### 2016　Calculus I / Recitation

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Basic science and technology courses
Instructor(s)
Kato Fumiharu    Kitayama Takahiro
Class Format
Lecture / Exercise
Media-enhanced courses
Day/Period(Room No.)
Mon1-2(H121)  Wed3-4(H136)  Fri3-4(H121)
Group
G（41〜47）
Course number
LAS.M101
Credits
2
2016
Offered quarter
1Q
Syllabus updated
2017/1/11
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

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.

### Student learning outcomes

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.

### Keywords

Multivariate functions, partial differentiation, multiple integral

### Competencies that will be developed

 Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

Besides lectures, recitation class is opened every week in accordance with the progress of the lectures.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Mapping and function, exponential, 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, etc. 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 Multivariate function, limit, contnuity Understand multivariate functions.
Class 7 Partial differentiation, partial derivative, extreme value Understand 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 partial differentiation.
Class 10 Partial derivative of composite functions (chain rule) Understand partial differentiation of composition functions.
Class 11 Recitation class is opened in accordance with lectures. Cultivate a better understanding of lectures.
Class 12 Area, volume Understand area and volume.
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 order of integration Understand changing 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 Indefinite integral Understand indefinite integrals.
Class 23 Recitation class is opened in accordance with lectures. Cultivate a better understanding of lectures.

### Textbook(s)

No English textbook

### Reference books, course materials, etc.

None in particular

### Assessment criteria and methods

Based on overall evaluation of the results for quizzes, report, mid-term and final examinations. Details will be announced during a lecture.

### Related courses

• LAS.M105 ： Calculus II
• LAS.M107 ： Calculus Recitation II

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

None in particular

### Other

None in particular.