工学解析：エンジニアのための先端数学的手法（テキスト） Engineering Analysis : Advanced Mathematical Methods for Engineers

Jin, Zhihe

Academic Press Inc（2024/10発売）

Academic Press Inc（2024/10発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 496 p.
• 言語 ENG
• 商品コード 9780323953979
• DDC分類 620.00151

Full Description

Engineering Analysis: Advanced Mathematical Methods for Engineers introduces graduate engineering students to the fundamental but advanced mathematics tools used in engineering application, especially in mechanical, aerospace, and civil engineering. Most engineering problems are described by differential equations, particularly partial differential equations (PDEs). Deformation and failure in solid structures, fluid flow, heat transfer, and mass diffusion are all governed by PDEs in general. Many physical quantities in engineering are tensors, including deformation gradient, strain rates, stresses, elastic stiffness, and thermal conductivity of composite materials. This book helps engineering graduate students develop the skills to establish the mathematical models of engineering problems and to solve the problems described by the mathematical models.

Contents

PART I ORDINARY DIFFERENTIAL EQUATIONS - ADVANCED TOPICS
1. Ordinary Differential Equations and Power Series Solutions
2. The Frobenius Method
3. The Laplace Transform Method
4. Numerical Solutions of Ordinary Differential Equations

PART II FOURIER ANALYSIS
5. Fourier Series
6. Fourier Transforms

PART III PARTIAL DIFFERENTIAL EQUATIONS
7. Partial Differential Equations in Engineering
8. Separation of Variables Method
9. Separation of Variables Method - Circular and Spherical Regions
10. Integral Transform Methods
11. The Finite Difference Method

PART IV TENSOR ANALYSIS
12. Cartesian Tensors
13. Tensor Analysis