Multivariable Calculus with Matlab(r): With Applications to Geometry and Physics

ISBN-13: 9783319879420 / Angielski / Miękka / 2018 / 276 str.

Ronald L. Lipsman; Jonathan M. Rosenberg

Recenzje

"The book is addressed to students as well as to instructors of calculus. It helps to understand multivariable analysis utilysing visualization of such geometric structures like domains, curves and surfaces. It also develops the skill of students to use a powerful software for solving modern problems." (Ivan Podvigin, zbMATH 1400.26001, 2019)

Spis treści

1. Introduction.- 2. Vectors and Graphics.- 3. Geometry of Curves.- 4. Kinematics.- 5. Directional Derivatives.- 6. Geometry of Surfaces.- 7. Optimization in Several Variables.- 8. Multiple Integrals.- 9. Multidimensional Calculus.- 10. Physical Applications of Vector Calculus.- 11. MATLAB Tips.- Sample Solutions.- Index.

O autorze

Ronald Lipsman retired in 2010 after a 41-year career as Professor of Mathematics at the University of Maryland. During his last decade on campus, he served as Senior Associate Dean of the College of Computer, Mathematical and Physical Sciences. His research interests include group representations and harmonic analysis on Lie groups. He received his Ph.D. from MIT in 1967 and was a Gibbs Instructor at Yale University, 1967-1969.

Jonathan Rosenberg is Ruth M. Davis Professor of Mathematics at the University of Maryland, a Fellow of the American Mathematical Society, and a Managing Editor of Annals of K-Theory. His research interests include geometry, topology, and mathematical physics.  He received his Ph.D. from the University of California, Berkeley, in 1976, and joined the faculty at Maryland in 1981.

Professors Lipsman and Rosenberg have collaborated on numerous research and educational projects. Among their educational texts is: A Guide to MATLAB, 3rd&n

bsp;ed, 2014.

Blurb

This comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students.

MATLAB® is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers.