Topics: Partial Differential Equation

Topics: linear equation, quadratic equation, cubic equation

Topics: First Order Differential Equations, Laplace Transform, Second Order Constant Coefficient Linear Differential Equations, Linear Constant Coefficient Differential Equations, Second Order Linear Differential Equations, Discontinuous Functions, Power Series

Topics: Engineering Mathematics, Algebra, power, logarithms, polynomials, linear equations, polynomial equations, binomials, binomial expansions, sigma notation, factorials, combinations, partial fractions, trigonometry, Trigonometric identities, Trigonometric functions, exponential functions, differentiation, Newton–Raphson iterative method, integration, complex numbers, hyperbolic functions, determinants, matrices, eigenvalues, eigenvectors, Cayley–Hamilton theorem, vector, vector representation, sequences, infinite series, curves, curve fitting, Asymptotes, Systematic curve sketching, Correlation, partial differentiation, reduction formulas, approximate integration, integration application polar coordinate systems, multiple integrals, first-order differential equations, homogenous equations, Laplace transform, probability, Conditional probability, Probability distributions, Continuous probability distributions

Topics: Machine Arithmetic, Real Numbers, Machine Numbers, Rounding, Condition Numbers, Approximation, Interpolation, Least Squares Approximation, Polynomial Interpolation, Spline Functions, Numerical Differentiation, Numerical Integration, Nonlinear Equations, Iteration, Convergence, Efficiency, Method of False Position, Secant Method, Newton’s Method, Fixed Point Iteration, Algebraic Equations, Systems of Nonlinear Equations, Initial Value Problems for ODE, One-Step Methods, Numerical Methods, Euler’s Method, Taylor Expansion, Runge–Kutta Method, Error Monitoring, Step Control, Stiff Problems, Multistep Methods, Adams–Bashforth Method, Adams–Moulton Method, Predictor–Corrector Method, Two-Point Boundary Value Problems for ODEs, Initial Value Technique, Finite Difference Methods, Variational Methods

Topics: Linear Algebra, Algebra of Matrices, matrix, Determinants, Matrix Inverse, Systems of Linear Equations, Vector Space, linear equation, Subspaces of Vector Spaces, Rank of a Matrix, Linear Transformations, Linear Transformation, Homogeneous Systems of Linear Equations, Non-Homogeneous Systems of Linear Equations, Eigenvalue, Eigenvector, Minimal Polynomial, Matrix Polynomial, Companion Matrix, Similar Matrix, Diagonal Matrix, Triangular Matrix

Topics: Calculus, Trigonometric Functions, functions, limits, continuity, One-Sided Limits, Differentiation Rules, Derivatives, chain rule, implict differentiation, related rates, linearization, differentials, Mean Value Theorem, integrals, Monotonic Functions, First Derivative Test, Concavity, Curve Sketching, Applied Optimization, antiderivatives, Sigma Notation, limits of Finite Sums, Definite integral, Transcendental Functions, inverse functions, natural logarithms, exponential functions, exponential change, seperable differential equation, Indeterminate Form, L’Hôpital’s Rule, Inverse Trigonometric Functions, Hyperbolic Functions, Integration by Parts, integration, trigonometric integrals, trigonometric substitution, Integral Tables, Computer Algebra Systems, probability, numerical integration, improper integrals, probability, First-Order Differential Equations, Slope Fields, Euler’s Method, First-Order Linear Equations, Infinite Sequences, infinite Series, integral test, comparison test, absolute convergence, power series, alternating series, Taylor series, Maclaurin series, Parametric Equations, Polar Coordinates, Conic Sections, vector, Partial Derivatives, Lagrange Multipliers, Multiple Integrals, vector fields, Path Independence, Conservative Fields, Potential Functions, Green’s Theorem, Surface Integrals, Stokes Theorem, Divergence Theorem

Topics: Calculus, Trigonometric Functions, functions, limits, continuity, One-Sided Limits, Differentiation Rules, Derivatives, chain rule, implict differentiation, related rates, linearization, differentials, Mean Value Theorem, integrals, Monotonic Functions, First Derivative Test, Concavity, Curve Sketching, Applied Optimization, antiderivatives, Sigma Notation, limits of Finite Sums, Definite integral, Transcendental Functions, inverse functions, natural logarithms, exponential functions, exponential change, seperable differential equation, Indeterminate Form, L’Hôpital’s Rule, Inverse Trigonometric Functions, Hyperbolic Functions, Integration by Parts, integration, trigonometric integrals, trigonometric substitution, Integral Tables, Computer Algebra Systems, probability, numerical integration, improper integrals, probability, First-Order Differential Equations, Slope Fields, Euler’s Method, First-Order Linear Equations, Infinite Sequences, infinite Series, integral test, comparison test, absolute convergence, power series, alternating series, Taylor series, Maclaurin series, Parametric Equations, Polar Coordinates, Conic Sections, vector, Partial Derivatives, Lagrange Multipliers, Multiple Integrals, vector fields, Path Independence, Conservative Fields, Potential Functions, Green’s Theorem, Surface Integrals, Stokes Theorem, Divergence Theorem

Topics: Algebra, Arithmetic Reviews, Self-Tests, Sequences, Series, Limits, Continuity of Functions, One Variable, Optimization, Linear Equations, Matrices, Determinants, Inverse Matrix, n-Variables, Constrained Optimization, Comparative Statics, Concave Programming, Kuhn-Tucker Conditions, Integration, First-Order Difference Equations, Second-Order Difference Equations, Simultaneous Systems, Optimal Control

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