多様体を構成するために、位相空間に完全アトラスを導入するところで質問です。 完全アトラスを導入するメリットとして、この文章の下線部を「異なる座標系を用いたのに同じ計算ができてしまうという問題が解消される」解釈したのですが、そこがよくわかりません。座標系を変えて計算する... 続きを読む

1 Two n-dimensional coordinate systems & and ŋ in S overlap smoothly provided the functions on¯¹ and ŋo §¯¹ are both smooth. Explicitly, if : U → R" and ŋ: R", then ŋ 1 is defined on the open set ε (ur) → ° (UV) V and carries it to n(u)—while its inverse function § 4-1 runs in the opposite direction (see Figure 1). These functions are then required to be smooth in the usual Euclidean sense defined above. This condition is con- sidered to hold trivially if u and do not meet. Č (UV) R" Ĕ(U) n(UV) R" S n(v) Figure 1. 1. Definition. An atlas A of dimension n on a space S is a collection of n-dimensional coordinate systems in S such that (A1) each point of S is contained in the domain of some coordinate system in, and (A2) any two coordinate systems in ✅ overlap smoothly. An atlas on S makes it possible to do calculus consistently on all of S. But different atlases may produce the same calculus, a technical difficulty eliminated as follows. Call an atlas Con S complete if C contains each co- ordinate system in S that overlaps smoothly with every coordinate system in C. 2. Lemma. Each atlas ✅ on S is contained in a unique complete atlas. Proof. If has dimension n, let A' be the set of all n-dimensional coordinate systems in S that overlap smoothly with every one contained in A. (a) A' is an atlas (of the same dimension as ✅).

なんで反比例の式は一次関数ではないのでしょうか！

この問題が全くわかりません。どう因数分解すればよいんでしょうか？わかる人いたらお願いします。

.Ill docomo Previous Problem Next Problem Let A be the following matrix: Ã = det A = A A 1 = ああ X (1) Find the adjugate matrix of A. = -3 -3 (2) Compute the determinant of A. 2:26 1 Problem List (3) Then the inverse matrix of A is given by 1 det A -Ã. - 3 X 1 -1 1 -3 x + 1 webwork.sci.hokudai.ac.jp m 100% 2 Ć

逆三角関数の式について質問です。式を変形するときにこんがらがってしまいます。どなたか教えていただけると嬉しいです。

Right Triangle Trigonometry - Finding Angles (Inverse sh Functions adjacent side hypotenuse cos @=cos½ O opposite side hypotenuse sin 8 = Sin-1(2) cos eps tan 0 = リンクをコ opposite side adjacent side

逆三角関数について質問です。 なぜ両方にsin^-1をかけるのかと、y=sin^-1xになるかがわからないので教えて欲しいです。

Inverse Trigonometric Functions Understanding Inverse Trigonometric Function その他の動画 tab y = sin x x = sin y sin ¹(x) = sin ¹(sin y) y = sin-¹x caps lock 1:08/6:53 Q W S #1 3 E $ 4 R % 5 T 6 7 U I 9 O O P 字幕 (c) HD YouTube # } 1 ( delete

逆行列を求める問題です。 答えがなく分からないので教えていただきたいです。

1 2 -1 3. (1) B= -2 -3 4 の逆行列を求めよ。 2 4 -1 1B| - 3+ 16+ & - よって Bの逆行刻 B-'はる在し 6-16+4= 9 fo (2) (1) の結果を用いて, 次の連立方程式を解け。 + 2y - 2 = 2 -2c - 3y + 4z = = -2 2c + 4y - 2 = 4

他1つでも分かるところあればお願いします😭

Rules in the School Library Grammar Focus Time and Place, Inversion We use phrases with prepositions and adverbs when we describe time and place. They are usually placed at the end of a clause or sentence. However, some emphatic expressions should be placed at the beginning of aclause or sentence and need to have an unusual structure, called inversion. Choose a phrase from the box below to complete each of the following sentences. Use a capital letter to begin the first word of each sentence. 1. The blueprints for the new buildingare on hold ( 2. A radical change in the formula fora new drug will take place ( 3. The scientific program has aired continuously ( ) did scientists decide that air, earth and fire were not really elements at all. 5. The Earth pulls on all objects with a force of gravity ( L). 6. My adviser will have been teaching for forty years ( 7. Most of the undergraduate students in the Faculty of Global Studies study abroad ( 8. All the classes during the first period are required to start ( ) were wriggling angleworms. f 10. Lithium batteries are prohibited to be sent ( a. by air in many countries b. by the end of the school year at the beginning of the year C。 d. until the end of October e. not until the eighteenth century f. since April 5, 2009, on the QBS Television Network g. during their second year h. under piles of leaves i. downward, that is, toward the center of the Earth on time, at 9:00 in the morning j.

教えてください！

Rules in the School Library Grammar Focus Time and Place, Inversion We use phrases with prepositions and adverbs when we describe time and place. They are usually placed at the end of a clause or sentence. However, some emphatic expressions should be placed at the beginning of aclause or sentence and need to have an unusual structure, called inversion. Choose a phrase from the box below to complete each of the following sentences. Use a capital letter to begin the first word of each sentence. 1. The blueprints for the new buildingare on hold ( 2. A radical change in the formula fora new drug will take place ( 3. The scientific program has aired continuously ( ) did scientists decide that air, earth and fire were not really elements at all. 5. The Earth pulls on all objects with a force of gravity ( 6. My adviser will have been teaching for forty years ( 7. Most of the undergraduate students in the Faculty of Global Studies study abroad ( 8. All the classes during the first period are required to start ( ) were wriggling angleworms. 10. Lithium batteries are prohibited to be sent ( by air in many countries b. bythe end of the school year a. at the beginning of the year C。 d. until the end of October e. not until the eighteenth century f. since April 5, 2009, on the QBS Television Network g. during their second year h. under piles of leaves i. downward, that is, toward the center of the Earth on time, at 9:00 in the morning j.

1番と3番が答えが出せない為計算の仕方を教えて頂きたいです