Differential and Integral Calculus 1

Course title

G0410200

	suwa masanori
	ohnuki koji
	tanaka hidekazu

Course description

Differential and integral calculus 1 is not only the introduction part of analysis but also the foundation of many mathematical subjects in university. Analysis is a field that is a major pillar of mathematics that describes numerous phenomena appearing in natural science and engineering by mathematical expressions and contributes to elucidating these phenomena. First, with regard to the main function of one variable, we treat the basic matters such as limit, continuity, differentiability, derivative, concept of integration, primitive function, typical integral, simple differential equation, higher order derivatives, Taylor's theorem, Maclaurin's theorem and its application, typical definite integral calculations, improper integration, etc. And these items will continue to appear not only in analytical subjects such as probability and statistics, function theory, differential equation, vector analysis, etc. but also in specialized subjects after the second derivative integral. The existence of such a flow differs from mathematics to high school. Please work hard so as to lead to future learning, such as the method of handling functions, grasping the properties of individual functions, and the shape of graphs.

Note on Course: Mathematics is a stacked-up subject, so please make sure by reviewing the content of each lecture to solve the exercise problem inside and outside the lecture.

Purpose of class

It aims to be able to handle basic ideas and matters of differential and integral calculus of one variable for future work in university.

Goals and objectives

Understand the continuity and differentiability of functions, and apply to specific functions.
Understand the nature of the function (including the inverse trigonometric function and the limit of the indefinite form), and can reliably calculate the derivative of the basic function.
Understand the concept of Taylor's theorem and Maclaurin's theorem. Be able to apply them to specific functions.
Be able to reliably calculate the definite integral (including improper integral) of the basic function.
Able to solve the elementary differential equation.

Language

Japanese

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Limit of function and continuity, hyperbolic function, inverse trigonometric function	Review the limit of function, and the concept of continuity and the trigonometric function	60minutes
1.		Problem exercises in the relevant part	120minutes
2.	Differential coefficient, derivatives	Review the fundamentals of derivative coefficients and derivatives, and the differentiation of synthetic functions, the log differential method and the derivative of the parameterized function	60minutes
2.	Differential coefficient, derivatives	Problem exercises in the relevant part	130minutes
3.	Rolle's theorem, Lagrange's mean value theorem, L'Hospital's Theorem, limit of function in indeterminate form	Review Rolle's theorem, Lagrange's mean value theorem and L'Hospital's Theorem	60minutes
3.		Problem exercises in the relevant part	130minutes
4.	Primitive function and indefinite integrals, integration by substitution, integration by parts, recurrence formula	Review primitive function, indefinite integrals, integration by substitution and integration by parts	60minutes
4.		Problem exercises in the relevant part	130minutes
5.	Integration of rational functions, integration of transcendental functions and integration of irrational functions	Review partial fractions and integration of rational functions, integration of transcendental functions and integration of irrational functions	60minutes
5.		Problem exercises in the relevant part	130minutes
6.	Elementary differential equations	Review the solution technique of elementary differential equations	60minutes
6.	Elementary differential equations	Problem exercises in the relevant part	130minutes
7.	Midterm exam and commentary	Preparation for the midterm exam	190minutes
8.	Higher order derivative of basic functions, Leibniz's theorem	Review Higher order derivative of basic functions and Leibniz's theorem	60minutes
8.		Problem exercises in the relevant part	130minutes
9.	Taylor's theorem and Maclaurin's theorem, Apply these theorems to basic functions	Review Taylor's theorem and Maclaurin's theorem, Apply these theorems to basic functions	60minutes
9.		Problem exercises in the relevant part	130minutes
10.	Taylor's expansion, Maclaurin expansion and approximation and its application to extreme values	Review Taylor's expansion, Maclaurin expansion and approximation and its application to extreme values	60minutes
10.		Problem exercises in the relevant part	130minutes
11.	Integration by substitution and by parts for definite integral, Integration of rational functions	Review Integration by substitution and by parts for definite integral, and integration of rational functions	60minutes
11.		Problem exercises in the relevant part	130minutes
12.	Integration of transcendental functions and irrational functions, integration when the integrand has discontinuities	Review Integration of transcendental functions and irrational functions, and integration when the integrand has discontinuities	60minutes
12.		Problem exercises in the relevant part	130minutes
13.	Integration when the interval of integration is infinite, quadratic problem	Review Integration when the interval of integration is infinite and quadratic problem	60minutes
13.		Problem exercises in the relevant part	130minutes
14.	Final exam and commentary	Preparation for final exam	190minutes
Total.	-	-	2650minutes

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	中間試験等	期末試験	Total.
1.	3%	5%	8%
2.	14%	20%	34%
3.	6%	10%	16%
4.	14%	20%	34%
5.	3%	5%	8%
Total.	40%	60%	-

Evaluation method and criteria

Mid-term exams, exercises, reports, quizzes etc. are set to 40%, final exams are set to 60%, and a total score of 60 or more is accepted.

Textbooks and reference materials

"Introduction to Differential and Integral calculus" Miyake (Baihuukan publishing)

Prerequisites

Be sure to check the contents of Mathematics III of senior high school.

Office hours and How to contact professors for questions

For full-time faculty, please refer to office hours of faculty profile. About part-time teachers are before and after class hours.
In mathematics department, basically each faculty does not rely on office hours, but as long as time permits, questions on subjects, etc. are accepted at any time so please do not hesitate to ask questions.
In the "Faculty of Engineering Learning Support Room" located on the 2nd floor of the University Hall, we give support for students with uneasy points and matters related to subjects on a one to one basis, so actively use it.

Relation to the environment

Non-environment-related course

Regionally-oriented

Non-regionally-oriented course

Development of social and professional independence

Course that cultivates an ability for utilizing knowledge
Course that cultivates a basic problem-solving skills

Active-learning course

About half of the classes are interactive

Course by professor with work experience

Work experience	Work experience and relevance to the course content if applicatable
N/A	該当しない

Last modified : Thu Mar 21 14:06:58 JST 2019