Mathematics Ⅲ A

Course Information

College	Akashi College	Year	2020
Course Title	Mathematics Ⅲ A
Course Code	0050	Course Category	General / Compulsory
Class Format	Lecture	Credits	Academic Credit: 4
Department	Mechanical Engineering	Student Grade	3rd
Term	Year-round	Classes per Week	2
Textbook and/or Teaching Materials
Instructor	MATSUMIYA Atusi

Course Objectives

Develop important mathematical thinking and problem solving skills as engineering technicians based on the mathematics learned previously. The goal of this class is for students to acquire the ability to understand more specialized applied mathematics.
(1) First, understand the convergence of a sequence, the convergence and divergence of a series, and the Maclaurin series. Then understand the function of two variables as a curved surface in space, and are able to calculate partial differentials and multiple integrals.
(2) Acquire a faithful understanding of theories and the ability to express them theoretically.
(3) Acquire the ability to apply an abstract framework to specific issues.

Rubric

	Ideal Level	Standard Level	Unacceptable Level
Achievement 1	Fully understand the convergence and divergence of a sequence, the convergence and divergence of a series, and the Maclaurin series. Then fully understand two-variable functions as curved surfaces in space, and sufficiently calculate partial derivatives and multiple integrals.	Understand the convergence and divergence of a sequence, the convergence and divergence of a series, and the Maclaurin series. Understand a two-variable function as a curved surface in space, and can calculate partial differentials and multiple integrals.	Cannot understand the convergence and divergence of a sequence, the convergence and divergence of a series, and the Maclaurin series. Do not understand a two-variable function as a curved surface in space, and cannot calculate partial differentials or multiple integrals.
Achievement 2	Fully have a good understanding of theories and the ability to express them theoretically.	Have a understanding of theories and the ability to express them in theoretically.	Do not have a understanding of theories and the ability express them theoretically.
Achievement 3	Fully have the ability to apply an abstract framework to specific issues.	Have the ability to apply an abstract framework to specific issues.	Do not have the ability to apply an abstract framework to specific issues.

Assigned Department Objectives

学習・教育到達度目標 (D) See

学習・教育到達度目標 (G) See

学習・教育到達度目標 (H) See

Teaching Method

Outline:

Students will acquire the basic concepts of differential integration and the various computational methods developed from it, and the necessary resources for analyzing various events in the specialized fields. We will mainly teach the convergence and divergence of a sequence, the convergence and divergence of a series, the evolution of the Maclaurin series, the partial differentiation of a two-variable function and its application, and the application of double integrals.

Style:

Classes will assume the pre-study has been done, and follow the textbook accordingly. There will also be problem exercises. Students will be asked questions to check their understanding during classes. In the classes, focus on understanding, and ask questions about things do not understand in the pre-study or class, rather than doing nothing about them. Make an effort to always review the material on the same day, and solve the problems in the textbook and the workbook. Some of the classes will use ICT. Tests will sometimes be held without prior notice to confirm attainment. Consequently, please study properly on a daily basis.

Notice:

Try to understand the material thoroughly during the classes. Make an effort to always ask about things that are unclear, and solve them then and there. Also, always review the material on the same day, and do the problem exercises properly by solving the problems in the textbook and the workbook. Quizzes will sometimes be given without prior notice, so study properly on a daily basis. The overall evaluation will be based 50% on exams, 20% on submitted assignments, etc., and 30% on presentations and general effort toward classes. The minimum score for a pass will be 60 marks. However, evaluation scores based on these weightings will be calculated at the end of the school year. The cumulative evaluation up to the second semester midterm be based on interim weightings rather than the ones given above. Students who do well in assignments, presentations, etc. may get them evaluated with a higher weighting. CBT will be conducted in any week. Students who miss 1/3 or more of classes will not be eligible for a passing grade. This course's content will amount to 180 hours of study in total. These hours include the learning time guaranteed in classes and the standard self-study time required for pre-study / review, and completing assignment reports.

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Expansion of functions	Can calculate an approximation by polynomials. Can calculate the local primary approximation of a simple one-variable function.
		2nd	Expansion of functions	Can calculate an approximation by polynomials.
		3rd	Expansion of functions	Can calculate various columns of extremes, including indeterminate shapes.
		4th	Expansion of functions	Can investigate and calculate the sum of the convergence and divergence of simple series such as infinite equalization series.
		5th	Expansion of functions	Can investigate and calculate the sum of the convergence and divergence of simple series such as infinite equalization series.
		6th	Expansion of functions	Understand the Taylor expansion of one-variable functions and can calculate the Maclaurin expansion of basic functions.
		7th	Expansion of functions	Understand the Taylor expansion of one-variable functions and can calculate the Taylor expansion of basic functions. Can use the Euler formula to perform simple computation of the exponential function of a complex variable.
		8th	Midterm exam
	2nd Quarter
		9th	Partial differentiation method	Understand two-variable functions and can draw simple curves. Understand the definition area of a two-variable function and can represent it by inequality or graph.
		10th	Partial differentiation method	Can calculate partial derivatives.
		11th	Partial differentiation method	Can calculate the total derivative.
		12th	Partial differentiation method	Can calculate the equation of a tangent plane.
		13th	Partial differentiation method	Can use the partial derivative of a synthesis function to calculate the partial derivative.
		14th	Applying the partial differentiation method	Can calculate a second partial derivative for a simple function. Can calculate a high-order polarization derivative for a simple function.
		15th	Applying the partial differentiation method	Can calculate the extrema of a basic two-variable function using .
		16th	Final exam
2nd Semester
	3rd Quarter
		1st	Applying the partial differentiation method	Can perform applied computation using the negative derivative method.
		2nd	Applying the partial differentiation method	Can solve problems of conditional extrema.
		3rd	Applying the partial differentiation method	Can calculate the equation of the envelope line. Can solve applied problems related to partial differentials.
		4th	Double integrals	Understand the definition of dual integration.
		5th	Double integrals	Understand the nature of dual integration.
		6th	Double integrals	Understand the definition of double integrals, and can convert calculate simple double integrals by converting them into iterated integrals.
		7th	Double integrals	Can switch the order of double integrals. Can perform various computation of double integrals.
		8th	Midterm exam
	4th Quarter
		9th	Double integrals	Can use double integrals to calculate the volume of a simple solid.
		10th	Variable conversion and multiple integrals	Can calculate double integrals by converting to polar coordinates.
		11th	Variable conversion and multiple integrals	Can compute variable conversion for multiple integrals.
		12th	Variable conversion and multiple integrals	Can calculate improper integrals.
		13th	Variable conversion and multiple integrals	Can use multiple integrals to calculate curvature areas.
		14th	Variable conversion and multiple integrals	Can use multiple integrals to calculate the average and center of gravity.
		15th	Variable conversion and multiple integrals	Can solve applied problems using multiple integrals.
		16th	Final exam

Evaluation Method and Weight (%)

	Examination	Task	Status of efforts	Total
Subtotal	50	20	30	100
Basic Proficiency	50	20	30	100
Specialized Proficiency	0	0	0	0
Cross Area Proficiency	0	0	0	0