دانلود کتاب ریاضیات مهندسی با کاربردهای MATLAB – جلد ۱، مبانی

Engineers design structures or systems by conducting mechanical, thermal, _low, electrical, or other types of analyses through theoretical or computer methods. Mathematical methods and their ingredients in such analyses are referred to as engineering mathematics. Engineering mathematics should be learned very well in order to take its maximum advantage in real applications. In the solution of engineering problems, the problem is first expressed with a mathematical equation and then solved with an appropriate method. Mathematical expression of the engineering problem is also called the mathematical model of the problem. Mathematical models are often expressed in algebraic, differential, or optimization form. Engineering problems are transformed into such forms using intermediate methods such as derivative, integral, interpolation, and curve fitting. Problems expressed in such forms are then solved using appropriate mathematical (Analytical, Approximate/Semi-analytical, or Numerical) methods. Solution method is determined based on the size, complexity (difficulty) of the engineering problem, available time, and the desired precision (accuracy) in the solution. In this book, classical and modern mathematical methods within the context of engineering mathematics are introduced in detail. Content of the book is tailored specifically for the needs of engineers and enriched with worked out examples from the engineering applications. The book is organized in 16 chapters in two volumes. Volume 1 covers basic topics while Volume 2 focuses on advanced topics. Volumes 1 and 2 together constitute a complete and comprehensive reference source in engineering mathematics. Volume 1 (this book) covers basic topics in ten chapters. Computer tools such as MATLAB software are increasingly used in the solution of engineering problems. Therefore, in Chap. 1, MATLAB software is introduced. In this chapter, readers learn how to use MATLAB commands and write their own programs to solve engineering problems. In Chap. 2, basic calculus and mathematical information are summarized for the convenience of readers. Various types of error such as modeling, cutting, and rounding error occur in the expression and solution stages of engineering problems. Chapter 3 explains error source and types in computer solutions. Engineering problems are expressed in final form as linear or nonlinear algebraic equations. Therefore, Chap. 4 describes solution of linear algebraic equations using direct methods of Gauss elimination, Decomposition, Cramer and matrix inverse, and iterative methods of Jacobi and Gauss-Seidel. In Chap. 5, root finding and solution of nonlinear algebraic equations are explained. In this chapter, root finding with bracketing methods of Bisection and False position and point-based methods of Simple iteration, Newton-Raphson, and Secant methods are covered. In Chap. 6, interpolation with single and multivariate functions is explained using global interpolation methods of Newton-divided difference, Lagrange, and Hermite and local interpolation methods of Linear, Parabolic, and Cubic splines. Chapter 7 explains curve fitting with single and multivariate functions. In this chapter, Response Surface Methodology, Artificial Neural Networks (ANNs), and Kriging methods are covered in detail. Chapter 8 introduces numerical derivative methods. In this chapter, expressions of ordinary and partial derivatives using classical Finite Difference and relatively new Differential Quadrature methods are explained. In Chap. 9, numerical integral methods are covered. In this chapter, numerical calculation of single and multiple integrals on regions with and without regular boundaries using Newton-Cotes methods of Trapezoidal and Simpson and quadrature methods of Gauss, Gauss-Lobatto, and Gauss-Legendre is explained. Chapter 10 explains numerical solution of eigenvalue problems, which are a special type of algebraic equations. Polynomial and iterative methods are covered in this chapter.