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.