
Mathematical Preliminaries 


1  (47) 


2  (16) 

Roundoff Errors and Computer Arithmetic 


18  (13) 

Algorithms and Convergence 


31  (9) 


40  (7) 

Solutions of Equations in One Variable 


47  (57) 


48  (7) 


55  (11) 


66  (12) 

Error Analysis for Iterative Methods 


78  (8) 


86  (5) 

Zeros of Polynomials and Muller's Method 


91  (10) 

Survey of Methods and Software 


101  (3) 

Interpolation and Polynomial Approximation 


104  (62) 

Interpolation and the Lagrange Polynomial 


107  (15) 


122  (11) 


133  (8) 

Cubic Spline Interpolation 


141  (15) 


156  (7) 

Survey of Methods and Software 


163  (3) 

Numerical Differentiation and Integration 


166  (83) 

Numerical Differentiation 


167  (11) 

Richardson's Extrapolation 


178  (8) 

Elements of Numerical Integration 


186  (10) 

Composite Numerical Integration 


196  (11) 


207  (6) 

Adaptive Quadrature Methods 


213  (7) 


220  (7) 


227  (14) 


241  (6) 

Survey of Methods and Software 


247  (2) 

InitialValue Problems for Ordinary Differential Equations 


249  (95) 

The Elementary Theory of InitialValue Problems 


251  (5) 


256  (10) 

HigherOrder Taylor Methods 


266  (6) 


272  (10) 

Error Control and the RungeKuttaFehlberg Method 


282  (7) 


289  (12) 

Variable StepSize Multistep Methods 


301  (6) 


307  (6) 

HigherOrder Equations and Systems of Differential Equations 


313  (11) 


324  (10) 

Stiff Differential Equations 


334  (8) 

Survey of Methods and Software 


342  (2) 

Direct Methods for Solving Linear Systems 


344  (73) 

Linear Systems of Equations 


345  (14) 


359  (11) 

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  (66) 

Norms of Vectors and Matrices 


418  (12) 

Eigenvalues and Eigenvectors 


430  (7) 

Iterative Techniques for Solving Linear Systems 


437  (17) 

Error Bounds and Iterative Refinement 


454  (11) 

The Conjugate Gradient Method 


465  (16) 

Survey of Methods and Software 


481  (2) 


483  (67) 

Discrete Least Squares Approximation 


484  (14) 

Orthogonal Polynomials and Least Squares Approximation 


498  (9) 

Chebyshev Polynomials and Economization of Power Series 


507  (10) 

Rational Function Approximation 


517  (12) 

Trigonometric Polynomial Approximation 


529  (8) 


537  (11) 

Survey of Methods and Software 


548  (2) 

Approximating Eigenvalues 


550  (50) 

Linear Algebra and Eigenvalues 


551  (9) 


560  (17) 


577  (8) 


585  (12) 

Survey of Methods and Software 


597  (3) 

Numerical Solutions of Nonlinear Systems of Equations 


600  (45) 

Fixed Points for Functions of Several Variables 


602  (9) 


611  (9) 


620  (8) 

Steepest Descent Techniques 


628  (7) 

Homotopy and Continuation Methods 


635  (8) 

Survey of Methods and Software 


643  (2) 

BoundaryValue Problems for Ordinary Differential Equations 


645  (46) 

The Linear Shooting Method 


646  (7) 

The Shooting Method for Nonlinear Problems 


653  (7) 

FiniteDifference Methods for Linear Problems 


660  (7) 

FiniteDifference Methods for Nonlinear Problems 


667  (5) 


672  (16) 

Survey of Methods and Software 


688  (3) 

Numerical Solutions to Partial Differential Equations 


691  (52) 

Elliptic Partial Differential Equations 


694  (10) 

Parabolic Partial Differential Equations 


704  (14) 

Hyperbolic Partial Differential Equations 


718  (8) 

An Introduction to the FiniteElement Method 


726  (15) 

Survey of Methods and Software 


741  (2) 
Bibliography 

743  (10) 
Answers to Selected Exercises 

753  (78) 
Index 

831  