Notes pour le cours MAT 2522 Calcul différentiel de plusieurs variables à l’Université d’Ottawa. Nous nous pencherons principalement sur les fonctions à valeurs réelles à entrées multiples à valeurs réelles. De nombreux concepts seront discutés en utilisant le langage des vecteurs et de l’algèbre linéaire puisque c’est le cadre le plus naturel pour le calcul à plusieurs variables. Nous verrons comment une grande partie du calcul que vous avez appris dans les cours précédents se généralise en dimensions multiples. Cela nous permettra d’explorer des mathématiques nouvelles et intéressantes, comme l’intégration sur des surfaces et des régions tridimensionnelles. Traduction des notes du cours MAT 2122 Multivariable Calculus.

Le contenu de ce manuel couvre la grande majorité des sujets présentés dans les cours de calcul différentiel et intégral pour les étudiants en sciences et génie. Les seuls préalables sont les mathématiques normalement enseignées au secondaire en Ontario. Ce manuel peut être utilisé pour trois des variantes des cours de calcul différentiel et intégral que nous retrouvons dans la majorité des universités en Ontario : Calcul différentiel et intégral pour les étudiants en génie, Calcul différentiel et intégral pour les étudiants en sciences de la vie et Calcul différentiel et intégral pour les étudiants en administration.

Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.

In addition to the Textbook, there is also an online Instructor's Manual and a student Study Guide. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.

This series of videos focusing on calculus covers sample questions from the A.P, Calculus AB and AC exams (both multiple choice and free answer).

The Calculus BC AP exam is a super set of the AB exam. It covers everything in AB as well as some of the more advanced topics in integration, sequences and function approximation. This tutorial is great practice for anyone looking to test their calculus mettle!

Calculus-Based Physics is an introductory physics textbook designed for use in the two-semester introductory physics course typically taken by science and engineering students.

This series of videos focusing on calculus covers minima, maxima, and critical points, rates of change, optimization, rates of change, L'Hopital's Rule, mean value theorem.

A single definite integral can be used to find the area under a curve. with double integrals, we can start thinking about the volume under a surface!

This is about as many integrals we can use before our brains explode. Now we can sum variable quantities in three-dimensions (what is the mass of a 3-D wacky object that has variable mass)!

This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)

This site provides lectures and guided lecture notes for students for a second-semester calculus course.

This course is an introduction to the calculus of functions of several variables. It begins with studying the basic objects of multidimensional geometry: vectors and vector operations, lines, planes, cylinders, quadric surfaces, and various coordinate systems. It continues with the elementary differential geometry of vector functions and space curves. After this, it extends the basic tools of differential calculus - limits, continuity, derivatives, linearization, and optimization - to multidimensional problems. The course will conclude with a study of integration in higher dimensions, culminating in a multidimensional version of the substitution rule.

The most important way to learn calculus is through problem-solving. While going through the solution to a problem, students are often faced with several issues. They may not see the connection between the concept taught in class and the solution. Others may not understand the solution because a step is missing or there are insufficient explanations. Or because they have weak algebra skills. The main goal of this exercise book is to address these issues to help students learn the material more efficiently and get better results. The book contains a wide variety of problems in integral calculus and multivariable calculus, with applications in differential equations, probability, management, and economics. Every problem has a very detailed solution, and the book is self-contained, as the summary for every concept is provided.

Complete course available at MyOpenMath. Course ID:142672
.   This work was supported in part by a Wright College grant to create ancillary materials to augment OER materials.

Master the calculus of derivatives, integrals, coordinate systems, and infinite series.
In this three-part series you will learn the mathematical notation, physical meaning, and geometric interpretation of a variety of calculus concepts. Along with the fundamental computational skills required to solve these problems, you will also gain insight into real-world applications of these mathematical ideas.

Part 1: Differentiation
Part 2: Integration
Part 3: Coordinate Systems & Infinite Series

This series of courses is part of the Open Learning Library, which is free to use. You have the option to sign up and enroll in the courses if you want to track your progress, or you can view and use all the materials without enrolling.

This workbook, designed for use with OpenStax Calculus Volume 1, was developed under a Round 17 Mini-Grant.

The most important way to learn calculus is through problem-solving. While going through the solution to a problem, students often face several issues. They may not see the connection between the concept taught in class and the solution. Others may not understand the solution because a step is missing or there are insufficient explanations. Or because they have weak algebra skills. The main goal of this exercise book is to address these issues to help students learn the material more efficiently and get better results. The book contains a wide variety of problems in differential calculus with applications in management and economics. Every problem has a very detailed solution, and the book is self-contained, as the summary for every concept is provided.

This series of videos focusing on calculus covers indefinite integral as anti-derivative, definite integral as area under a curve, integration by parts, u-substitution, trig substitution.

This 9-minute video lesson provides an introduction to L'Hopital's Rule. [Calculus playlist: Lesson 36 of 156]

This series of videos focusing on calculus covers limit introduction, squeeze theorem, and epsilon-delta definition of limits.