In this chapter, we discuss basic mathematical concepts and methods that will be used as tools in the development of finite element formulations and solution of finite element models. Basic knowledge of linear algebra, calculus of vectors and matrices, variational calculus, and integral equations is necessary in the derivation of finite element formulations. These fundamental mathematical concepts and methods are reviewed as the building blocks for the following content of this book. Numerical methods for numerical approximation, differentiation, integration, discretization, and solution of linear systems will be discussed in Chapter 3. The mathematical tools and numerical methods are then utilized, along with relevant physical principles, in the illustration of the FEA procedure for different types of physical problems in later chapters.
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