surface integrals. 
Chapter 2 presents the important operators that can be performed on scalar and vector fields. This refers to, for instance, engineering, physics, and computer sciences, in general, but particularly solid mechanics, aerodynamics,  aeronautics, fluid flow, heat flow, robotics as well as other areas have  applications that require an understanding of vector calculus.
 Multiple integrals constitute the object of Chapter 3. The double and triple integrals and their applications for computing volumes, masses, and centroids of more general regions are presented in this chapter. We will learn how to apply different types of coordinates such as polar coordinates, cylindrical coordinates and spherical coordinates for calculating multiple integrals over specific regions depending on types of integration regions.
 Chapter 4 presents differential forms as an alternative to vector calculus which is ultimately simpler and more flexible. In this chapter, a brief supplement is provided to explain how to work with them. 
Chapter 5, devoted to define the line integral in vector fields. In Chapter 4 the line integral using the differential form presents a coordinate free way to deal with general principles. However, in many physical circumstances, equations need to be expressed on coordinates. The line integral in vector fields, therefore, is presented in this chapter. 
Chapter 6 presents the surface intefral which describes the flow of a field through a surface. This chapter first gives the representations of parametric surface and show us how to parametrize surfaces to give the convenient ways of computing surface integrals. Then, we will learn how to integrate over different types of surfaces. Finally, we will apply the general surface area formula to special surfaces.

Chapter 7 presents important theorems which give the relationships between line, surface and multiple integrals. Greenriemann theorem relates a line integral around a simple closed curve to a double integral over the plane region. Stoke's theorem establish the relations between the integral of a vector field along a curve and the flux of that field over a surface. Frean-Ostrogradski relates a surface integral of a field to a triple integral over a region bounded by a surface.
Chapter 8 presents Fourier series of an arbitrary function. Fourier pointed out that an arbitrary function can be represented by a trigonometric series. Fourier series is advantageous than a power series in many phenomenons that are periodic such as astronomical phenomena, heartbeats, tides, vibration.
The Fourier transform is the topic of Chapter 9. Fourier transform is useful in many fields such as partial differential equation, signal and image processing, LTI system & circuit analysis. In this chapter the relationship between the Fourier series and Fourier transform will be presented. The properties of the Fourier transform are provided and some of its applications are then explored.
Chapter 10 presents the Laplace transform as well as the inverse Laplace transform. The Laplace transform has many applications in science and engineering because it is a tool for solving differential equations. The application of the Laplace transform for solving ordinary differential equations is demonstrated. Finally, some engineering problems are presented and solved by using Laplace transforms.
Each chapter provides some examples as solved problems to clarify the introduced concepts. Abstraction discussion are avoided and the mechanical application and illustrations are given. Some appropriate proofs are provided to help student understand the theorems. Some of the example are taken from the recent literature to illustrate the applications in the field of mechanical engineering. At the end of each chapter, there are exercises to help students better understand the contents of the chapter and improve the calculating
techniques. To yield the good knowledge from the book, students need
to read the text carefully and do the exercises as much as they can. Some
answers or hints are given to help student do the exercises effectively