After preparations about elementary functions, this course with recitation focuses on the theory and applications of partial differentiation and multiple integrals of multivariate function.
The aim of this lecture is to provide fundamental knowledge about multivariate calculus, which will be a basis of
science and engineering.
The first aim is to understand basic facts which are required for every student in science and engineering. Based on calculus for functions of one variable in high-school level, this course deals with basics and applications of partial differentiation and multiple integrals of multivariate functions.
Multivariate functions, partial differentiation, multiple integral
Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Besides lectures, recitation class is opened every week in accordance with the progress of the lectures.
Course schedule | Required learning | |
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Class 1 | Mapping and function, various functions | Understand mappings and examples of important functions (exponential function, logarithmic function, trigonometric function, hyperbolic function, inverse trigonometric function). |
Class 2 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 3 | Differentiation and integration of elementary functions, indefinite integrals of rational functions | Understand differentiation and integration of elementary functions. |
Class 4 | Definite integral, improper integral | Understand definite integral and improper integral. |
Class 5 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 6 | Multivariate function, limit, continuity | Understand multivariate functions. |
Class 7 | Differentiation of multivariable functions | Understand the differentiation of multivariable functions, in particuar, partial differentiation. |
Class 8 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 9 | Higher-order derivatives, order of partial differentiation | Understand higher-order derivatives, in particular higher-order partial differentiation. |
Class 10 | Derivative of composite functions (chain rule) | Understand differentiation of composition functions. |
Class 11 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 12 | Integration of multivariate functions | Understand multiple integrals. |
Class 13 | Multiple integral and repeated integral | Understand multiple integrals and repeated integrals. |
Class 14 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 15 | Changing the order of integration | Understand changing the order of integration. |
Class 16 | Transformation of variables in integration | Understand transformation of variables in integration. |
Class 17 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 18 | Examples of coordinate transformation | Understand coordinate transformation. |
Class 19 | Applications of multiple integrals (area, volume, etc.) | Understand various applications of multiple integrals. |
Class 20 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 21 | 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.
Introduction to Analysis I・Mitsuo Sugiura・University of Tokyo Press
None in particular
Based on overall evaluation on the results of quizzes, reports, mid-term and final examinations. Details will be announced in class.
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None in particular.