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2020　Introduction to Analysis III

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Academic unit or major
Undergraduate major in Mathematics
Instructor(s)
Kagei Yoshiyuki  Miura Tatsuya 
Class Format
Lecture / Exercise    (ZOOM)
Media-enhanced courses
Day/Period(Room No.)
Mon3-8(H103)  
Group
-
Course number
MTH.C203
Credits
2
Academic year
2020
Offered quarter
3Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

In this course we will teach "vector calculus", that is a calculus for scalar fields (single-valued functions) and vector fields (multivalued functions) . Each lecture will be followed by a recitation (a problem-solving session). This course will be succeeded by "Introduction to Analysis IV" in the fourth quarter.

The students will learn basic operations of vector fields, such as "divergence" or "rotation". They will also learn "Green's theorem", which is a multivariable analogue of "the fundamental theorem of calculus".

Student learning outcomes

At the end of this course, students are expected to:
-- be able to calculate inner and outer products
-- be able to calculate line integrals of vector fields along curves
-- be familiar with parametrization of curves and surfaces
-- understand the meaning of gradient, divergence, and rotation, and be able to calculate them
-- understand what Green's theorem means and know how to use it

Keywords

Outer product, vector fields, line integral, gradient, divergence, rotation, Green's theorem on the plane

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

This is a standard lecture course with recitation sessions. Homework will be assigned every week. There will be occasional quizzes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Outer product of vectors and derivatives of multivalued functions Details will be provided in class.
Class 2 Recitation Details will be provided in class.
Class 3 Curves and surfaces in the space Details will be provided in class.
Class 4 Recitation Details will be provided in class.
Class 5 scalar fields and gradient vectors Details will be provided in class.
Class 6 Recitation Details will be provided in class.
Class 7 Line integrals of vector fields Details will be provided in class.
Class 8 Recitation Details will be provided in class.
Class 9 Green's theorem and its application Details will be provided in class.
Class 10 Recitation Details will be provided in class.
Class 11 Divergence and rotation of vector fields Details will be provided in class.
Class 12 Recitation Details will be provided in class.
Class 13 Surface integrals and divergence theorem Details will be provided in class.
Class 14 Recitation Details will be provided in class.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

None required

Reference books, course materials, etc.

None required

Assessment criteria and methods

Based on the final exam, quizzes, and the problem solving situation in the recitation sessions. Details will be provided in the class.

Related courses

  • MTH.C201 ： Introduction to Analysis I
  • MTH.C202 ： Introduction to Analysis II
  • MTH.C204 ： Introduction to Analysis IV

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are expected to have passed
-- Calculus (I/II), Linear Algebra (I/II), and their recitations.
-- Introduction to Analysis I/II.

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