Calculus Volume I 2nd Ed One Variable Calculus With An Introduction To Linear Algebra
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Calculus, Volume I, 2nd Ed One-variable Calculus, with an Introduction to Linear Algebra
· Some Basic Concepts Of The Theory Of Sets · A Set Of Axioms For The Real Number System · Mathematical Induction, Summation Notation, And Related Topics · The Concepts Of The Integral Calculus · Some Applications Of Differentiation · Continuous Functions · Differential Calculus · The Relation Between Integration And Differentiation · The Logarithm, The Exponential, And The Inverse Trigonometric Functions · Polynomial Approximations To Functions · Introduction To Differential Equations · Complex Numbers · Sequences, Infinite Series, Improper Integrals · Sequences And Series Of Functions · Vector Algebra · Applications Of Vector Algebra To Analytic Geometry · Calculus Of Vector-Valued Functions · Linear Spaces · Linear Transformations And Matrices
Multivariable Calculus, Linear Algebra, and Differential Equations
Author: Stanley I. Grossman
language: en
Publisher: Academic Press
Release Date: 2014-05-10
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.
Calculus of Several Variables
Author: Serge Lang
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The present course on calculus of several variables is meant as a text, either for one semester following A First Course in Calculus, or for a year if the calculus sequence is so structured. For a one-semester course, no matter what, one should cover the first four chapters, up to the law of conservation of energy, which provides a beautiful application of the chain rule in a physical context, and ties up the mathematics of this course with standard material from courses on physics. Then there are roughly two possibilities: One is to cover Chapters V and VI on maxima and minima, quadratic forms, critical points, and Taylor's formula. One can then finish with Chapter IX on double integration to round off the one-term course. The other is to go into curve integrals, double integration, and Green's theorem, that is Chapters VII, VIII, IX, and X, §1. This forms a coherent whole.