Mathematics Ⅲ

Course Information

College	Toyama College	Year	2021
Course Title	Mathematics Ⅲ
Course Code	0093	Course Category	General / Elective
Class Format	Lecture	Credits	School Credit: 2
Department	Department of International Business	Student Grade	3rd
Term	Year-round	Classes per Week	2
Textbook and/or Teaching Materials
Instructor	Kawai Hitoshi,Sakurai Hideto,Nakagawa Yoshihiko

Course Objectives

At the completion of this course, students will be able to
1) understand and carry out fundamental calculations on sequences (e.g. a general term of them, and a sum of them) correctly.
2) understand and carry out fundamental calculations on the derivatives of functions of one real variable correctly.
3) understand and carry out fundamental calculations on the integral calculus of functions of one real variable correctly.

Rubric

	Ideal Level	Standard Level	Unacceptable Level
Achievement 1	Students can ask general terms of given arithmetic progresion, or geometriac progession, and ask partial sum of these	Students can ask general terms of given arithmetic progresion, or geometriac progession	Students can't ask general terms of given arithmetic progresion, or geometriac progession
Achievement 2	Students can ask derivatives of fundamental functions and can applay these to find out increasing or decreasing of graph	Students can ask derivatives of fundamental functions	Students can't ask derivatives of fundamental functions
Achievement 3	Students can calculate indefinite integral by integration by subinstitution and integration by part	Students can calculate indefinite integral of elementary functions	Students can't calculate indefinite integral of elementary functions

Assigned Department Objectives

ディプロマポリシー 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:

In this course, students will learn about basic calculus of functions of one real variable. And, students will make basics calculations of them.

Style:

Lectures and exercises

Notice:

The recognition of credit requires 60 points or more rating.

Characteristics of Class / Division in Learning

Aided by ICT

Applicable to Remote Class

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Guidance Sequence	Students can understand consepts of general term of sequence
		2nd	Arithmetic progressions and their sum	Students can find general terms of arithmetic progression and be sought their sum
		3rd	Geometria progressions and their sum	Students can find general termsof geometric progression and be sought their sum
		4th	Sums of sequences	Students can explain sums of sequence using sinbol "sigma" and can caluclus the sum
		5th	Sums of sequences	Students can explain sums of sequence using sinbol "sigma" and can caluclus the sum
		6th	Recurrence relation	Students can find general terms of given recurrence relations
		7th	Induction	Students can prove propsitions concernde with natural nuber n usiong induction
		8th	Mid-term exam
	2nd Quarter
		9th	Limit of sequences	Students can judge convergence or divergence of sequences
		10th	Sum of series	Students can judge convergence or divergence of series
		11th	Limit of functions	Students can judge various limit of functions
		12th	Continuous functions	Students can judge continuty of functions
		13th	Differencial coefficients and Derivatives	Students can understand the definition of differencial coefficients and derivatives
		14th	Derivatives	Students can find derivatives of various functions by definition
		15th	Final exam
		16th	Propsitions of derivatives	Students can find derivatives of various functions
2nd Semester
	3rd Quarter
		1st	Derivative	Students can find derivatives of various functions
		2nd	Derivative	Students can find derivatives of various functions
		3rd	Derivative	Students can find derivatives of various functions
		4th	Applications of derivatives	Students can find equations of tangents atgiven points
		5th	Applications of derivatives	Students can find maxmal piont and minimal point of given functions
		6th	Applications of derivatives	Students can judge the convexity of given functions
		7th	Mid-exam
		8th	Indefinite integral	Students can find indefinite integral of elementary functions
	4th Quarter
		9th	Integration by substitution Integration by part	Students can find indefinite integral using integration by substitution and integuration by part
		10th	Indefinite integral	Students can find indefinite integral of various functions
		11th	Definite integral	Students can find Idefinite integral of elementary functions
		12th	Integration by substitution Integration by part of definite integral	Students can find Idefinite integral of various functions
		13th	Applications of definite integral	Students can find area of figures determined graph of functions
		14th	Applications of definite integral	Students can find volume of figures determined graph of functions
		15th	Final exam
		16th	Applications of definite integral	Students can find limits of certain series by using definite integral

Evaluation Method and Weight (%)

	Examination	Presentation	Mutual Evaluations between students	Behavior	Portfolio	Other	Total
Subtotal	70	0	0	0	0	30	100
Basic Proficiency	70	0	0	0	0	30	100
Specialized Proficiency	0	0	0	0	0	0	0
Cross Area Proficiency	0	0	0	0	0	0	0