We will conduct online teaching in Spring 2021.
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 Maclaulin series as well as how to approximate a function using Taylor polynomials.
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 Maclaulin series as well as how to approximate a function using Taylor polynomials.
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.
| Goals and objectives | Course Outcomes | |
|---|---|---|
| 1. | The students can compute integrals of various functions using integration by parts, trigonometric integrals, and trigonometric substitution. |
A-1
|
| 2. | The students can compute areas between curves, volumes of solids, arc length, and area of a surface of revolution using integration. |
A-1
|
| 3. | The students can solve basic differential equations such as separable equations and linear equations. |
A-1
|
| 4. | 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. |
A-1
|
| 5. | The students can use Taylor and Maclaurin series to represent a given function and you can use Taylor polynomials to approxiate a value of a given function. |
A-1
|
| 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) | 180分 |
| Work on homework problems | 200分 | ||
| 2. | Integration by parts Trigonometric integrals |
Review the content of the lecture (7.1-7.2 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 3. | Trigonometric substitution Integration of rational functions |
Review the content of the lecture (7.3-7.4 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 4. | Strategy for integration Improper integrals |
Review the content of the lecture (7.5, 7.8 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 5. | Arc length Area of a surface of revolution |
Review the content of the lecture (8.1-8.2 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 6. | Modeling with differential equations Separable equations |
Review the content of the lecture (9.1, 9.3 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 7. | Mid-term presentation and discussions on the solutions afterwards | Preparation for the mid-term presentation | 380分 |
| 8. | Linear equations Second-order linear equations |
Review the content of the lecture (9.5, 17.1 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 9. | Parametrized curves Polar coordinates, area length in polar coordinates |
Review the content of the lecture (10.1-10.4 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 10. | Sequences Series and the integral test |
Review the content of the lecture (11.1-11.3 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 11. | Comparison tests Alternating series, absolute convergence, ratio and root tests |
Review the content of the lecture (11.4-11.6 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 12. | 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) | 100分 |
| Work on homework problems | 260分 | ||
| 13. | Taylor and Maclaurin series Applications of Taylor polynomials |
Review the content of the lecture (11.10-11.11 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 14. | Final exam and discussions on the solutions afterwards | Preparation for the final exam | 380分 |
| Total. | - | - | 5300分 |
| Homework | Mid-term presentation | Final exam | Total. | |
|---|---|---|---|---|
| 1. | 20% | 4% | 5% | 29% |
| 2. | 15% | 4% | 5% | 24% |
| 3. | 10% | 4% | 3% | 17% |
| 4. | 10% | 3% | 10% | 23% |
| 5. | 7% | 7% | ||
| Total. | 55% | 15% | 30% | - |
Homework and mid-term presentation will contribute 70% of your grade.
Final exam will contribute 30% of your grade.
Those who get at least 60% of the full score will pass this course.
Final exam will contribute 30% of your grade.
Those who get at least 60% of the full score will pass this course.
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.
- By appointment. Contact e-mail address: ikegami@shibaura-it.ac.jp
- 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 : Sun Mar 21 16:23:20 JST 2021