ABSTRACT
Understanding the vector fields, tensors, and transformation of vectors into a different coordinate system is fundamentals in wave propagation analysis that are used in CNDE modeling. This chapter presents the basic understanding of vector and vector fields. How a vector field is described in Cartesian coordinate system is graphically explained. Next to present the vector field in a generalized coordinate system index notation is introduced. Utilizing index notation, dot product, cross product, divergence, and curl of a vector field is explained. Further, concept of tensor is introduced, and transformation laws of tensors are briefly described. Covariant and contravariant tensors are briefly described to introduce the tensor transformation laws with Jacobian matrix. Further, Gauss divergence theorem and Stokes theorem are explained which are frequently used in the later chapters.
