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
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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Besides lectures, a recitation class is held every week in accordance with the progress of the lectures.
Course schedule | Required learning | |
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Class 1 | Limit of a sequence of numbers, supremum, infimum | Understand sequences of numbers and related notions. |
Class 2 | Continuity of real numbers, monotone sequences, Cauchy sequences | Understand the continuity of real numbers and related notions. |
Class 3 | Limits of functions of a single variable, continuity, maximum, intermediate value theorem | Understand the properties of continuous functions. |
Class 4 | Differentiation, Rolle's theorem, mean value theorem | Understand the properties of differentiable functions. |
Class 5 | Limits of indeterminate forms, l'Hospital's rule | Understand how to find limits of indeterminate forms. |
Class 6 | Taylor's theorem, extremal values | Understand Taylor's theorem. |
Class 7 | Definite integral | Understand the definition of the definite integral. |
Class 8 | Point sets on a plane, sequences of points | Understand point sets and their properties. |
Class 9 | Limits of multivariate functions, continuity | Understand the limit and continuity of multivariate functions. |
Class 10 | Partial derivative, total differentiation | Understand the partial differentiation of multivariate functions. |
Class 11 | Taylor's theorem for multivariate functions, extremal values | Understand Taylor's theorem and extremal values. |
Class 12 | Series, absolute convergence, conditional convergence | Understand series of numbers and their convergence. |
Class 13 | Criteria for the convergence of series, power series | Understand criteria for the convergence of series. |
Class 14 | Sequences of functions, series of functions | Understand sequences and series of functions. |
Class 15 | Advanced topics | Understand some advanced topics in analysis. |
Introduction to Calculus in English, Jan Brezina, Eiji Yanagida
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).
Students are required to complete Calculus Recitation II (LAS.M107) at the same time.
None in particular.