Numerical Mathematics
Numerical Mathematics
₹895.50 ₹995.00 Save: ₹99.50 (10%)
Go to cartISBN: 9789384323165
Bind: Paperback
Year: 2017
Pages: 682
Size: 172 x 216 mm
Publisher: Jones & Bartlett Learning
Published in India by: Jones & Bartlett India
Exclusive Distributors: Viva Books
Sales Territory: India, Nepal, Pakistan, Bangladesh, Sri Lanka
Description:
Numerical Mathematics presents the innovative approach of using numerical methods as a practical laboratory for all the 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 develop their mathematical intuition with an effective components of technology, while students using it as the primary text for numerical courses will have a broader, reinforced understanding of the subject.
Key Features of Numerical Mathematics:
- Numerical examples and inline MATLAB codes provide convenient tools for classroom use
- Detailed descriptions highlight the mathematical ideas behind the theorems and algorithms, providing students with a clearer understanding of the material at hand.
- The text provides a self-contained introduction and overview of undergraduate numerical analysis, including error analysis, computer arithmetic, and detailed algorithms for standard numerical techniques.
- Includes discussions on key theoretical concepts in all major areas of undergraduate mathematics for science and engineering (scalar and vector calculus, linear algebra, and differential equations) followed by step-by-step numerical implementation of milestone examples.
- Includes detailed explanations of selected examples from applied mathematics, providing students with hands-on experience in modeling, including the choice of appropriate methods, programming, and analysis of results.
Target Audience:
This book is helpful for the students and academicians of Mathematics.
Contents:
Chapter 1: Elements of the Laboratory • Getting Started • Scalars, Vectors, and Matrices • Matrix Operations • Built-in Functions • Programming with MATLAB • Graphics and Data Files • Floating-Point Arithmetic • Error Analysis • Summary and Notes • Exercises
Chapter 2: Linear Systems • Vector Spaces • Linear Maps • Systems of Linear Equations • Vector and Matrix Norms • Direct Methods • Iterative Methods • Cholesky Factorization • Determinants • Summary and Notes • Exercises
Chapter 3: Orthogonality • Inner Product Spaces • Orthogonal Projections • QR Factorization • The Least-Squares Method • Summary and Notes • Exercises
Chapter 4: Eigenvalues and Eigenvectors • Matrix Eigenvalue Problems • Properties of Eigenvalues • Properties of Eigenvectors • Normal Matrices • Sensitivity of Eigenvalues • Power Iterations • Simultaneous Iterations • Singular Value Decomposition • Summary and Notes • Exercises
Chapter 5: Polynomial Functions • Properties of Polynomials • Vandermonde Interpolation • Lagrange Interpolation • Newton Interpolation • Errors of Polynomial Interpolation • Polynomial Approximation • Approximation with Orthogonal Polynomials • Summary and Notes • Exercises
Chapter 6: Differential and Integral Calculus • Derivatives and Finite Differences • Higher-Order Numerical Derivatives • Multipoint First-Order Numerical Derivatives • Richardson Extrapolation • Integrals and Finite Sums • Newton-Cotes Integration Rules • Romberg Integration • Gaussian Quadrature Rules • Summary and Notes • Exercises
Chapter 7: Vector Calculus • Scalar Functions of Several Variables • Partial Derivatives and Differentiability • The Gradient Vector • Paths • Vector Fields • Line Integrals • Surface Integrals • Integral Theorems • Summary and Notes • Exercises
Chapter 8: Zeros and Extrema of Functions • One-Dimensional Root Finding • Multidimensional Root Finding • One-Dimensional Minimization • Multidimensional Minimization • Summary and Notes • Exercises
Chapter 9: Initial-Value Problems for ODEs • Approximations of Solutions • Single-Step Runge-Kutta Solvers • Adaptive Single-Step Solvers • Multistep Adams Solvers • Implicit Methods for Stiff Differential Equations • Summary and Notes • Exercises
Chapter 10: Boundary-Value Problems for ODEs and PDEs • Finite-Difference Methods for ODEs • Shooting Methods for ODEs • Finite-Difference Methods for Parabolic PDEs • Finite-Difference Methods for Hyperbolic PDEs • Finite-Difference Methods for Elliptic PDEs • Summary and Notes • Exercises
Chapter 11: Spectral Methods • Trigonometric Approximation and Interpolation • Errors of Trigonometric Interpolation • Trigonometric Methods for Differential Equations • Summary and Notes • Exercises
Chapter 12: Splines and Finite Elements • Spline Interpolation • Hermite Interpolation • Finite Elements for Differential Equations • Summary and Notes • Exercises
Bibliography
Index
About the Authors:
Matheus Grasselli and Dmitry Pelinovsky - they both teach in McMaster University.
