Course Objectives
Students can understand the position of Taylor's theorem in calculus.
Students can understand how to find the maximum and minimum values on a compact set of two-variable functions.
Rubric
| Ideal Level of Achievement | Standard Level of Achievement | Unacceptable Level of Achievement) |
Evaluation 1 | Students can use Taylor's theorem for problems with function behavior | Students can find Taylor's expanssion of certain functions | Students can't find Taylor's expanssion of certain functions |
Evaluation 2 | Students can understand implicit function theorems and solve conditional extrema problems. | Students can understand implicit function theorems. | Students can't understand implicit function theorems. |
Evaluation 3 | Students can find the maximum and minimum values of the function on a bounded closed set of planes | Students can find the maximum and minimum values of the function on the boundary of the bounded closed set of planes | Students can't find the maximum and minimum values of the function on the boundary of the bounded closed set of planes |
Assigned Department Objectives
Teaching Method
Outline:
We first review the limits of the function.
We explain the concepts of the mean value theorem, Taylor's theorem, and Macrolin's theorem.
Next, I will explain the implicit function theorem of two-variable functions, and deal with how to find the maximum and minimum values of functions on a bounded closed set of planes as its application.
Style:
Lectures and exercises by the teacher alone
Notice:
Those who do not have a score of 60 can take the certification test upon request.
Course Plan
|
|
|
Theme |
Goals |
1st Semester |
1st Quarter |
1st |
Guidance |
We explain the outline and evaluation method of this lecture
|
2nd |
Various limits |
Student can find various limit values.
|
3rd |
Continuties and differentiability of certain functions |
Students can identify if they are cuntinuous functions.
|
4th |
Mean value theorem, Taylor Maclaurin theorem |
Students can understand the concept of Taylor Maclaurin theorem
|
5th |
Taylor Maclaurin theorem |
Students can find Talylar Maclaurin expansions for certain functions.
|
6th |
Leibniz's formula |
Students can apply Leibniz's formula to certain problems.
|
7th |
Leibniz's formula |
Students can apply Leibniz's formula to certain problems.
|
8th |
Intermediate examination
|
We do the test to confirm the students' level of understanding.
|
2nd Quarter |
9th |
Fundamental theorem of culculus |
Students can apply the basic formula of calculus to certain problems
|
10th |
Fundamental theorem of culculus |
Students can apply the basic formula of calculus to certain problems
|
11th |
Application of composite derivative of two-variable function |
Students can apply composite derivative of two-variable function to certain problems.
|
12th |
Maximum and minimum of 2-variable function |
Students can find Extreme value of a 2-variable function.
|
13th |
Maximum and minimum of 2-variable function |
Students can find Conditional extrema value.
|
14th |
Maximum and minimum of 2-variable function |
Students can find maximum value and minimum value on compact sets.
|
15th |
Final exam |
We do the test to confirm the students' level of understanding.
|
16th |
Explanation of final exam |
I will explain the items that are considered to be poorly understood by students in the final exam.
|
Evaluation Method and Weight (%)
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | Total |
Subtotal | 70 | 0 | 0 | 0 | 0 | 30 | 100 |
Basic Ability | 50 | 0 | 0 | 0 | 0 | 20 | 70 |
Technical Ability | 20 | 0 | 0 | 0 | 0 | 10 | 30 |
Interdisciplinary Ability | 0 | 0 | 0 | 0 | 0 | 0 | 0 |