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Engineering Analysis

Advanced Mathematical Methods for Engineers

  • 1st Edition - May 20, 2024
  • Latest edition
  • Author: Zhihe Jin
  • Language: English

Engineering Analysis: Advanced Mathematical Methods for Engineers introduces graduate engineering students to the fundamental but advanced mathematics tools used in engineeri… Read more

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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.

Key features

  • Incorporates numerous engineering examples to help students better understand mathematical concepts and methods for developing mathematical models and finding the solutions of engineering problems
  • Integrates the MATLAB computation tool with many MATLAB programs to enhance students’ ability to solve engineering problems
  • Includes tensor analysis to better prepare students for advanced engineering courses such as theory of elasticity, fluid dynamics, and heat transfer. Inclusion of tensor analysis also allows a unified treatment of vector and tensor calculus

Readership

Graduate engineering students studying advanced engineering math primarily in mechanical and aerospace engineering programs / Navstem estimates the overall US academic market size at 32,000 students. The number of students taking engineering analysis/advanced math at the graduate level is estimated to be about half, or approximately 16,000 students

Table of 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

Product details

  • Edition: 1
  • Latest edition
  • Published: May 20, 2024
  • Language: English

About the author

ZJ

Zhihe Jin

Zhihe Jin is a Professor in the Department of Mechanical Engineering at the University of Maine. He obtained his Ph.D. in Engineering Mechanics from Tsinghua University in 1988. His research areas include fracture mechanics, thermal stresses, poromechanics, biomechanics and thermoelectricity. His research is mainly concerned with the mathematical theories and solutions of fracture, deformation, heat conduction, porous fluid flow and thermoelectric energy conversion efficiency. He has published more than 100 refereed journal papers and 6 book chapters. He also co-authored a textbook on fracture mechanics published in 2011 (Sun & Jin, Fracture Mechanics 1e, Elsevier). He has taught 11 undergraduate and graduate courses including Mechanical Engineering Analysis at the University of Maine.
Affiliations and expertise
Department of Mechanical Engineering, University of Maine, Maine, USA

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