Mathematics Ⅱ A-2

Course Information

College	Akashi College	Year	2023
Course Title	Mathematics Ⅱ A-2
Course Code	5206	Course Category	General / Compulsory
Class Format	Lecture	Credits	School Credit: 2
Department	Civil Engineering	Student Grade	2nd
Term	Second Semester	Classes per Week	4
Textbook and/or Teaching Materials	differentials and integrals I
Instructor	OMODA Yasuhiro

Course Objectives

1. Understand limits of functions, the meaning of a derivative at a point, the definition of the derivative, the product and quotient rules for derivatives, composite functions, and inverse trigonometric functions, and can calculate the derivatives of various functions.
2. Can write a derivative sign chart for a function, find its extrema, and sketch its graph. Can use extrema to calculate functions' maximum and minimum values. Also, can investigate the shapes of graphs using second derivatives. Understand parametric representations of functions, and can use them to calculate their derivatives.
3. Understand the definition of definite integration and the fundament theorem of calculus, and can calculate simple definite integrals. Understand the definition of indefinite integration, and can calculate simple indefinite integrals. Also, can calculate indefinite and definite integrals using integration by substitution and integration by parts.
4. Can calculate indefinite and definite integrals of fractional, irrational, trigonometric, exponential, and logarithmic functions. Can use definite integration to calculate the areas of shapes enclosed by curves, the lengths of curves, and the volumes of solids in simple cases.

Rubric

	Ideal Level	Standard Level	Unacceptable Level
Achievement 3	Fully understand the definition of definite integration and the fundament theorem of calculus, and can fully calculate simple definite integrals. Fully understand the definition of an indefinite integral, and can fully calculate simple indefinite integrals. Also, can fully calculate indefinite and definite integrals using integration by substitution and integration by parts.	Understand the definition of definite integration and the fundament theorem of calculus, and can calculate simple definite integrals. Understand the definition of indefinite integration, and can calculate simple indefinite integrals. Also, can calculate indefinite and definite integrals using integration by substitution and integration by parts.	Do not understand the definition of definite integrals and the fundament theorem of calculus, and cannot calculate simple definite integrals. Do not understand the definition of indefinite integrals, and cannot calculate simple indefinite integrals. Also, cannot calculate indefinite and definite integrals using integration by substitution and integration by parts.
	Can fully calculate indefinite and definite integrals of fractional, irrational, trigonometric, exponential, and logarithmic functions. Can fully use definite integration to calculate the areas of shapes enclosed by curve, the lengths of curves, and the volumes of solids in simple cases.	Can calculate indefinite and definite integrals of fractional, irrational, trigonometric, exponential, and logarithmic functions. Can use definite integration to calculate the areas of shapes enclosed by curves, the lengths of curves, and the volumes of solids in simple cases.	Cannot calculate indefinite and definite integrals of fractional, irrational, trigonometric, exponential, and logarithmic functions. Cannot use definite integration to calculate the areas of shapes enclosed by curves, the lengths of curves, and the volumes of solids in simple cases.

Assigned Department Objectives

Teaching Method

Outline:

Students will learn integral as the basis of the calculus.

Style:

Lessons by lecture and practice-type, timely assignments, quizzes, etc.

Notice:

CBT will be carried out in a certain week.
Students can not obtain a passing grade if they miss 1/3 or more of classes.

Characteristics of Class / Division in Learning

Active Learning	Aided by ICT	Applicable to Remote Class	Instructor Professionally Experienced

Course Plan

			Theme	Goals
2nd Semester
	3rd Quarter
		1st	Indefine and definite integrals	Can find indefinite integrals.
		2nd	Indefine and definite integrals	Can find definite integrals.
		3rd	Computing integrals	Can find the integrals using substitution.
		4th	Computing integrals	Can find the integrals using parts.
		5th	Computing integrals	Can find the integrals using partial fractions.
		6th	Exercise	Exercise
		7th	Applications of integral	Can find the area of figures.
		8th	Applications of integral	Can find the length of curves.
	4th Quarter
		9th	Applications of integral	Can find the volume and surface area of solids.
		10th	Applications of integral	Can check the outline of figures by parametric and polar curves.
		11th	Applications of integral	Can find the value of the improper integrals and the rate of changes
		12th	First order differential equations	Can solve separable and homogeneous differential equations.
		13th	First order differential equations	Understand the model of differential equations and the meaning of directional fields.
		14th	Exercise	Exercise
		15th	Summary	Review / development
		16th

Evaluation Method and Weight (%)

	Exam	Presentation	Attitude・Attendance etc	Total
Subtotal	30	40	30	100
Basic Proficiency	30	40	30	100
Specialized Proficiency	0	0	0	0
Cross Area Proficiency	0	0	0	0