Mathematics for Civil Engineers : An Introduction [E-Book]
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.
Saved in:
Full text |
|
Personal Name(s): | Yang, Xin-She, author |
Edition: |
1st edition |
Imprint: |
Edinburgh :
Dunedin Academic Press,
2017
|
Physical Description: |
1 online resource (327 pages) |
Note: |
englisch |
ISBN: |
9781780466385 |
- 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.