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 | Continuity of the real numbers, supremum, infimum | Understand basic properties of real numbers. |
Class 2 | Limits of sequences, monotone sequences, Cauchy sequences | Understand basic facts related to sequences. |
Class 3 | Limits of functions of a single variable, continuity, maximum, intermediate value theorem | Understand the properties of continuous functions. |
Class 4 | Differentiation, mean value theorem, limits of indeterminate forms | Understand the properties of differentiable functions. |
Class 5 | Taylor's theorem, extremal values | Understand Taylor's theorem. |
Class 6 | Definite integral | Understand the definition of the definite integral. |
Class 7 | Point sets on a plane, sequences of points | Understand point sets and their properties. |
Class 8 | Limits of multivariate functions, continuity | Understand the limit and continuity of multivariate functions. |
Class 9 | Differentiation of multivariate functions, total derivative and partial derivative | Understand the differentiation of multivariate functions. |
Class 10 | Taylor's theorem for multivariate functions, extremal values | Understand Taylor's theorem and extremal values. |
Class 11 | Series, absolute convergence, conditional convergence | Understand series of numbers and their convergence. |
Class 12 | Sequences of functions | Understand sequences of functions. |
Class 13 | Series of functions, power series | Understand series of functions and, as a special case of them, power series. |
Class 14 | Advanced topics | Understand some advanced topics in analysis. |
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Calculus for Science and Engineering, Nobuyuki Suita and Tsunehiko Sinbo, Gakujutsu tosho shuppansha
None in particular.
Based on overall evaluation on the results of quizzes, reports, mid-term and final examinations. Details will be announced in class.
Students are supposed to have completed Calculus I / Recitation (LAS.M101).
An end-of-term examination will be planned at the lecture room.