Based on "Calculus I", this course focuses on more rigorous mathematical analysis of 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 course is to provide knowledge about 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 |
Besides lectures, 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 | Understand sequences of numbers and related notions. |
Class 2 | Point set on a plane, sequence of points | Understand the definition of point set and their properties. |
Class 3 | Continuity of real numbers, monotone sequence, Cauchy sequence | Understand the continuity of real numbers and related notions. |
Class 4 | Limit of functions of a single variable, continuity, maximum, intermediate-value theorem | Understand the properties of continuous functions. |
Class 5 | Limit of multivariate functions, continuity | Understand the limit and continuity of multivariate functions. |
Class 6 | Differentiation, Roll's theorem, mean-value theorem | Understand the properties of differentiable functions. |
Class 7 | Limit of indeterminate forms, l'Hospital's rule | Understand how to find a limit of indeterminate forms. |
Class 8 | Taylor's theorem | Understand Taylor's theorem. |
Class 9 | Partial differentiation, partial derivatives, Taylor's theorem for multivariate functions | Understand the partial differentiation of multivariate functions. |
Class 10 | Extreme value | Understand the properties of extreme values. |
Class 11 | Definite integral, fundamental theorem of calculus | Understand the definition of definite integrals. |
Class 12 | Series, absolute convergence, conditional convergence | Understand series of numbers and convergence. |
Class 13 | Criteria for the convergence of series | Understand criteria for the convergence of series. |
Class 14 | Sequences of functions, series of functions | Understand a sequence and series of functions. |
Class 15 | Advanced topics | Understand advanced topics of analysis. |
"Analysis-basic course (in Japanese)", by Kastuhiko Mizuno published by Gakujyutsutosyo syuppan.
None in particular.
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 are required to complete Calculus Recitation II (LAS.M107) at the same time.
None in particular.