Numerical analysis with applications in mechanics and engineering /

• Κύριος συγγραφέας: Teodorescu, P. P.
• Άλλοι συγγραφείς: Stănescu, Nicolae-Doru, Pandrea, Nicolae
• Μορφή: Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Hoboken, New Jersey : John Wiley & Sons Inc., [2013]
• Θέματα: Numerical analysis.; Engineering mathematics.; TECHNOLOGY & ENGINEERING > Engineering (General); TECHNOLOGY & ENGINEERING > Reference.; Electronic books.

"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 ou...

Πίνακας περιεχομένων:

• 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