Spring 2018 MATH 2121
Advanced Calculus 2 高等微積分(二)

Syllabus 課程大綱

宣導事項

教學進度

  • 2/26/2018(星期一): Greetings, definition of normed vector spaces, operator norms.
  • 2/28/2018(星期三): 二二八紀念日放假.
  • 3/5/2018(星期一): more properties on operator norms, some topologies on linear maps.
  • 3/7/2018(星期三): Introduction to multi-variable differentiation, basic properties and chain rules.
  • 3/12/2018(星期一): directional derivative, gradient, and mean value theorem.
  • 3/14/2018(星期三): differentiability and partial derivatives.
  • 3/19/2018(星期一): inverse function theorem.
  • 3/21/2018(星期三): proof of inverse function theorem.
  • 3/26/2018(星期一): implicit function theorem.
  • 3/28/2018(星期三): More on implicit function theorem.
  • 4/2/2018, 4/4/2018 (星期一、三): Spring break - no class.
  • 4/9/2018(星期一): The rank theorem.
  • 4/11/2018(星期三): Differentiation under integrations.
  • 4/16/2018(星期一): Taylor's Theorem for functions of several variables.
  • 4/18/2018(星期三): Midterm 1.
  • 4/23/2018(星期一): Itereated integrals.
  • 4/25/2018(星期三): Preparatory knowledge for formula for change of variables.
  • 4/30/2018(星期一): Proof of change of variable formula (unoriented version).
  • 5/2/2018(星期三): Introduction to differential forms.
  • 5/7/2018(星期一): Elementary properties of differential forms, wedge product, exterior differentiations.
  • 5/9/2018(星期三): pullbacks, introductory knowledge for change of variable formula (oriendted version).
  • 5/14/2018(星期一): Change of Variable Formula.
  • 5/16/2018(星期三): Introduction to simplices.
  • 5/21/2018(星期一): Simplicies, chains, and boundaries.
  • 5/23/2018(星期三): Differentiable boundaries, triangulation.
  • 5/28/2018(星期一): Stoke's Theorem
  • 5/30/2018(星期三): Consequences of Stoke's Theorem, closed and exact forms.
  • 6/4/2018(星期一): More on closes and exact forms.
  • 6/6/2018(星期三): Vector anaylsis in R^3: curl/divergence of vector fields.
  • 6/11/2018(星期一): Stoke's Theorem in R^3.
  • 6/13/2018(星期三): Midterm 2.
  • 6/18/2018(星期一): No Class 端午節.
  • 6/20/2018(星期三): Explainatino of area form, discuss midterm 2.

    作業

    若無另行宣布，第n組負責報告第n題。
  • Homework 0 (所有人皆須繳交，截止日3/5/2018):
    Download here
  • Homework 1 (所有人皆須繳交，截止日3/7/2018):
    Download here Solutions
  • Homework 2 (分組繳交，截止日3/14/2018):
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  • Homework 3 (分組繳交，截止日3/21/2018，報告日3/19/2018):
    Download here 報告截影 Solutions
    欲參與報告之組別，請於星期五3/16/2018前登記
  • Homework 4 (分組繳交，截止日3/28/2018):
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  • Homework 5 (分組繳交，截止日4/11/2018，報告日4/9/2018):
    Download here 欲參與報告之組別，請於星期五3/30/2018前登記 Solutions
  • Homework 6 (分組繳交，截止日4/18/2018):
    Download here Solution for Problem 2
  • Homework 7 (分組繳交，截止日5/2/2018，報告日4/30/2018):
    Download here 欲參與報告之組別，請於星期五4/27/2018前登記
    Solutions 報告截影
  • Homework 8 (分組繳交，截止日5/9/2018):
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  • Homework 9 (分組繳交，截止日5/16/2018):
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  • Homework 10 (分組繳交，截止日5/23/2018，報告日5/21/2018):
    Download here 欲參與報告之組別，請於星期五5/18/2018前登記 Solutions 報告截影
  • Homework 11 (分組繳交，截止日5/30/2018):
    Download here Solutions
  • Homework 12 (分組繳交，截止日6/4/2018，報告日6/6/2018):
    Download here 欲參與報告之組別，請於星期五5/18/2018前登記 報告截影 Solutions
  • Homework 13 (分組繳交，截止日6/20/2018 請注意6/13前有可能會再追加，請留意動態):
    Download here 請踴躍填寫 教學評量

    分組資訊

    本學期分組資訊
    Homework 3 報名結果
    Homework 5 報名結果
    Group Work 1
    Group Work 2
    Group Work 3

    考試相關

    Exam 1 Info
    Exam 1 Room
    Exam 2 Info
    Exam 2 Room
    Final Exam Info
    Final Exam Room

    講義

  • A constructive illustration for the proof inverse function theorem.