| Program / Major | mDP | Goals |
|---|---|---|
| 先進国際課程 | A-1 | A-1 Students shall obtain basic and advanced knowledge and skills in mathematics, natural and computer sciences as well as presentation skills to communicate on their knowledge with scholars from various fields. |
| (改組前)先進国際課程 | A-1 | A-1 Students shall obtain basic and advanced knowledge and skills in mathematics, natural and computer sciences as well as presentation skills to communicate on their knowledge with scholars from various fields. |
Together with Calculus I, you are expected to obtain skills, knowledge, and understandings of basics of one-variable calculus,
which are widely used in science and engineering.
This is a continuation of Calculus I followed by Calculus III. You will learn how to use integration to compute areas of regions,
volumes of solids, and lengths of arcs. Then you will study how to model a real-world problem using differential equations
through many examples as well as how to solve basic 1st-order linear differential equations such as separable equations with
its applications to problems in nature. Lastly, you will learn the basics of infinite series to represent a function using
Taylor and Maclaurin series as well as how to approximate a function using Taylor polynomials.
- The students can compute integrals of various functions using integration by parts, trigonometric integrals, and trigonometric substitution.
- The students can compute areas between curves, volumes of solids, arc length, and area of a surface of revolution using integration.
- The students can solve basic differential equations such as separable equations and linear equations.
- The students can argue to see whether a given infinite series is convergent or not using integral tests, comparison tests, ratio tests, and root tests.
- The students can use Taylor and Maclaurin series to represent a given function and you can use Taylor polynomials to approximate a value of a given function.
| Final exam | Total. | |
|---|---|---|
| 1. | 25% | 25% |
| 2. | 25% | 25% |
| 3. | 25% | 25% |
| 4. | 15% | 15% |
| 5. | 10% | 10% |
| Total. | 100% | - |
Final exam will contribute 100% of your grade.
Those who get at least 60% of the full score will pass this course.
Those who get at least 60% of the full score will pass this course.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Review of integration Areas between curves Volumes |
Review the content of the lecture (5.2-5.5, 6.1-6.3 in the textbook) | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 2. | Integration by parts Trigonometric integrals |
Review the content of the lecture (7.1-7.2 in the textbook) | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 3. | Trigonometric substitution Integration of rational functions |
Review the content of the lecture (7.3-7.4 in the textbook) | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 4. | Strategy for integration Improper integrals |
Review the content of the lecture (7.5, 7.8 in the textbook) | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 5. | Arc length Area of a surface of revolution |
Review the content of the lecture (8.1-8.2 in the textbook) | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 6. | Modeling with differential equations Separable equations Linear equations |
Review the content of the lecture (9.1, 9.3, 9.5 in the textbook) | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 7. | Review | Work on exercises | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 8. | Sequences Series and the integral test |
Review the content of the lecture (11.1-11.3 in the textbook) | 120minutes |
| Preparation before the lecture. | 260minutes | ||
| 9. | Comparison tests Alternating series, absolute convergence, ratio and root tests |
Review the content of the lecture (11.4-11.6 in the textbook) | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 10. | Strategy for testing series Power series, representations of functions as power series |
Review the content of the lecture (11.7-11.9 in the textbook) | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 11. | Taylor and Maclaurin series | Review the content of the lecture (11.10 in the textbook) | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 12. | Applications of Taylor polynomials | Review the content of the lecture (11.11 in the textbook) | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 13. | Review | Work on exercises | 120minutes |
| Preparation before the lecture | 260minutes | ||
| 14. | Final exam and discussions on the solutions afterwards | Preparation for ＆ Review of the final exam | 380minutes |
| Total. | - | - | 5320minutes |
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback in the class |
Calculus: Early Transcendentals, 9th edition, James Stewart. ISBN: 978-1-285-74155-0
Content of the syllabus of the course ”Calculus I”. In particular, the topics such as derivatives of various functions, the
product and quotient rules, the chain rule, areas and distances, definite ＆ indefinite integrals, net change theorem, the
substitution rule, and the fundamental theorem of calculus.
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Sat Mar 14 13:24:51 JST 2026