We will conduct online teaching for this course in Fall 2020.
This is an introductory course on calculus followed by Calculus II and Calculus III. You will study the basics of derivatives and integrals through tangent lines and areas of regions as well as the basic connection between derivatives and integrals through the fundamental theorem of calculus. You will also learn how to compute derivatives and integrals of various functions such as polynomials, trigonometric functions, exponentials and logarithms as well as the chain rule, the substitution rule, and integration by parts while how to use differentiation to compute maximum and minimum values of a function, and to investigate the shape of the graph of a function. People with enough background and understanding of the mathematics at the IB higher level do not need to take this course.
This is an introductory course on calculus followed by Calculus II and Calculus III. You will study the basics of derivatives and integrals through tangent lines and areas of regions as well as the basic connection between derivatives and integrals through the fundamental theorem of calculus. You will also learn how to compute derivatives and integrals of various functions such as polynomials, trigonometric functions, exponentials and logarithms as well as the chain rule, the substitution rule, and integration by parts while how to use differentiation to compute maximum and minimum values of a function, and to investigate the shape of the graph of a function. People with enough background and understanding of the mathematics at the IB higher level do not need to take this course.
Together with Calculus II, 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 understand the notions of continuity and differentiability of a function and can check if concrete functions are continuous / differentiable or not with clear reasoning. |
A-1
|
| 2. | The students can compute limits and derivatives of basic functions using the product & quotient rules, and the chain rule. |
A-1
|
| 3. | The students can use the theory of derivatives to compute maximum and minimum values and to describe the shape of concrete functions. |
A-1
|
| 4. | The students understand the notions of definite & indefinite integrals as well as the connection between derivatives and integrals, and can compute the integrals of basic functions. |
A-1
|
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Trigonometric functions Exponential functions Inverse functions and logarithms |
Review the content of the lecture (Chapter 1 in the textbook) | 180分 |
| Work on homework problems | 200分 | ||
| 2. | The limit of a function Calculating limits |
Review the content of the lecture (2.1-2.3 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 3. | Continuity Derivatives and rates of changes |
Review the content of the lecture (2.5-2.7 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 4. | The Derivative as a function Derivatives of polynomials and exponential functions The product and quotient rules |
Review the content of the lecture (2.8, 3.1-3.2 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 5. | Derivatives of the trigonometric functions The chain rule Implicit differentiation |
Review the content of the lecture (3.3-3.5 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 6. | Derivatives of logarithmic functions Linear approximation |
Review the content of the lecture (3.6-3.10 in the textbook) | 160分 |
| Work on homework problems | 220分 | ||
| 7. | Mid-term presentation and discussion on the solutions afterwards | Preparation for presentations | 380分 |
| 8. | Maximum and minimum values The mean value theorem Derivatives and the shape of a graph |
Review the content of the lecture (4.1-4.3 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 9. | Indeterminate forms and L’Hospital’s rule Summary of curve sketching |
Review the content of the lecture (4.3-4.5 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 10. | Optimization problems Antiderivatives |
Review the content of the lecture (4.7 and 4.9 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 11. | Areas and distances The definite integral |
Review the content of the lecture (5.1-5.2 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 12. | The fundamental theorem of calculus | Review the content of the lecture (5.3 in the textbook) | 100分 |
| Work on homework problems | 260分 | ||
| 13. | Indefinite integrals and the net change theorem The substitution rule |
Review the content of the lecture (5.4-5.5 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 14. | Final presentation and discussion on the solutions afterwards | Preparation for presentations | 380分 |
| Total. | - | - | 5300分 |
| Homework | Presentations | Total. | |
|---|---|---|---|
| 1. | 14% | 6% | 20% |
| 2. | 21% | 9% | 30% |
| 3. | 21% | 9% | 30% |
| 4. | 14% | 6% | 20% |
| Total. | 70% | 30% | - |
Homework will contribute 70% of your grade.
Presentations will contribute 30% of your grade.
Those who get at least 60% of the full score will pass this course.
Presentations will contribute 30% of your grade.
Those who get at least 60% of the full score will pass this course.
Calculus: Early Transcendentals (8th edition) by James Stewart
ISBN: 978-1285741550
ISBN: 978-1285741550
Content of the syllabus of the course "Pre-calculus". In particular, the topics such as Quadratic Equations and Complex Numbers,
Functions and Graphs, Sequences and Series, Exponentials and Logarithms, Binomials, The Unit Circle and Radian Measure, Trigonometry,
Vectors in 2 and 3 Dimensions.
- 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 applicatable |
|---|---|
| N/A | N/A |
Last modified : Tue Sep 01 04:14:34 JST 2020