Multivariable Calculus, Linear Algebra, and Differential Equations

The third edition combines coverage of multivariable calculus with linear algebra and differential equations. Grossman's unique approach provides maths, engineering, and physical science students with a continuity of level and style. The intuitive approach is stressed over a more rigorous/formal treatment of the topics. An abundance of examples, graded exercises, and numerous applications all contribute to student appeal. Features: \* Historical notes and biographical sketches describe the development of an idea or identify an important person in mathematics. \* Graphs and exercises sets are incorporated thoughout the text to help students visualize mathematics and better understand concepts. \* An optional discussion of Newton's method for two variables is part of Section 3.12. \* The Summing Up Theorem is used to tie together seemingly disparate topics in the study of linear algebra. \* Section 10.3 contains an answer to the question ''When is a differential equation separable ?'' \* Numerous examples throughout the text contain all the algebraic steps needed to complete the solution. \* The text contains over 5,500 exercises graded according to difficulty, and there is a balance between technique and proof. New to this edition: \* Solving Linear Systems Numerically: Gaussian Elimination with Divoting has been added to Chapter 6. \* Coverage of Least Squares Approximation and Isomorphisms has been added to Chapter 8. \* True/False and multiple choice ''Self-Quiz'' exercises now begin each problem set. Students can use these exercises to access their comprehension before tackling the exercise set. \* Each chapter now ends with a review of the important results of that chapter. \* Examples and figures are now titled so that students can easily grasp the essential concept each one illustrates Multivariable Calculus, Linear Algebra, and Differential Equations, Second Edition contains a comprehensive coverage of the study of advanced calculus, linear algebra, and differential equations for sophomore college students. The text includes a large number of examples, exercises, cases, and applications for students to learn calculus well. Also included is the history and development of calculus. The book is divided into five parts. The first part includes multivariable calculus material. The second part is an introduction to linear algebra. The third part of the book combines techniques from calculus and linear algebra and contains discussions of some of the most elegant results in calculus including Taylor's theorem in'n'variables, the multivariable mean value theorem, and the implicit function theorem. The fourth section contains detailed discussions of first-order and linear second-order equations. Also included are optional discussions of electric circuits and vibratory motion. The final section discusses Taylor's theorem, sequences, and series. The book is intended for sophomore college students of advanced calculus.