Book Details

Both algebra and calculus are essential branches of mathematics. The earliest known equations in algebra were found in ancient Egypt in 1650 BC. Calculus originated in the 17th century. Linear Algebra is a branch of mathematics that deals with solving equations to find out the unknown variable while calculus is a branch of mathematics that deals with finding out the change in the rates in entities or functions concerning each other. While Linear Algebra uses basic arithmetic operations, Calculus performs the functions of differentiation and integration. Linear Algebra is used in various fields such as engineering, physics, and computer science. Calculus is employed for higher functions in advanced sciences; one such example is the use of differential geometry in formulating Einstein’s General Theory of relativity. This book gives some basic knowledge about Linear Algebra. It touches the concepts of vector spaces and their four fundamental subspaces. The concepts of Moore-Penrose inverse and Generalized inverse are explained. The solution of inconsistent non-homogeneous algebraic equations by least square methods and Gram-Schmidt QR factorization are illustrated. The method of matrix diagonalization and the concept of singular value decomposition (SVD) are described. Vectors norms, matrix norms and induced norms are defined. The topics of condition number and round-off errors are covered. Different types of ordinary differential equations (ODE) and solving them by different methods are demonstrated. The solution of non-homogeneous differential equations by various methods like elimination, diagonalization, undetermined coefficients, variation of parameters and matrix exponential is illustrated. Examples using MATLAB programming can be found in the Appendix.