Spring 2023 MATH 2121
Advanced Calculus 2 高等微積分(二)

Syllabus 課程大綱

宣導事項

教學進度

  • 2/13/2023(星期一): Course introduction, Darboux-Stieltjes integration.
  • 2/15/2023(星期三): Equivalences of Darboux and Riemann integrations, other properties.
  • 2/20/2023(星期一): Fundamental Theorem of Calculus, change of variables and related formula.
  • 2/22/2023(星期三): Integrals and sequences of functions, integrals depending on parameters.
  • 3/1/2023(星期三): Introduction to improper integrals.
  • 3/6/2023(星期一): Improper integrals and various convergence tests.
  • 3/8/2023(星期三): Functions defined by improper integrals.
  • 3/13/2023(星期一): Uniform convergence and improper integrals, gamma function.
  • 3/15/2023(星期三): More on gamma functions, more uniform convergence and improper integrals.
  • 3/20/2023(星期一): Finish uniform convergence and improper integrals, introduction to infinite series.
  • 3/22/2023(星期三): Infinite series and tests for absolute convergence.
  • 3/27/2023(星期一): Integral tests.
  • 3/29/2023(星期三): Midterm 1.
  • 4/3/2023(星期一): No class (spring break).
  • 4/5/2023(星期三): No class (spring break).
  • 4/10/2023(星期一): Dirichlet and abel's tests on infinite series, alternating series.
  • 4/12/2023(星期三): Series of functions, Dirichlet/abel's tests on series of functions.
  • 4/17/2023(星期一): Power series, radius and interval of convergences.
  • 4/19/2023(星期三): Finish power series, introduction to Fourier series.
  • 4/24/2023(星期一): Basics of Fourier series, convergence of Fourier series.
  • 4/26/2023(星期三): Finish Fourier series.
  • 5/1/2023(星期一): Review of linear algebras, operator norms.
  • 5/3/2023(星期三): More on operator norms, conceptual introduction to differentiations.
  • 5/8/2023(星期一): Introduction to differentiations, basic properties, chain rules.
  • 5/10/2023(星期三): Partial derivatives, directional derivatives, mean value theorem.
  • 5/15/2023(星期一): Higher order derivatives.
  • 5/17/2023(星期三): Equality of mixed partials, Taylor's Theorem.
  • 5/22/2023(星期一): Finish Taylor's Theorem, the contraction principle.
  • 5/24/2023(星期三): Midterm 2.
  • 5/29/2023(星期一): Inverse Function Theorem.
  • 5/31/2023(星期三): Implicit Function Theorem.
  • 6/5/2023(星期一): Rank Theorem and equivalences.
  • 6/7/2023(星期三): Second derivative tests and critical points.

    作業

  • Homework 1 (截止日 2/22/2023):
    Section 30 (pp.235-237): A, D, E, F, J, K, L, O, Q.
  • Homework 2 (截止日 3/8/2023、3/6/2023演習課抽題小考):
    Section 31 (pp. 252-254): B, C, D, F, L, M, N, P.
    Notes: HW1 可與 HW2 一起繳交。
  • Homework 3 (截止日 3/15/2023):
    Section 32 (pp. 266-267): D, F, G, I, J.
    Section 33 (p.280): B, D, E.
  • Homework 4 (截止日 3/22/2023):
    Section 33: I, L, M, N.
    Section 34: C, D, E.
  • Homework 5 (截止日 3/29/2023，3/27/2023 演習課抽題小考):
    Seciton 35 (pp. 302-303): A, C, G, I, N, Q.
  • Homework 6 (截止日 4/19/2023, 4/17/2023 演習課抽題小考):
    Section 36 (p. 314) C, D, E, H.
    Section 37 (pp. 326-327): A, B, C.
  • Homework 7 (截止日 4/26/2023):
    Section 37 (p. 327): F, H, K, N.
    Section 38 (pp. 340): A, B, C.
  • Homework 8 (截止日 5/3/2023， 5/1/2023 演習課抽題小考):
    Section 38: E, G, H, N.
    Complete the proof of Theorem 30 mentioned in class.
  • Homework 9 (截止日 5/12/2023 in mailbox by 17:00):
    Download Here
  • Homework 10 (截止日 5/19/2023 in mailbox by 17:00):
    Section 39: B, D, H, N, T.
    Section 40: A, E, J, K, M, U, X, Y.
  • Homework 11 (截止日 6/7/2023 in class, 6/5/2023 演習課抽題小考):
    Download Here

    分組資訊

    考試相關

    講義