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 | |
---|---|---|
Class 1 | Mapping and function, exponential function, logarithmic function, trigonometric function | Understand mappings and functions. |
Class 2 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 3 | Hyperbolic function, inverse trigonometric function | Understand various functions. |
Class 4 | Differentiation and integration of elementary functions, indefinite integrals of rational functions | Understand differentiation and integration of elementary functions. |
Class 5 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 6 | Definite integral, improper integral | Understand definite integral and improper integral. |
Class 7 | Multivariate function, limit, continuity | Understand multivariate functions. |
Class 8 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 9 | Partial differentiation, partial derivative | Understand partial differentiation. |
Class 10 | Higher order derivatives, order of partial differentiation | Understand higher-order partial differentiation. |
Class 11 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 12 | Partial derivative of composite functions (chain rule) | Understand partial differentiation of composition functions. |
Class 13 | Integration of multivariate functions | Understand multiple integrals. |
Class 14 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 15 | Multiple integral and repeated integral | Understand multiple integrals and repeated integrals. |
Class 16 | Changing the order of integration | Understand changing the order of integration. |
Class 17 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 18 | Transformation of variables | Understand transformation of variables. |
Class 19 | Examples of coordinate transformation | Understand coordinate transformation. |
Class 20 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
Class 21 | Applications of multiple integrals (area, volume, etc.) | Understand various applications of multiple integrals. |
Class 22 | Advanced topics | Understand advanced topics in Calculus. |
Class 23 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
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Introductory calculus・Toshiaki Miyake・baifukan
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.