calculus of several variables lang solutions

The second part of the text covers maxima, minima, Lagrange multipliers, and Taylor's Formula for functions of two variables. It is an expanded version of the corresponding chapters in his A First Course in Calculus. From there, Lang proceeds to differentiation of vectors, functions of several variables (scalar fields), partial differentiation, the gradient, and the Chain Rule. It begins with vectors, including the dot (scalar) product, norm, parametric lines, planes, and the cross product. The first part of the text, which covers vector functions, is a prerequisite for the remaining parts of the book. 2: Multi-Variable Calculus and Linear Algebra with Applications, many results are proved, others are proved in special cases, and still others are justified through intuitive arguments. While Lang's text is not as rigorous as Tom M. Answers to most of the problems, including many fully worked out solutions, are provided in a 107 page appendix, making this text suitable for self-study. The exercises, which are generally challenging and occasionally daunting, reinforce these concepts and skills.

Methods of solution are clearly explained, then effectively demonstrated through the examples.

Like that text, this one clearly conveys the key concepts, places them in context, gives the reader a sense of how mathematicians think about the subject, and teaches the reader the skills needed to solve challenging problems. Serge Lang's Calculus of Several Variables provides an effective introduction to readers with a solid understanding of single variable calculus, such as that gained by working through his A First Course in Calculus (Undergraduate Texts in Mathematics).

Calculus of several variables lang solutions