Mathematics for Civil Engineers : An Introduction / / Xin-She Yang

• Autore: Yang Xin-She
• Pubblicazione: Edinburgh : , : Dunedin Academic Press Ltd, , [2018]; ©2018
• Edizione: First edition.
• Descrizione fisica: 1 online resource (327 pages)
• Disciplina: 620.00151
• Soggetto topico: Engineering mathematics - Data processing
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover -- Contents -- Preface -- I. Revision of Fundamentals -- 1. Numbers and Functions -- 1. Real Numbers and Significant Digits -- 1.1. Notations and Conventions -- 1.2. Rounding Numbers and Significant Digits -- 2. Sets -- 3. Equations -- 3.1. Simple Equation -- 3.2. Simultaneous Equations -- 3.3. Inequality -- 4. Functions -- 4.1. Domain and Range -- 4.2. Linear Function and Modulus Function -- 4.3. Power Functions -- 4.4. Exponentials and Logarithms -- 4.5. Trigonometrical Functions -- 4.6. Composite Functions -- 2. Equations and Polynomials -- 1. Index Notation -- 2. Binomial Expansions -- 3. Floating Point Numbers -- 4. Quadratic Equations -- 5. Polynomials and Roots -- II. Main Topics -- 3. Vectors and Matrices -- 1. Vectors -- 2. Vector Products -- 2.1. Dot Product -- 2.2. Cross Product -- 2.3. Triple Product of Vectors -- 3. Matrix Algebra -- 3.1. Matrix, Addition and Multiplication -- 3.2. Transformation and Inverse -- 4. System of Linear Equations -- 5. Eigenvalues and Eigenvectors -- 5.1. Eigenvalues and Eigenvectors of a Matrix -- 5.2. Definiteness of a Matrix -- 6. Tensors -- 6.1. Summation Notations -- 6.2. Tensors -- 6.3. Elasticity -- 4. Calculus I: Differentiation -- 1. Gradient and Derivative -- 2. Differentiation Rules -- 3. Maximum, Minimum and Radius of Curvature -- 4. Series Expansions and Taylor Series -- 5. Partial Derivatives -- 6. Differentiation of Vectors -- 6.1. Polar Coordinates -- 6.2. Three Basic Operators -- 6.3. Cylindrical Coordinates -- 6.4. Spherical Coordinates -- 7. Jacobian and Hessian Matrices -- 5. Calculus II: Integration -- 1. Integration -- 2. Integration by Parts -- 3. Integration by Substitution -- 4. Double Integrals and Multiple Integrals -- 5. Jacobian Determinant -- 6. Special Integrals -- 6.1. Line Integral -- 6.2. Gaussian Integrals -- 6.3. Error Functions -- 6. Complex Numbers. ; 1. Complex Numbers -- 2. Complex Algebra -- 3. Hyperbolic Functions -- 4. Analytical Functions -- 5. Complex Integrals -- 5.1. Cauchy's Integral Theorem -- 5.2. Residue Theorem -- 7. Ordinary Differential Equations -- 1. Differential Equations -- 2. First-Order Differential Equations -- 3. Second-Order Equations -- 3.1. Solution Technique -- 3.2. Sturm-Liouville Eigenvalue Problem -- 4. Higher-Order ODEs -- 5. System of Linear ODEs -- 6. Harmonic Motions -- 6.1. Undamped Forced Oscillations -- 6.2. Damped Forced Oscillations -- 8. Fourier Transform and Laplace Transform -- 1. Fourier Series -- 1.1. Fourier Series -- 1.2. Orthogonality and Fourier Coefficients -- 2. Fourier Transforms -- 3. Discrete and Fast Fourier Transforms -- 4. Laplace Transform -- 4.1. Laplace Transform Pairs -- 4.2. Scalings and Properties -- 4.3. Derivatives and Integrals -- 5. Solving ODE via Laplace Transform -- 6. Z-Transform -- 7. Relationships between Fourier, Laplace and Z-transforms -- 9. Statistics and Curve Fitting -- 1. Random Variables, Means and Variance -- 2. Binomial and Poisson Distributions -- 3. Gaussian Distribution -- 4. Other Distributions -- 5. The Central Limit Theorem -- 6. Weibull Distribution -- 7. Sample Mean and Variance -- 8. Method of Least Squares -- 8.1. Linear Regression and Correlation Coefficient -- 8.2. Linearization -- 9. Generalized Linear Regression -- III. Advanced Topics -- 10. Partial Differential Equations -- 1. Introduction -- 2. First-Order PDEs -- 3. Classification of Second-Order PDEs -- 4. Classic PDEs -- 5. Solution Techniques -- 5.1. Separation of Variables -- 5.2. Laplace Transform -- 5.3. Similarity Solution -- 6. Integral Equations -- 6.1. Fredholm and Volterra Integral Equations -- 6.2. Solutions of Integral Equations -- 11. Numerical Methods and Optimization -- 1. Root-Finding Algorithms -- 2. Numerical Integration. ; 3. Numerical Solutions of ODEs -- 3.1. Euler Scheme -- 3.2. Runge-Kutta Method -- 4. Optimization -- 4.1. Feasible Solution -- 4.2. Optimality Criteria -- 5. Unconstrained Optimization -- 5.1. Univariate Functions -- 5.2. Multivariate Functions -- 6. Gradient-Based Methods -- 7. Nonlinear Optimization -- 7.1. Penalty Method -- 7.2. Lagrange Multipliers -- 7.3. Karush-Kuhn-Tucker Conditions -- A. Answers to Exercises -- Bibliography -- Index.
• Sommario/riassunto: A concise introduction to the fundamental concepts of mathematics that are closely related to civil engineering. By using an informal and theorem-free approach with more than 150 step-by-step examples, all the key mathematical concepts and techniques are introduced.
• Titolo autorizzato: Mathematics for Civil Engineers
• ISBN: 1-78046-577-7; 1-5231-1310-3; 1-78046-638-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910818256003321
• Lo trovi qui: Univ. Federico II