Includes bibliographical references and index.

"Bridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results. Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon."--Publisher's website.

Print version record.

Series; Title Page; Copyright; Preface; Chapter 1: Errors in Numerical Analysis; 1.1 Enter Data Errors; 1.2 Approximation Errors; 1.3 Round-Off Errors; 1.4 Propagation of Errors; 1.5 Applications; Further Reading; Chapter 2: Solution of Equations; 2.1 The Bipartition (Bisection) Method; 2.2 The Chord (Secant) Method; 2.3 The Tangent Method (Newton); 2.4 The Contraction Method; 2.5 The Newton-Kantorovich Method; 2.6 Numerical Examples; 2.7 Applications; Further Reading; Chapter 3: Solution of Algebraic Equations; 3.1 Determination of Limits of the Roots of Polynomials; 3.2 Separation of Roots

3.3 Lagrange'S Method3.4 The Lobachevski-Graeffe Method; 3.5 The Bernoulli Method; 3.6 The Bierge-Viète Method; 3.7 Lin Methods; 3.8 Numerical Examples; 3.9 Applications; Further Reading; Chapter 4: Linear Algebra; 4.1 Calculation of Determinants; 4.2 Calculation of the Rank; 4.3 Norm of a Matrix; 4.4 Inversion of Matrices; 4.5 Solution of Linear Algebraic Systems of Equations; 4.6 Determination of Eigenvalues and Eigenvectors; 4.7 QR Decomposition; 4.8 The Singular Value Decomposition (SVD); 4.9 Use of the Least Squares Method in Solving the Linear Overdetermined Systems

4.10 The Pseudo-Inverse of a Matrix4.11 Solving of the Underdetermined Linear Systems; 4.12 Numerical Examples; 4.13 Applications; Further Reading; Chapter 5: Solution of Systems of Nonlinear Equations; 5.1 The Iteration Method (Jacobi); 5.2 Newton's Method; 5.3 The Modified Newton Method; 5.4 The Newton-Raphson Method; 5.5 The Gradient Method; 5.6 The Method of Entire Series; 5.7 Numerical Example; 5.8 Applications; Further Reading; Chapter 6: Interpolation and Approximation of Functions; 6.1 Lagrange's Interpolation Polynomial; 6.2 Taylor Polynomials

6.3 Finite Differences: Generalized Power6.4 Newton's Interpolation Polynomials; 6.5 Central Differences: Gauss's Formulae, Stirling's Formula, Bessel's Formula, Everett's Formulae; 6.6 Divided Differences; 6.7 Newton-Type Formula with Divided Differences; 6.8 Inverse Interpolation; 6.9 Determination of the Roots of an Equation by Inverse Interpolation; 6.10 Interpolation by Spline Functions; 6.11 Hermite's Interpolation; 6.12 Chebyshev's Polynomials; 6.13 Mini-Max Approximation of Functions; 6.14 Almost Mini-Max Approximation of Functions

6.15 Approximation of Functions by Trigonometric Functions (Fourier)6.16 Approximation of Functions by the Least Squares; 6.17 Other Methods of Interpolation; 6.18 Numerical Examples; 6.19 Applications; Further Reading; Chapter 7: Numerical Differentiationand Integration; 7.1 Introduction; 7.2 Numerical Differentiation by Means of an Expansion into a Taylor Series; 7.3 Numerical Differentiation by Means of Interpolation Polynomials; 7.4 Introduction to Numerical Integration; 7.5 The Newton-Côtes Quadrature Formulae; 7.6 The Trapezoid Formula; 7.7 Simpson's Formula

Physical Science