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: Mechanics, Properties of Matter, Matter, trignometric functions, force, momentum, angular momentum, scalar, vector, kinematics, Newton’s Law of Motion, motion, force, Gravitational Force of Attraction, Gravitational Force, Acceleration Due to Gravity, Earth Gravitational Potential, energy, work, kinetic energy, potential energy, linear momentum, collision, Equilibrium, Elasticity, Hooke’s Law, fluids

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: Dynamics, Newtonian mechanics, kinematics, rectangular coordinates, curvilinear motion, Force-Mass-Acceleration Method, work-energy, impulse-momentum, power, efficiency, impulse, momentum, plastic impact, impulsive motion, elastic impact, mass flow, planar angular motion, equations of motion, planar kinetics, impulse-momentum methods, vibrations, rigid-body vibration, forced vibrations

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: measurement, dimension, vectors, scalars, linear kinematics, dynamics, work, energy, power, conservation of linear momentum, dynamics of circular motion, dynamics of rotational motion, Rotational Kinetic Energy, Law of Conservation of Angular Momentum, Parallel Axis Theorem, center of gravity, moment, Oscillation, simple harmonic motion, Elastic Potential Energy, elasticity, Bulk Modulus, mechanics of fluid, density, Pascal’s principle, Capillarity, Atmospheric Pressure, pressure, Archimedes’ principle, surface tension, unit conversion, Parallelogram Law of Vectors