About Product
Multivariate Calculus through Linear Algebra, true to its title, attempts to study calculus of functions of several variables by first giving the prerequisites from linear algebra. It is suitable as a text for the first and second years of B.E./B.Tech./B.Sc. courses. In a traditional curriculum, these two topics are relegated to separate courses. But the present work is based on the theme that differentiability is nothing but approximability by a linear function. So, logically, linear algebra should precede calculus. The book is divided into two parts: Part I (Chapters 1 to 9) on Linear Algebra and Part II (Chapters 10 to 20) on Multivariate Calculus. Part I deals with standard topics of linear algebra such as vector spaces, linear transformations, matrices, determinants, eigenvalues, diagonalisation, orthogonal and unitary matrices. Chapter 9 covers a relatively less common topic of multilinear forms and quadratic forms. Part II deals with functions of several variables. However, prerequisites from calculus (and analysis) of functions of one variable are reviewed in Chapter 10. After introducing topological preliminaries in Chapter 11, topics of continuity, differentiation, tangency and optimisation are handled in Chapters 12 to 14, culminating in the Implicit Function Theorem in Chapter 15. Chapters 16 to 20 deal with integral calculus, including vector calculus. The theory of multiple integrals is developed both in the naïve manner and in the analytical manner. Detailed answers to nearly all exercises are included.
Tags:
Calculus;
