Based on "Calculus I", this course provides recitation for the limit of sequences of numbers and functions, applications of differentiation of functions of a single variable and partial differentiation of multivariate functions, series of numbers and sequences of functions.
The aim of this recitation course is to cultivate a better understanding of analysis which will be important for
science and engineering.
Following "Calculus I", this course aims for a deeper understanding and development of the theory of calculus.
Limit, continuity, Taylor's theorem, series, sequence of functions
Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
A recitation class is held every week in accordance with the progress of the lectures.
Course schedule | Required learning | |
---|---|---|
Class 1 | Limit of a sequence of numbers, supremum, infimum | Help better understand sequences of numbers. |
Class 2 | Point set on a plane, sequence of points, continuity of real numbers, monotone sequence, Cauchy sequence | Help better understand sequences of points. |
Class 3 | Limit of functions of a single variable, continuity, maximum, intermediate-value theorem, limit of multivariate functions, continuity | Help better understand continuous functions. |
Class 4 | Differentiation, Roll's theorem, mean-value theorem, limit of indeterminate forms, l'Hospital's rule | Help better understand differentiation. |
Class 5 | Partial differentiation, partial derivatives, Taylor's theorem for multivariate functions | Help better understand Taylor's theorem. |
Class 6 | Extreme value, definite integral, fundamental theorem of calculus | Help better understand differentiation and integral. |
Class 7 | Series, absolute convergence, conditional convergence, criteria for the convergence of series | Help better understand series of numbers. |
Class 8 | Sequences of functions, series of functions, advanced topics | Help better understand sequences of functions. |
Katsuhiko Mizuno, Analysis-basic course (in Japanese), Gakujyutsutosyo Syuppan
To be announced.
Based on overall evaluation of the results for quizzes, report, mid-term and final examinations. Details will be announced during a lecture.
Students are supposed to have completed Calculus I / Recitation (LAS.M101).
Students must register Calculus II (LAS.M105) at the same time.