Advanced Mathematics Ⅰ

Course Information

College	Toyama College	Year	2023
Course Title	Advanced Mathematics Ⅰ
Course Code	0163	Course Category	General / Elective
Class Format	Lecture	Credits	Academic Credit: 1
Department	Department of Maritime Technology	Student Grade	5th
Term	First Semester	Classes per Week	1
Textbook and/or Teaching Materials
Instructor	Sakurai Hideto

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

MCCコア科目  

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