelioma, Pyogenic granuloma, Capillary malformation, port-wine stains, Lymphatic malformation, Venous malformation, urinary system, Kidney development, nephrogenesis, Pronephros, Mesonephros, Metanephros, Ureter Development, Urinary Bladder Development

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: Ordinary Differential Equations, Separable Ordinary Differential Equations, exact Ordinary Differential Equations, linear Ordinary Differential Equations, Orthogonal Trajectories, Homogeneous Linear Ordinary Differential Equations, Differential Operators, Euler–Cauchy Equations, Higher Order Linear Ordinary Differential Equations, nonlinear Ordinary Differential Equations, Power Series, egendre’s Equation, Legendre Polynomials, Extended Power Series, Frobenius Method, Bessel’s Equation, Bessel Functions, Laplace Transforms, First Shifting Theorem, Linear Algebra, Vector Calculus, Matrices, Vectors, Determinants, Linear Systems, Determinants, Cramer’s Rule, Gauss–Jordan Elimination, linear transformation, Matrix Eigenvalue Problems, Eigenvalues, Eigenvectors, Eigenbase, Vector Differential Calculus, vector product, Vector Integral Calculus, Integral Theorems, line integrals, Surface Integrals, Stokes’s Theorem, Fourier Analysis, Partial Differential Equations, Fourier series, Sturm–Liouville Problems, Forced Oscillations, Fourier Integral, Fourier Cosine, Sine Transforms, Fourier Transform, Fast Fourier Transforms, Rectangular Membrane, Double Fourier Series, heat equation, Complex Numbers, Complex Differentiation, Cauchy–Riemann Equations, Exponential Function, Complex Integration, Cauchy’s Integral Formula, Cauchy’s Integral Theorem, Taylor series, Laurent Series, Residue Integration, Conformal Mapping, Complex Analysis, Potential Theory, Numeric Analysis, Numeric Linear Algebra, Unconstrained Optimization, Linear Programming, Combinatorial Optimization, Probability, Statistics, Data Analysis, Probability Theory, Mathematical Statistics

Topics: Ordinary Differential Equations, Separable Ordinary Differential Equations, exact Ordinary Differential Equations, linear Ordinary Differential Equations, Orthogonal Trajectories, Homogeneous Linear Ordinary Differential Equations, Differential Operators, Euler–Cauchy Equations, Higher Order Linear Ordinary Differential Equations, nonlinear Ordinary Differential Equations, Power Series, egendre’s Equation, Legendre Polynomials, Extended Power Series, Frobenius Method, Bessel’s Equation, Bessel Functions, Laplace Transforms, First Shifting Theorem, Linear Algebra, Vector Calculus, Matrices, Vectors, Determinants, Linear Systems, Determinants, Cramer’s Rule, Gauss–Jordan Elimination, linear transformation, Matrix Eigenvalue Problems, Eigenvalues, Eigenvectors, Eigenbase, Vector Differential Calculus, vector product, Vector Integral Calculus, Integral Theorems, line integrals, Surface Integrals, Stokes’s Theorem, Fourier Analysis, Partial Differential Equations, Fourier series, Sturm–Liouville Problems, Forced Oscillations, Fourier Integral, Fourier Cosine, Sine Transforms, Fourier Transform, Fast Fourier Transforms, Rectangular Membrane, Double Fourier Series, heat equation, Complex Numbers, Complex Differentiation, Cauchy–Riemann Equations, Exponential Function, Complex Integration, Cauchy’s Integral Formula, Cauchy’s Integral Theorem, Taylor series, Laurent Series, Residue Integration, Conformal Mapping, Complex Analysis, Potential Theory, Numeric Analysis, Numeric Linear Algebra, Unconstrained Optimization, Linear Programming, Combinatorial Optimization, Probability, Statistics, Data Analysis, Probability Theory, Mathematical Statistics

Topics: fluid pressure, hydrostatic forces, submerged surfaces, buoyancy, floatation, fluid kinematics, fluid dynamics, vortex flow, potential flow, ideal fluid flow, laminar flow, viscous flow, boundary layer theory, compressible flow, model similitude, free jets, fluid machines, pelton turbine, impulse turbine, francis turbine, radial flow reaction turbines, propeller, kaplan turbine, axial flow reaction turbines, hydraulic turbines, centrifugal pumps, reciprocation pumps, hydraulic systems, fluid continuum, fluid properties, specific weight, weight density, viscosity, perfect gas law, isobaric process, adiabatic process, surface tension, capillarity, capillary effect, vapour pressure, cavitation, pascal's law, hydrostatic law, Bouyant force, centre of buoyancy, archimedes principle, metacentre, metacentric height, cauchy-reimann equations, Euler's equation, Bernoulli's equation, continuity equation, orfices, hydraulic coefficients, uniform flow, source flow, sink flow, free vortex flow, notches, weirs, francis formula, bazin formula, rehbock formula, cipolletti weir, reynolds experiment, Navier-stoke equation, efflux viscometer, ogee weir, boundary layers, stagnation pressure, stagnation density, stagnation temperature, specific energy curve, critical depth, critical velocity, sub-critical flow, hydraulic jump, francis turbine, velocity triangle, draft tube, rotodynamic turbine

