The material is integrated to emphasize the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author includes all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible, and also includes complete proofs. It includes most of the required material from multivariable calculus, linear algebra, and basic analysis.
An intuitive approach and a minimum of prerequisites make it a valuable companion for students of mathematics and physics. The main focus is on manifolds in Euclidean space and the metric properties they inherit from it. Among the topics discussed are curvature and how it affects the shape of space, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations.
Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathematics. In this text, the basic algebraic, analytic, and geometric concepts of multivariable and vector calculus are carefully explained, with an emphasis on developing the student's intuitive understanding and computational technique. A wealth of figures supports geometrical interpretation, while exercise sets, review sections, practice exams, and historical notes keep the students active in, and involved with, the mathematical ideas.
All necessary linear algebra is developed within the text, and the material can be readily coordinated with computer laboratories. Incorporating many features from these highly respected texts, it is both a synthesis of the authors' previous work and a new and original textbook. The authors make it clear that Mathematica is not algorithms, but at the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The sets of problems give students an opportunity to practice their newly learned skills, covering simple calculations, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numerical integration, and also cover the practice of incorporating text and headings into a Mathematica notebook.
The accompanying diskette contains both Mathematica 2. It is assumed that students will also have access to an introductory primer for Mathematica. Multivariable Calculus Author : L. Designed as ajunior-level textbook for an advanced calculus course, this book covers a variety of notions,including continuity , differentiation, multiple integrals, line and surface integrals, differentialforms, and infinite series.
Numerous exercises and examples throughout the book facilitatethe student's understanding of important concepts.
The level of rigor in this textbook is high; virtually every result is accompanied by a proof. Toaccommodate teachers' individual needs, the material is organized so that proofs can be deemphasizedor even omitted. Linear algebra for n-dimensional Euclidean space is developedwhen required for the calculus; for example, linear transformations are discussed for the treatmentof derivatives.
Featuring a detailed discussion of differential forms and Stokes' theorem, Multivariable Calculusis an excellent textbook for junior-level advanced calculus courses and it is also usefulfor sophomores who have a strong background in single-variable calculus. A two-year calculussequence or a one-year honor calculus course is required for the most successful use of thistextbook. Students will benefit enormously from this book's systematic approach to mathematicalanalysis, which will ultimately prepare them for more advanced topics in the field.
It covers the notions including continuity, differentiation, multiple integrals, line and surface integrals, differential forms, and infinite series. The book is intended for use in an advanced calculus course. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus.
This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals.
Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike. The ideas of multivariable calculus are presented in a context that is informed by their non-mathematical applications.
It incorporates collaborative learning strategies and the sophisticated use of technology, which asks students to become active participants in the development of their own understanding of mathematical ideas.
This teaching and learning strategy urges students to communicate mathematically, both orally and in writing. With extended examples and exercises and a student-friendly accessible writing style, Multivariable Calculus is an exciting and engaging journey into mathematics relevant to students everyday lives.
Fractional and Multivariable Calculus Author : A. As a complement to the main text, an extended bibliography with some of the Calculus: Early Transcendentals. Calculus: Early Transcendentals, originally by D. Guichard, has been redesigned by the Lyryx editorial team. Substantial portions of the content, examples, and diagrams have been redeveloped, with additional contributions provided by experienced and practicing instructors. This approachable textbook provides a comprehensive understanding of the nec Regression Models for Data Science in R.
The ideal reader for this book will be quantitatively literate and has a basic understanding of statistical concepts and R programming. The student should have a basic understanding of statistical inference such as contained in "Statistical inference for data science".
The book gives a rigorous treatment of the elementary concepts of regr This book integrates the vital areas of object-orientation, functional programming, design patterns, and language design. Stochastics of Environmental and Financial Economics. These Proceedings offer a selection of peer-reviewed research and survey papers by some of the foremost international researchers in the fields of finance, energy, stochastics and risk, who present their latest findings on topical problems.
The papers cover the areas of stochastic modeling in energy and financial markets; risk management with envir This book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants.
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