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2024　Applied Calculus

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Instructor(s)
Arai Zin  Nishibata Shinya  Umehara Masaaki  Murofushi Toshiaki  Suzuki Sakie  Tsuchioka Shunsuke 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(M-B43(H106))  Fri3-4(M-B43(H106))  
Group
-
Course number
MCS.T211
Credits
2
Academic year
2024
Offered quarter
2Q
Syllabus updated
2024/3/14
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

We first review the basic concepts in calculus using rigorous arguments such as the epsilon-delta method. Then, we study the basic treatment of series and sequences of functions. The latter part of the lecture covers advanced topics such as differential equations, curves, surfaces, and the fundamentals of vector analysis.

Student learning outcomes

This lecture aims to clearly understand concepts such as limits and continuity through rigorous epsilon-delta arguments. The lecture also aims to cultivate analytical thinking and computational skills for applying mathematics to real-world problems by studying differential equations and vector analysis.

Keywords

epsilon-delta method, termwise integration, differential equations, vector analysis, integral theorems

Competencies that will be developed

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

Class flow

The lectures provide the fundamentals of calculus.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Epsilon delta definition of convergence Understand the contents covered by the lecture.
Class 2 Continuity of real number Understand the contents covered by the lecture.
Class 3 Continuity of function Understand the contents covered by the lecture.
Class 4 Uniform continuity of function Understand the contents covered by the lecture.
Class 5 Convergence of series Understand the contents covered by the lecture.
Class 6 Convergence of function series Understand the contents covered by the lecture.
Class 7 Differentiation and integration of function series Understand the contents covered by the lecture.
Class 8 General solution and particular solution of differential equation Understand the contents covered by the lecture.
Class 9 Separation of variables type equation Understand the contents covered by the lecture.
Class 10 First order linear differential equation Understand the contents covered by the lecture.
Class 11 Second-order linear differential equation Understand the contents covered by the lecture.
Class 12 Curves Understand the contents covered by the lecture.
Class 13 Surfaces Understand the contents covered by the lecture.
Class 14 Line integral and surface integral Understand the contents covered by the lecture.
Class 15 Integral theorem Understand the contents covered by the lecture.

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 afterward (including assignments) for each class.

Textbook(s)

Undecided.

Reference books, course materials, etc.

Not specified in particular.

Assessment criteria and methods

By scores of examinations and reports.

Related courses

  • LAS.M101 ： Calculus I / Recitation

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

None.

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