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Unformatted text preview: 18.022 Lecture notes The course is divided into 6 parts: Part 1 (Lectures I VII): Euclidean Spaces and Vector Algebra Part 2 (VIII XIII): Differential Calculas for Scalar Fields and Functions of Several Real Variables. Part 3 (XIV XVII): Multiple Integrals Part 4 (XVIII XXII): Line Integrals and Surface Integrals in Scalar and Vector Fields Part 5 (XXIII XXVIII): Vector Integral Calculus in Two and Three Dimensions Part 6 (XXIX XXXV): Linear Algebra in Multivariable Calculus Lecture I The Three-dimensional Space We refer to the Euclidean two- and three-dimensional spaces as E 2 and E 3 , respectively. Euclidean spaces have a measure of distance between points; for every two points P and Q, we denote it by d(P, Q). This measure satisfies the following two laws: i) For any two given points P and Q, d(P, Q) = 0 if and only if P = Q. ii) For any three given points P, Q and R, d (P, R) d (P,Q) + d (Q, R)....
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