• Đề thi môn: Toán 3 - Mã môn học: 1001013Đề thi môn: Toán 3 - Mã môn học: 1001013

    Câu 4 (1đ): Xác định cận của tích phân  , ,  V  f x y z dxdydz với 2 : 2 x y z V z       trong hệ tọa độ trụ. Câu 5 (3đ): Giải các phương trình vi phân a) y x e y 2 x 0 x    b) y y y x       3 4 1 2 Câu 6 (1đ): Tìm đạo hàm riêng hàm ẩn z(x,y) xác định từ phương trình z z f xy x   3 3   trong đó f u   ...

    pdf2 trang | Chia sẻ: huyhoang44 | Ngày: 19/03/2020 | Lượt xem: 4 | Lượt tải: 0

  • Toán học - Chapter 13: Modeling computationToán học - Chapter 13: Modeling computation

    Syntax (form of a sentence) vs. semantics (meaning of a sentence) The sentence the frog writes neatly is a valid sentence according to the rules of English grammar. That is, it is syntactically correct, even though it’s nonsensical (unless we are talking about a fantasy world). The sequence of words swims quickly mathematics is not a valid senten...

    pptx56 trang | Chia sẻ: huyhoang44 | Ngày: 19/03/2020 | Lượt xem: 4 | Lượt tải: 0

  • Toán học - Chapter 12: Boolean algebraToán học - Chapter 12: Boolean algebra

    Definition: Let B = {0, 1}. Then Bn = {(x1, x2, , xn) | xi ∈ B for 1 ≤ i ≤ n } is the set of all possible n-tuples of 0s and 1s. The variable x is called a Boolean variable if it assumes values only from B, that is, if its only possible values are 0 and 1. A function from Bn to B is called a Boolean function of degree n. Example: The function F(x...

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  • Toán học - Chapter 11: TreesToán học - Chapter 11: Trees

    Theorem: An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices. Proof: Assume that T is a tree. Then T is connected with no simple circuits. Hence, if x and y are distinct vertices of T, there is a simple path between them (by Theorem 1 of Section 10.4). This path must be unique - for if there ...

    pptx43 trang | Chia sẻ: huyhoang44 | Ngày: 19/03/2020 | Lượt xem: 3 | Lượt tải: 0

  • Toán học - Chapter 10: GraphsToán học - Chapter 10: Graphs

    When we build a graph model, we use the appropriate type of graph to capture the important features of the application. We illustrate this process using graph models of different types of computer networks. In all these graph models, the vertices represent data centers and the edges represent communication links. To model a computer network whe...

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  • Toán học - Chapter 9: RelationsToán học - Chapter 9: Relations

    Definition: R is symmetric iff (b,a) ∊ R whenever (a,b) ∊ R for all a,b ∊ A. Written symbolically, R is symmetric if and only if ∀x∀y [(x,y) ∊R ⟶ (y,x) ∊ R] Example: The following relations on the integers are symmetric: R3 = {(a,b) | a = b or a = −b}, R4 = {(a,b) | a = b}, R6 = {(a,b) | a + b ≤ 3}. The following are not symmetric: R1 = {...

    pptx52 trang | Chia sẻ: huyhoang44 | Ngày: 19/03/2020 | Lượt xem: 4 | Lượt tải: 0

  • Toán học - Chapter 8: Advanced counting techniquesToán học - Chapter 8: Advanced counting techniques

    Example: A young pair of rabbits (one of each gender) is placed on an island. A pair of rabbits does not breed until they are 2 months old. After they are 2 months old, each pair of rabbits produces another pair each month. Find a recurrence relation for the number of pairs of rabbits on the island after n months, assuming that rabbits never die. ...

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  • Toán học - Chapter 7: Discrete probabilityToán học - Chapter 7: Discrete probability

    Example: In a lottery, a player wins a large prize when they pick four digits that match, in correct order, four digits selected by a random mechanical process. What is the probability that a player wins the prize? Solution: By the product rule there are 104 = 10,000 ways to pick four digits. Since there is only 1 way to pick the correct digit...

    pptx74 trang | Chia sẻ: huyhoang44 | Ngày: 19/03/2020 | Lượt xem: 3 | Lượt tải: 0

  • Toán học - Chapter 6: CountingToán học - Chapter 6: Counting

    Example: How many different license plates can be made if each plate contains a sequence of three uppercase English letters followed by three digits? Solution: By the product rule, there are 26 ∙ 26 ∙ 26 ∙ 10 ∙ 10 ∙ 10 = 17,576,000 different possible license plates.

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  • Toán học - Chapter 5: Induction and recursionToán học - Chapter 5: Induction and recursion

    Example: Use mathematical induction to prove that n < 2n for all positive integers n. Solution: Let P(n) be the proposition that n < 2n. BASIS STEP: P(1) is true since 1 < 21 = 2. INDUCTIVE STEP: Assume P(k) holds, i.e., k < 2k, for an arbitrary positive integer k. Must show that P(k + 1) holds. Since by the inductive hypothesis, k < 2k, it f...

    pptx74 trang | Chia sẻ: huyhoang44 | Ngày: 19/03/2020 | Lượt xem: 4 | Lượt tải: 0