Calculus 1
| Lecturer | Serge RICHARD, Professor |
|---|---|
| Department | G30, 2024 Fall |
| Recommended for: | Hu(J)･La(S)･Ec(S)･Sc(P･C･B)･En(C･Au)･Ag(B) 1st year (2.0・1.5 hours / session One session / week 15 weeks / semester) |
Goals of the Course
【Standardized across all programs】 The field of mathematics that describes and analyzes quantitative changes is analysis, and its central method is calculus. It is an essential research method in the natural sciences, but in recent years it has been widely applied to the social sciences. The goal of this course is to understand the basics of one-variable differentiation and integration as the first half of the year-round lecture. In particular, it is important to understand the essence of the limit and to be able to handle elementary functions such as logarithmic functions and trigonometric functions freely.
Objectives of the Course
The aim of the first half of this one-year course is to provide a solid understanding of functions of one real variable. The students will become familiar with the various tools necessary for the analysis of such functions and for their applications.
Course Prerequisites
Some basic knowledge on calculus from high school is assumed, including differentiation and integration of polynomial functions.
Course Contents/Plan
- Limits and continuity: Basic properties of limits of sequences and functions, continuous functions and their basic properties, maxima and minima, asymptotic properties of functions.
- Differentiation: Basic properties of the derivative and its interpretation, mean value theorem, higher derivatives, Taylor series.
- Integration: Riemann integral and its properties, improper integrals, the fundamental theorem of calculus.
Course Evaluation Methods
The final grade will be determined by quizzes (30%), the midterm (30%) and a final exam (40%). The grading scale will be A+, A, B, C, C-, F. This course uses the course withdrawal system. It is necessary to submit a Course Withdrawal Request Form when the student has no intention of finishing the course during the semester.
Notice for Students
Students are expected to read their notes, and to be familiar with the content of the previous lecture of Calculus I before attending the next lecture.
Textbook
Free reference books and lecture notes are available on the website of the course
Reference Book
Free reference books and lecture notes are available on the website of the course
https://www.math.nagoya-u.ac.jp/~richard/teaching/f2024/Calculus_I.pdf
Last updated
January 24, 2025