Topics: abstract Algebra, linear Algebra, Sets, Cartesian products, Hausdorff maximality principle, groups, Homomorphisms, permutations, rings, domains, fields, Polynomial rings, Chinese remainder theorem, Boolean rings, matrices, matrix rings, Systems of equations, Determinants, Summands, transpose principle, Nilpotent homomorphisms, Jordan canonical form, Eigenvalues, Euclidean domains, jordan blocks, Jordan canonical form

Topics: linear equation, quadratic equation, cubic equation

Topics: vector space, linear map, polynomial, Eigenvalues, Eigenvectors, Invariant Subspaces, inner product space, complex vector spaces, real vector space, trace, determinant

Topics: Differential Equations, first order equations, Linear First Order Equations, separable equations, exact equations, integrating factors, numerical methods, Euler's method, Improved Euler Method, Runge-Kutta Method, Autonomous Second Order Equations, Linear Second Order Equations, Homogeneous Linear Equations, Constant Coefficient Homogeneous Equations, Non homogeneous Linear Equations, power series, Laplace transforms, inverse Laplace transform, initial value problem, unit step function, convolution, Linear Higher Order Equations, Linear Systems of Differential Equations, Constant Coefficient Homogeneous Systems

Topics: Differential Equations, first order equations, Linear First Order Equations, separable equations, exact equations, integrating factors, numerical methods, Euler's method, Improved Euler Method, Runge-Kutta Method, Autonomous Second Order Equations, Linear Second Order Equations, Homogeneous Linear Equations, Constant Coefficient Homogeneous Equations, Non homogeneous Linear Equations, power series, Laplace transforms, inverse Laplace transform, initial value problem, unit step function, convolution, Linear Higher Order Equations, Linear Systems of Differential Equations, Constant Coefficient Homogeneous Systems

Topics: simplex method, degeneracy, duality theory, primal simplex method, Lagrangian duality, sensitivity analysis, parametric analysis, implementation issues, convex analysis, game theory, regression, structural optimization, interior-point methods, central path, Lagrange multipliers, path-following method, KKT system, affine-scaling, method, integer programming, quadratic programming, convex programming, Markowitz model

Topics: Logic, abstract thinking, Permutation, Combination, Binomial Theorem, Algebraic Expressions, matrix, determinant

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: statistics, single-variable data, bivariate data, probability, probability distributions, discrete variables, normal probability distributions, sample variability, statistical inference, Chi-square, analysis of variance, linear correlation, regression analysis, nonparametric statistics, data collection, measurability, variability, measure of central tendency, linear correlation, linear regression, random variables, Binomial probability distribution, normal probability distributions, notation, sampling distributions, inferential statistics, Chi-square statistic, ANOVA, linear correlation analysis, linear regression analysis

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