Description
Engineering Mathematics with Examples and Applications provides a compact and concise primer in the field, starting with the foundations, and then gradually developing to the advanced level of mathematics that is necessary for all engineering disciplines. Therefore, this book's aim is to help undergraduates rapidly develop the fundamental knowledge of engineering mathematics.
The book can also be used by graduates to review and refresh their mathematical skills. Step-by-step worked examples will help the students gain more insights and build sufficient confidence in engineering mathematics and problem-solving. The main approach and style of this book is informal, theorem-free, and practical. By using an informal and theorem-free approach, all fundamental mathematics topics required for engineering are covered, and readers can gain such basic knowledge of all important topics without worrying about rigorous (often boring) proofs.
Certain rigorous proof and derivatives are presented in an informal way by direct, straightforward mathematical operations and calculations, giving students the same level of fundamental knowledge without any tedious steps. In addition, this practical approach provides over 100 worked examples so that students can see how each step of mathematical problems can be derived without any gap or jump in steps. Thus, readers can build their understanding and mathematical confidence gradually and in a step-by-step manner.
Chapter
1.5 Simultaneous Equations
2.2 Floating Point Numbers
3 Binomial Theorem and Expansions
3.3 Binomial Theorem and Pascal's Triangle
5 Exponentials and Logarithms
5.3 Change of Base for Logarithm
6.2 Trigonometrical Functions
7.1 Why Do Need Complex Numbers?
Part III Vectors and Matrices
8 Vectors and Vector Algebra
8.4 Triple Product of Vectors
9.2 Matrix Addition and Multiplication
9.3 Transformation and Inverse
9.4 System of Linear Equations
9.5 Eigenvalues and Eigenvectors
10.1 Gradient and Derivative
10.2 Differentiation Rules
10.3 Series Expansions and Taylor Series
11.2 Integration by Parts
11.3 Integration by Substitution
12 Ordinary Differential Equations
12.1 Differential Equations
12.2 First-Order Equations
12.3 Second-Order Equations
12.5 System of Linear ODEs
13 Partial Differentiation
13.1 Partial Differentiation
13.2 Differentiation of Vectors
13.4 Three Basic Operators
14 Multiple Integrals and Special Integrals
Part V Fourier and Laplace Transforms
16 Fourier Series and Transform
16.3 Solving Differential Equations Using Fourier Transforms
16.4 Discrete and Fast Fourier Transforms
17.3 Solving ODE via Laplace Transform
17.5 Relationships between Fourier, Laplace and Z-transforms
Part VI Statistics and Curve Fitting
18 Probability and Statistics
18.3 Binomial and Poisson Distributions
18.4 Gaussian Distribution
18.6 The Central Limit Theorem
18.7 Weibull Distribution
19 Regression and Curve Fitting
19.1 Sample Mean and Variance
19.2 Method of Least Squares
19.3 Correlation Coefficient
19.5 Generalized Linear Regression
Part VII Numerical Methods
20.3 Newton-Raphson Method
20.4 Numerical Integration
20.5 Numerical Solutions of ODEs
21 Computational Linear Algebra
21.1 System of Linear Equations
21.5 Newton-Raphson Method
21.6 Conjugate Gradient Method
23.3 Unconstrained Optimization
23.4 Gradient-Based Methods
23.5 Nonlinear Optimization
23.6 Karush-Kuhn-Tucker Conditions
23.7 Sequential Quadratic Programming
24 Partial Differential Equations
24.3 Classification of Second-Order PDEs
24.4 Classic Mathematical Models: Some Examples
25.3 Hooke's Law and Elasticity
26 Calculus of Variations
26.1 Euler-Lagrange Equation
26.2 Variations with Constraints
26.3 Variations for Multiple Variables
27.2 Solution of Integral Equations
28.1 Mathematical Modeling
28.3 Different Levels of Approximations
28.4 Parameter Estimation
28.5 Types of Mathematical Models
28.6 Brownian Motion and Diffusion: A Worked Example
A.1 Differentiation and Integration
A.4 Fourier Series and Transform
B Mathematical Software Packages
B.2 Software Packages Similar to Matlab
B.3 Symbolic Computation Packages
Engineering Mathematics with Examples and Applications
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
