Mathematical Analysis Ⅰ

Course Information

College	Toyama College	Year	2022
Course Title	Mathematical Analysis Ⅰ
Course Code	0041	Course Category	General / Elective
Class Format	Lecture	Credits	School Credit: 2
Department	Department of Mechanical Engineering	Student Grade	3rd
Term	First Semester	Classes per Week	4
Textbook and/or Teaching Materials
Instructor	Yamamoto Hisashi

Course Objectives

1. Having a calculation skill of approximate expression using the higher order derivatives, Taylor expansion, Maclaurin expansion and series expansion.
2. Having a calculation skill of approximate expression using the higher order derivatives to multivariable function, maximum and minimum, derivative of implicit function, Tangent line and tangent plane, extreme value under the particular condition, envelope line.

Rubric

	Ideal Level of Achievement	Standard Level of Achievement	Unacceptable Level of Achievement)
Evaluation 1	Clearly understanding for calculation about approximate expression using the higher order derivatives, Taylor expansion, Maclaurin expansion and series expansion.	Somewhat clear understanding of calculations for approximate expressions using the higher order derivatives, Taylor expansion, Maclaurin expansion and series expansion.	Not understanding for calculation about approximate expression using the higher order derivatives, Taylor expansion, Maclaurin expansion and series expansion.
Evaluation 2	Clearly understanding for calculation about approximate expression using the higher order derivatives to multivariable function, maximum and minimum, derivative of implicit function, Tangent line and tangent plane, extreme value under the particular condition and envelope line.	Somewhat clear understanding of calculations for approximate expressions using the higher order derivatives to multivariable function, maximum and minimum, derivative of implicit function, Tangent line and tangent plane, extreme value under the particular condition and envelope line.	Not understanding for calculation about approximate expression using the higher order derivatives to multivariable function, maximum and minimum, derivative of implicit function, Tangent line and tangent plane, extreme value under the particular condition and envelope line.

Assigned Department Objectives

Diploma policy 3 （豊かな教養と倫理観を身につけ，社会に貢献できる。）

Teaching Method

Outline:

Understanding approximate expressions using the higher order derivatives, series expansion, partial differential function and more.

Style:

Lecture

Notice:

The class schedule will be changed based on student conditions and more.

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Approximate expressions using the higher order derivatives	understanding about approximate expression
		2nd	Extreme value of sequence and series expansion	understanding about extreme value of sequence and series expansion
		3rd	Power series and Maclaurin expansion Pt. I	understanding about power series, Maclaurin expansion and expansion
		4th	Power series and Maclaurin expansion Pt. II	understanding about power series, Maclaurin expansion and expansion
		5th	Euler's formula	understanding about Euler's formula
		6th	Exercise
		7th	Multivariable functions	understanding about multivariable function
		8th	Mid term examination
	2nd Quarter
		9th	Partial differential function Pt. I	understanding about partial differential function Pt. I
		10th	Partial differential function Pt. II	understanding about partial differential function Pt. II
		11th	Partial differential function Pt. III	understanding about partial differential function Pt. III
		12th	Application of partial differential function Pt. I	understanding about application of partial differential function Pt. I
		13th	Application of partial differential function Pt. II	understanding about application of partial differential function Pt. II
		14th	Application of partial differential function Pt. III	understanding about application of partial differential function Pt. III
		15th	Final examination
		16th	Conclusion

Evaluation Method and Weight (%)

	Mid-Examination	homework Pt. 1	Final-Examination	homework Pt. 2	Total
Subtotal	160	40	160	40	400
Basic Ability	80	20	80	20	200
Technical Ability	80	20	80	20	200