Numerical MathematicsNumerical Mathematics presents the innovative approach of using numerical methods as a practical laboratory for all undergraduate mathematics courses in science and engineering streams. The authors bridge the gap between numerical methods and undergraduate mathematics and emphasize the graphical visualization of mathematical properties, numerical verification of formal statements, and illustrations of the mathematical ideas. Students using Numerical Mathematics as a supplementary reference for basic mathematical courses will be encouraged to deveolp their mathematical intuition with an effective component of technology, while students using it as the primary text for numerical courses will have a broader, reinforced understanding of the subject. |
Contents
Elements of the Laboratory | 1 |
Linear Systems | 47 |
Orthogonality | 121 |
Eigenvalues and Eigenvectors | 165 |
Polynomial Functions | 235 |
Differential and Integral Calculus | 287 |
Vector Calculus | 351 |
Zeros and Extrema of Functions | 405 |
InitialValue Problems for ODEs | 451 |
BoundaryValue Problems for ODEs and PDEs | 511 |
Spectral Methods | 579 |
Splines and Finite Elements | 615 |
Bibliography | 653 |
Common terms and phrases
Adams method algebraic algorithm boundary conditions boundary-value problem calculate central difference coefficients components computations condition number convergence corresponding cubic spline curve data points defined diagonal entries differential equations discrete eigenvalues eigenvectors Euler method exact solution example Exercise explicit method Figure finite finite-difference method first-order function f(x Gaussian quadrature given global error global truncation error graph grid points Hermite interpolation Heun method implemented implicit inner product integration rules interpolating polynomial interval inverse linear map linear system linspace MATLAB function MATLAB script matrix nonlinear norm numerical approximation numerical derivatives numerical solution obtained ODE problem ODE solvers orthogonal output plot Pn(x polynomial interpolation quadratic Richardson extrapolations roots round-off error Runge-Kutta methods secant method second-order Section solution y(t solving step h step size h subspace Theorem trapezoidal rule trigonometric interpolation unitary matrix values variables vector field vector space xInt yInt Yk+1 zero