Applied engineering analysis

Intro; Title Page; Copyright; Table of Contents; Dedication; Preface; Suggestions to instructors; About the companion website; Chapter 1: Overview of Engineering Analysis; 1.1 Introduction; 1.2 Engineering Analysis and Engineering Practices; 1.3 â#x80;#x9C;Toolboxâ#x80;#x9D; for Engineering Analysis; 1.4 The Four Stages in Engineering Analysis; 1.5 Examples of the Application of Engineering Analysis in Design; 1.6 The â#x80;#x9C;Safety Factorâ#x80;#x9D; in Engineering Analysis of Structures; Problems; Chapter 2: Mathematical Modeling; 2.1 Introduction; 2.2 Mathematical Modeling Terminology; 2.3 Applications of Integrals.

2.4 Special Functions for Mathematical Modeling2.5 Differential Equations; Problems; Chapter 3: Vectors and Vector Calculus; 3.1 Vector and Scalar Quantities; 3.2 Vectors in Rectangular and Cylindrical Coordinate Systems; 3.3 Vectors in 2D Planes and 3D Spaces; 3.4 Vector Algebra; 3.5 Vector Calculus; 3.6 Applications of Vector Calculus in Engineering Analysis; 3.7 Application of Vector Calculus in Rigid Body Dynamics; Problems; Chapter 4: Linear Algebra and Matrices; 4.1 Introduction to Linear Algebra and Matrices; 4.2 Determinants and Matrices; 4.3 Different Forms of Matrices.

4.4 Transposition of Matrices4.5 Matrix Algebra; 4.6 Matrix Inversion, [A]â#x88;#x92;1; 4.7 Solution of Simultaneous Linear Equations; 4.8 Eigenvalues and Eigenfunctions; Problems; Chapter 5: Overview of Fourier Series; 5.1 Introduction; 5.2 Representing Periodic Functions by Fourier Series; 5.3 Mathematical Expression of Fourier Series; 5.4 Convergence of Fourier Series; 5.5 Convergence of Fourier Series at Discontinuities; Problems; Chapter 6: Introduction to the Laplace Transform and Applications; 6.1 Introduction; 6.2 Mathematical Operator of Laplace Transform.

6.3 Properties of the Laplace Transform6.4 Inverse Laplace Transform; 6.5 Laplace Transform of Derivatives; 6.6 Solution of Ordinary Differential Equations Using Laplace Transforms; 6.7 Solution of Partial Differential Equations Using Laplace Transforms; Problems; Chapter 7: Application of First-order Differential Equations in Engineering Analysis; 7.1 Introduction; 7.2 Solution Methods for First-order Ordinary Differential Equations; 7.3 Application of First-order Differential Equations in Fluid Mechanics Analysis; 7.4 Liquid Flow in Reservoirs, Tanks, and Funnels.

7.5 Application of First-order Differential Equations in Heat Transfer Analysis7.6 Rigid Body Dynamics under the Influence of Gravitation; Problems; Chapter 8: Application of Second-order Ordinary Differential Equations in Mechanical Vibration Analysis; 8.1 Introduction; 8.2 Solution Method for Typical Homogeneous, Second-order Linear Differential Equations with Constant Coefficients; 8.3 Applications in Mechanical Vibration Analyses; 8.4 Mathematical Modeling of Free Mechanical Vibration: Simple Massâ#x80;#x93;Spring Systems.

8.5 Modeling of Damped Free Mechanical Vibration: Simple Massâ#x80;#x93;Spring Systems.