Fundamental Mathematics AⅡ

Course Information

College	Toyama College	Year	2024
Course Title	Fundamental Mathematics AⅡ
Course Code	0002	Course Category	General / Compulsory
Class Format	Lecture	Credits	School Credit: 2
Department	Department of Mechanical Engineering	Student Grade	1st
Term	Second Semester	Classes per Week	4
Textbook and/or Teaching Materials	Textbook: "Shin Kiso Sugaku Kaitei-ban(Fundamental Mathematics)" / Exercise book: "Shin Kiso Sugaku Mondai-shu Kaitei-ban", written by S. Takato et al., published by Dai-nippon Tosho (in Japanese)
Instructor	Kasatani Masahiro

Course Objectives

At the completion of this course, students will be able to
1) Understand the properties of quadratic functions, draw graphs, and find the maximum and minimum values.
2) Understand the relationship between graphs of quadratic function, discriminants and quadratic equations, and solve quadratic inequalities.
3) Understand basic properties of power functions, fractional functions, irrational functions, and inverse functions and draw graphs.
4) Understand properties of exponential and logarithmic functions and calculate basic numerical values.
5) Understand characteristics of graphs of exponential and logarithmic functions and draw graphs.

Rubric

	Ideal Level of Achievement (Very Good)	Standard Level of Achievement (Good)	Unacceptable Level of Achievement (Fail)
Evaluation 1	Can draw graphs of various quadratic functions, and find the maximum and minimum values.	Can draw graphs of basic quadratic functions, and find the maximum and minimum values.	Can't draw graphs of basic quadratic functions, and find the maximum and minimum values.
Evaluation 2	Can sufficiently understand the relationship between graphs of quadratic functions, discriminants and quadratic equations, and solve various quadratic inequalities.	Can basically understand the relationship between graphs of quadratic functions, discriminants and quadratic equations, and solve basic quadratic inequalities.	Can't understand the relationship between graphs of basic quadratic functions, discriminants and quadratic equations, and solve basic quadratic inequalities.
Evaluation 3	Can sufficiently understand the properties of power functions, fractional functions, irrational functions, and inverse functions, and can draw complicated graphs.	Can basically understand the properties of power functions, fractional functions, irrational functions, and inverse functions, and can draw basic graphs.	Can't understand the properties of power functions, fractional functions, irrational functions, and inverse functions, and can draw basic graphs.
Evaluation 4	Can sufficiently understand the properties of exponential and logarithmic functions, and calculate complicated numerical values.	Can basically understand the properties of exponential and logarithmic functions, and calculate basic numerical values.	Can't understand the properties of exponential and logarithmic functions, and calculate basic numerical values.
Evaluation 5	Can sufficiently understand the characteristics of graphs of exponential and logarithmic functions well and draw complicated graphs.	Can basically understand the characteristics of graphs of exponential and logarithmic functions and draw basic graphs.	Can't understand the characteristics of graphs of exponential and logarithmic functions and draw basic graphs.

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:

In this course, students will learn basic mathematical concepts and mathematical skills (quadratic functions, quadratic equations, quadratic inequalities, power functions, fractional functions, irrational functions, inverse functions, power law and power functions, logarithm and logarithmic functions, etc.).
Exercises are conducted in parallel with lectures to acquire mathematical and computational techniques required in engineering and other subjects.

Style:

The contents of this course will be more advanced, based on Fundamental Mathematics A I. We recommend that students prepare for each lectures.
If there is anything you do not understand in the lectures, please review it immediately and try to understand it. Active questions are always recommended.
It is not enough to understand basic contents once. Please train repeatedly.
The lectures plan may be changed according to the student's level of understanding.

Notice:

Mini-exams will be carried out up to several times.
Evaluations will be made comprehensively by written exams (making up about 80% of the grade), by exercises and homework (making up about 20% of the grade).

Can take makeup exam in need aid up to maximum of 50 points.

Characteristics of Class / Division in Learning

Active Learning

Aided by ICT

Applicable to Remote Class

Course Plan

			Theme	Goals
2nd Semester
	3rd Quarter
		1st	Proposition Proof by contradiction	Can understand and distinguish the necessary conditions and sufficient conditions.
		2nd	Functions and graphs Graphs of quadratic functions	Can understand concept of the functions and graphs on the coordinate plane. Can draw graphs of quadratic functions.
		3rd	Graphs of quadratic functions The maximum and minimum of quadratic functions	Can find the maximum and minimum values of the quadratic functions.
		4th	Quadratic equations Graphs of quadratic functions	Can understand the relationship between quadratic equations, graphs of quadratic functions, and discriminants.
		5th	Quadratic equations Quadratic inequalities.	Can solve quadratic equations and quadratic inequalities.
		6th	Power functions Fractional functions	Can understand power functions and fractional functions and draw graphs of them.
		7th	Irrational functions Inverse functions	Can understand irrational functions and inverse functions and draw graphs of them.
		8th	Mid-term exam Answers and explanations for mid-term exams
	4th Quarter
		9th	Higher roots Power law	Can understand higher roots and power law, and can calculate them
		10th	Exponential functions	Can understand exponential functions and draw graphs of them.
		11th	Applications of exponential functions	Can solve equations and inequalities expressed by exponential functions.
		12th	Logarithm	Can understand the definition of logarithm and can calculate basic logarithmic values using the properties of logarithm.
		13th	Logarithmic functions	Can understand logarithmic functions and draw graphs of them.
		14th	Application of logarithmic functions Common logarithms.	Can solve equations and inequalities expressed by logarithmic functions. Can understand and use common logarithms.
		15th	Final exam
		16th	Answers and explanations for final exams Summary of the 1st grade and advise for spring vacation and the 2nd grade

Evaluation Method and Weight (%)

	Examination	Presentation	Mutual Evaluations between students	Behavior	Portfolio	Other	Total
Subtotal	80	0	0	0	0	20	100
Basic Ability	80	0	0	0	0	20	100
Technical Ability	0	0	0	0	0	0	0
Interdisciplinary Ability	0	0	0	0	0	0	0