
Mathematical Preliminaries and Error Analysis 


1  (44) 


2  (15) 

Roundoff Errors and Computer Arithmetic 


17  (13) 

Algorithms and Convergence 


30  (8) 


38  (7) 

Solutions of Equations in One Variable 


45  (56) 


46  (7) 


53  (10) 


63  (12) 

Error Analysis for Iterative Methods 


75  (8) 


83  (4) 

Zeros of Polynomials and Muller's Method 


87  (10) 

Survey of Methods and Software 


97  (4) 

Interpolation and Polynomial Approximation 


101  (66) 

Interpolation and the Lagrange Polynomial 


104  (15) 


119  (11) 


130  (7) 

Cubic Spline Interpolation 


137  (20) 


157  (7) 

Survey of Methods and Software 


164  (3) 

Numerical Differentiation and Integration 


167  (82) 

Numerical Differentiation 


168  (11) 

Richardson's Extrapolation 


179  (8) 

Elements of Numerical Integration 


187  (9) 

Composite Numerical Integration 


196  (11) 


207  (5) 

Adaptive Quadrature Methods 


212  (8) 


220  (6) 


226  (15) 


241  (5) 

Survey of Methods and Software 


246  (3) 

InitialValue Problems for Ordinary Differential Equations 


249  (96) 

The Elementary Theory of InitialValue Problems 


250  (6) 


256  (10) 

HigherOrder Taylor Methods 


266  (7) 


273  (10) 

Error Control and the The RungeKuttaFehlberg Method 


283  (8) 


291  (11) 

Variable StepSize Multistep Methods 


302  (6) 


308  (5) 

HigherOrder Equations and Systems of Differential Equations 


313  (12) 


325  (10) 

Stiff Differential Equations 


335  (7) 

Survey of Methods and Software 


342  (3) 

Direct Methods for Solving Linear Systems 


345  (72) 

Linear Systems of Equations 


346  (14) 


360  (10) 

Linear Algebra and Matrix Inversion 


370  (13) 

The Determinant of a Matrix 


383  (5) 


388  (10) 

Special Types of Matrices 


398  (15) 

Survey of Methods and Software 


413  (4) 

Iterative Techniques in Matrix Algebra 


417  (64) 

Norms of Vectors and Matrices 


418  (11) 

Eigenvalues and Eigenvectors 


429  (7) 

Iterative Techniques for Solving Linear Systems 


436  (18) 

Error Bounds and Iterative Refinement 


454  (10) 

The Conjugate Gradient Method 


464  (15) 

Survey of Methods and Software 


479  (2) 


481  (66) 

Discrete Least Squares Approximation 


482  (12) 

Orthogonal Polynomials and Least Squares Approximation 


494  (9) 

Chebyshev Polynomials and Economization of Power Series 


503  (9) 

Rational Function Approximation 


512  (11) 

Trigonometric Polynomial Approximation 


523  (9) 


532  (12) 

Survey of Methods and Software 


544  (3) 

Approximating Eigenvalues 


547  (50) 

Linear Algebra and Eigenvalues 


548  (9) 


557  (17) 


574  (8) 


582  (12) 

Survey of Methods and Software 


594  (3) 

Numerical Solutions of Nonlinear Systems of Equations 


597  (44) 

Fixed Points for Functions of Several Variables 


598  (9) 


607  (10) 


617  (7) 

Steepest Descent Techniques 


624  (7) 

Homotopy and Continuation Methods 


631  (8) 

Survey of Methods and Software 


639  (2) 

BoundaryValue Problems for Ordinary Differential Equations 


641  (46) 

The Linear Shooting Method 


642  (7) 

The Shooting Method for Nonlinear Problems 


649  (7) 

FiniteDifference Methods for Linear Problems 


656  (6) 

FiniteDifference Methods for Nonlinear Problems 


662  (6) 

The RayleighRitz Method 


668  (16) 

Survey of Methods and Software 


684  (3) 

Numerical Solutions to Partial Differential Equations 


687  (50) 

Elliptic Partial Differential Equations 


690  (9) 

Parabolic Partial Differential Equations 


699  (14) 

Hyperbolic Partial Differential Equations 


713  (8) 

An Introduction to the FiniteElement Method 


721  (14) 

Survey of Methods and Software 


735  (2) 
Bibliography 

737  (10) 
Answers to Selected Exercises 

747  (90) 
Index 

837  