Calculus Ⅰ

Course Information

College	Toyama College	Year	2022
Course Title	Calculus Ⅰ
Course Code	0026	Course Category	General / Elective
Class Format	Lecture	Credits	School Credit: 2
Department	Department of Mechanical Engineering	Student Grade	2nd
Term	First Semester	Classes per Week	4
Textbook and/or Teaching Materials	"Shin Bibun Sekibun I Kaitei-ban (Differential and Integral I)" / "Shin Bibun Sekibun I mondai-shu Kaitei-ban(exercise book)", written by S. Takato et al., published by Dai-nippon Tosho (in Japanese)
Instructor	Kato Masaki

Course Objectives

At the completion of this course, students will be able to calculate
1) the derivative of a given function,
2) the maximal/minimal value and the maximum/minimum value of a given function,
3) the derivative (differential) of a function given in parametric form,
4) the velocity and the acceleration by using derivatives.

Rubric

	Ideal Level	Standard Level	Unacceptable Level
Evaluation 1	Can calculate the derivative of a complicated function.	Can calculate the derivative of a standard function.	Can't calculate the derivative of a function.
Evaluation 2	Can calculate the maximal/minimal value and the maximum/minimum value of a complicated function.	Can calculate the maximal/minimal value and the maximum/minimum value of a standard function	Can't calculate the maximal/minimal value nor the maximum/minimum value of a function.
Evaluation 3	Can calculate the derivative of various functions given in parametric form.	Can calculate the derivative of a simple function given in parametric form.	Can't calculate the derivative of a function given in parametric form.
Evaluation 4	Can calculate the velocity and the acceleration by using derivatives.	Can calculate the velocity or the acceleration by using derivatives.	Can't calculate the velocity nor the acceleration by using derivatives.

Assigned Department Objectives

Diploma policy 3 See

Teaching Method

Outline:

Calculus is necessary not only for mathematics but also for science and engineering.
Based on the first grade mathematics, students on the second grade will learn calculus in one variable for a year.
In this course (the first semester), students will learn about differential (derivative) and its application.

Style:

In advance, students should review the first grade mathematics.
It is recommended to prepare what you will learn in the next class hour.
Lecture and exercise are carried out in each class hour.
It is necessary to review early and repeatedly what you have learned.
Keep deadlines for homework and other submissions.

Notice:

Mini-exams will be carried out up to several times.
Evaluations will be made comprehensively by written exams (making up about 70% of the grade), by exercises and homework (making up about 30% 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	Instructor Professionally Experienced

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Properties of functions Limit of functions	Can calculate limit of functions by using properties of them.
		2nd	Diffential coefficients Derivatives	Can calculate diffential coefficients and derivatives of functions.
		3rd	Properties of differential Derivatives of trigonometric functions	Can calculate derivatives of power functions. Can use product rule and quotient rule of differential.
		4th	Derivatives of trigonometric functions Derivatives of exponential functions	Can calculate derivatives of trigonometric functions and exponential functions.
		5th	Chain rule of differential Derivatives of logarithmic functions	Can use chain rule of differential. Can calculate derivatives of logarithmic functions.
		6th	Inverse trigonometric functions and their derivatives	Can understand inverse trigonometric functions and can calculate their derivatives.
		7th	Continuous functions Exercise	Can understand continuous functions.
		8th	Mid-term exam
	2nd Quarter
		9th	Tangent line and normal line Increasing/decreasing function	Can calculate equations of tangent line and normal line. Can use first derivative test for a function.
		10th	Maximal and minimal value Maximum and minimum value	Can draw the graph of a given function by first derivative test. Can calculate maximal, minimal, maximum, minimum values.
		11th	Maximum and minimum value Indeterminate forms	Can calculate maximum and minimum values. Can caluculate limit of indeterminate forms.
		12th	Indeterminate forms Higher derivatives	Can caluculate limit of indeterminate forms. Can calculate higher derivatives of functions.
		13th	Higher derivatives Concavity and convexity	Can calculate higher derivatives of functions. Can determine concavity and convexity of a curve.
		14th	Functions given in parametric form and their derivatives	Can understand functions given in parametric form, and calculate their derivatives.
		15th	Velocity and acceleration Exercise	Can calculate the velocity and the acceleration by using derivatives.
		16th	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 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