- Bab 1
Pendahuluan Matematis dan Analisis Galat
Mathematical Preliminaries and Error Analysis
4 seksi
- 1.1 Review of Calculus
- 1.2 Round-off Errors and Computer Arithmetic
- 1.3 Algorithms and Convergence
- 1.4 Numerical Software
- Bab 2
Penyelesaian Persamaan Satu Variabel
Solutions of Equations in One Variable
7 seksi
- 2.1 The Bisection Method
- 2.2 Fixed-Point Iteration
- 2.3 Newton's Method and Its Extensions
- 2.4 Error Analysis for Iterative Methods
- 2.5 Accelerating Convergence
- 2.6 Zeros of Polynomials and Müller's Method
- 2.7 Survey of Methods and Software
- Bab 3
Interpolasi dan Hampiran Polinomial
Interpolation and Polynomial Approximation
7 seksi
- 3.1 Interpolation and the Lagrange Polynomial
- 3.2 Data Approximation and Neville's Method
- 3.3 Divided Differences
- 3.4 Hermite Interpolation
- 3.5 Cubic Spline Interpolation
- 3.6 Parametric Curves
- 3.7 Survey of Methods and Software
- Bab 4
Diferensiasi dan Integrasi Numerik
Numerical Differentiation and Integration
10 seksi
- 4.1 Numerical Differentiation
- 4.2 Richardson's Extrapolation
- 4.3 Elements of Numerical Integration
- 4.4 Composite Numerical Integration
- 4.5 Romberg Integration
- 4.6 Adaptive Quadrature Methods
- 4.7 Gaussian Quadrature
- 4.8 Multiple Integrals
- 4.9 Improper Integrals
- 4.10 Survey of Methods and Software
- Bab 5
Masalah Nilai Awal Persamaan Diferensial Biasa
Initial-Value Problems for Ordinary Differential Equations
12 seksi
- 5.1 The Elementary Theory of Initial-Value Problems
- 5.2 Euler's Method
- 5.3 Higher-Order Taylor Methods
- 5.4 Runge-Kutta Methods
- 5.5 Error Control and the Runge-Kutta-Fehlberg Method
- 5.6 Multistep Methods
- 5.7 Variable Step-Size Multistep Methods
- 5.8 Extrapolation Methods
- 5.9 Higher-Order Equations and Systems of Differential Equations
- 5.10 Stability
- 5.11 Stiff Differential Equations
- 5.12 Survey of Methods and Software
- Bab 6
Metode Langsung untuk Sistem Linear
Direct Methods for Solving Linear Systems
7 seksi
- 6.1 Linear Systems of Equations
- 6.2 Pivoting Strategies
- 6.3 Linear Algebra and Matrix Inversion
- 6.4 The Determinant of a Matrix
- 6.5 Matrix Factorization
- 6.6 Special Types of Matrices
- 6.7 Survey of Methods and Software
- Bab 7
Teknik Iteratif dalam Aljabar Matriks
Iterative Techniques in Matrix Algebra
7 seksi
- 7.1 Norms of Vectors and Matrices
- 7.2 Eigenvalues and Eigenvectors
- 7.3 The Jacobi and Gauss-Seidel Iterative Techniques
- 7.4 Relaxation Techniques for Solving Linear Systems
- 7.5 Error Bounds and Iterative Refinement
- 7.6 The Conjugate Gradient Method
- 7.7 Survey of Methods and Software
- Bab 8
Teori Aproksimasi
Approximation Theory
7 seksi
- 8.1 Discrete Least Squares Approximation
- 8.2 Orthogonal Polynomials and Least Squares Approximation
- 8.3 Chebyshev Polynomials and Economization of Power Series
- 8.4 Rational Function Approximation
- 8.5 Trigonometric Polynomial Approximation
- 8.6 Fast Fourier Transforms
- 8.7 Survey of Methods and Software
- Bab 9
Aproksimasi Nilai Eigen
Approximating Eigenvalues
7 seksi
- 9.1 Linear Algebra and Eigenvalues
- 9.2 Orthogonal Matrices and Similarity Transformations
- 9.3 The Power Method
- 9.4 Householder's Method
- 9.5 The QR Algorithm
- 9.6 Singular Value Decomposition
- 9.7 Survey of Methods and Software
- Bab 10
Penyelesaian Numerik Sistem Persamaan Nonlinear
Numerical Solutions of Nonlinear Systems of Equations
6 seksi
- 10.1 Fixed Points for Functions of Several Variables
- 10.2 Newton's Method
- 10.3 Quasi-Newton Methods
- 10.4 Steepest Descent Techniques
- 10.5 Homotopy and Continuation Methods
- 10.6 Survey of Methods and Software
- Bab 11
Masalah Nilai Batas Persamaan Diferensial Biasa
Boundary-Value Problems for Ordinary Differential Equations
6 seksi
- 11.1 The Linear Shooting Method
- 11.2 The Shooting Method for Nonlinear Problems
- 11.3 Finite-Difference Methods for Linear Problems
- 11.4 Finite-Difference Methods for Nonlinear Problems
- 11.5 The Rayleigh-Ritz Method
- 11.6 Survey of Methods and Software
- Bab 12
Penyelesaian Numerik Persamaan Diferensial Parsial
Numerical Solutions to Partial Differential Equations
5 seksi
- 12.1 Elliptic Partial Differential Equations
- 12.2 Parabolic Partial Differential Equations
- 12.3 Hyperbolic Partial Differential Equations
- 12.4 An Introduction to the Finite-Element Method
- 12.5 Survey of Methods and Software
Materi ini ringkasan belajar yang ditulis ulang dan disusun berdasarkan Numerical Analysis, 9th ed., R. L. Burden & J. D. Faires (Cengage, 2010). Bukan pengganti buku.