Topics: Mathematical Modeling, Engineering Problem Solving, Programming, Software, structured programming, Modular Programming, EXCEL, MATLAB, Mathcad, Significant Figures, accuracy, precision, error, Round-Off Errors, Truncation Errors, Taylor Series, Bracketing Methods graphical method, bisection method, False-Position Method, Simple Fixed-Point Iteration, Newton-Raphson Method, secant method, Brent’s Method, multiple roots, Roots of Polynomials, Müller’s Method, Bairstow’s Method, Roots of Equations pipe friction, Gauss Elimination, Naive Gauss Elimination, complex systems, Gauss-Jordan, LU Decomposition, Matrix Inversion, Special Matrices, Gauss-Seidel, Linear Algebraic Equations, Steady-State Analysis, One-Dimensional Unconstrained Optimization, Parabolic Interpolation, Golden-Section Search, Multidimensional Unconstrained Optimization, Constrained Optimization, linear programming, Nonlinear Constrained Optimization, Least-Squares Regression, linear regression, polynomial regression, Multiple Linear Regression, Nonlinear Regression, Linear Least Squares, interpolation, Newton’s Divided-Difference Interpolating Polynomials, Lagrange Interpolating Polynomials, Inverse Interpolation, Spline Interpolation, Multidimensional Interpolation, Fourier Approximation, Curve Fitting, Sinusoidal Functions, Continuous Fourier Series, Fourier Integral, Fourier Transform, Discrete Fourier Transform, Fast Fourier Transform, power spectrum, Newton-Cotes Integration Formulas, Trapezoidal Rule, Simpson’s Rules, multiple integrals, Newton-Cotes Algorithms, Romberg Integration, Adaptive Quadrature, Gauss Quadrature, Improper Integrals, Monte Carlo Integration, Numerical Differentiation, High-Accuracy Differentiation Formulas, Richardson Extrapolation, partial derivatives, Numerical Integration, Runge-Kutta Method, Euler’s Method, Boundary-Value Problems, Eigenvalue Problems, Finite Difference, Elliptic Equations, Laplace equation, Boundary Condition, Heat-Conduction Equation, Crank-Nicolson Method, Finite-Element Method

Topics: Monosaccharides, Disaccharides, Oligosaccharides, Polysaccharides, STEREOISOMERS, PROTEOGLYCANS, GLYCOPROTEINS, MUCOPLYSACCHARIDOSIS, DERMATAN SULPHATE, KERATAN SULPHATE, CHONDROITIN SULPHATE, HEPARIN, HYALURONIC ACID, MUCOPOLYSACCHARIDES, HETEROPOLYSACCHARIDES, Agar, chitin, insulin, GLYCOGEN STRUCTURE, cellulose, glycogen, amylase, starch, AMYLOPECTIN, amylose, HOMOPOLYSACCHARIDES, TREHALOSE, maltose, lactose, invert sugar, sucrose, DISACCHARIDES, DEOXY SUGARS, AMINO SUGARS, GLYCOSIDES, GLYCOSIDIC LINKAGE, GLYCOSIDE FORMATION, ester, OSAZONE CRYSTALS, OSAZONE FORMATION, FEHLING’S TEST, BARFOED’S TEST, BENEDICT’S TEST, ENEDIOL FORMATION, MUTAROTATION, ANOMERISM, EPIMERISM, glucose, fructose

Topics: Mathematics, quadratic equations, indices, logarithms, remainder theorem, undetermined coefficients, partial fractions, arithmetic progression, geometrical progression permutations, combinations, binomial theorem, trigonometric ratio, addition theorem, sine formula, cosine formula, tangent formula, differential calculus, differentiation, logarithmic functions, exponential functions, coordinates, coordinate geometry, parabola, ellipse, hyperbola, complex numbers, matrices

Topics: Geology, igneous rocks, metamorphic rocks, Basement complex, migmatite-Gneiss complex, Schist Belt, Younger granites, Metasomatism, Argillic Alteration, Cenozoic Magmatism, Volcanism, Benue trough, Bornu basin, Lithostratigraphy, Bima sandstone, Gongila formation, Fika shalel, Gombe sand stone, Kerri-kerri formation, Chad formation, Sokoto basin, Maastrichtian Deposits, Bida basin, Paleocene Deposits, Dahomey Basin, mineral resources, Niger delta basin, mineral resources, solid mineral resources, Dahomey Basin, Industrial Mineral Deposits, iron deposits, Gold, Tin-Tantalum-Niobium Pegmatites, Chromite, Nickel, Talc, Asbestos, uranium, Gemstones, coal, Coniacian coals, Petroleum Resources, clay