Calculus: Dynamic Mathematics, For Multivariable presents a complete multivariable calculus course in four major areas: linear algebra, partial derivatives, multiple integrals, and line and surface integrals. There is also a short concluding chapter on some aspects of differential equations. Concepts of linear algebra are introduced before any multivariable calculus concepts. The ideas of determinants, eigenvalues, and matrices justify some techniques in multivariable calculus, such as the Jacobian, the Lagrange multiplier, predator-prey differential equations, and substitution of variables in double integrals. The chapter on partial derivatives includes sections on the Jacobian, the Implicit Function Theorem, and Lagrange multipliers. The chapter on multiple integrals and line integrals showcases the three fundamental theorems of multivariable calculus, the theorems of Green, Gauss, and Stokes. It is assumed that students have had a prerequisite single-variable calculus course, such as AP Calculus BC. For a free preview, please go to my website, www.drchuckgarner.com.
