授業科目名 年度 学期 開講曜日・時限 学部・研究科 全担当教員 単位数
34758:Introduction to Differential Equations(G1) 2019 春セメスター 火3 情報理工学部 SVININ MIKHAIL 2

キャンパス

BKC

授業施設

フォレストハウス１０６号教室

授業で利用する言語

英語

授業の概要と方法

Ordinary differential equations are widely used in modeling of dynamic processes in engineering, physics, natural sciences, computer science, economics and social sciences. In this course, students will learn basic differential equations by setting up, solving, and interpreting them. The course will begin with some definitions, terminology, and typical mathematical models. First-order and higher-order differential equations, along with the methods of solutions and their applications will be then introduced. Modeling with higher-order, Laplace transform, and systems of linear first-order differential equations will also be covered. The content of this course will be studied in lectures and supported by in-class and homework exercises.

受講生の到達目標

This course is designed to accomplish the following objectives:
- Develop a clear understanding of differential equations as a tool for modeling dynamic processes (specifically, model simple physical systems to obtain a first order differential equation).
- Develop the ability to formulate and solve basic types of differential equations and interpret the solutions qualitatively (visualize solutions using direction fields) and quantitatively.
- Understand the basic notions of linearity, superposition, and existence and uniqueness of solutions to differential equations.
- Use the basic techniques (characteristic equation, exponential response formula, Laplace transform, variation of parameters, matrix eigenvalue method) to solve linear differential equations.
- Solve the main equations with various input functions including zero, constants, exponentials, sinusoids, step functions, impulses, and combinations of these functions.

事前に履修しておくことが望まれる科目

Linear Algebra and Single Variable Calculus are prerequisite for this course.

授業スケジュール

授業回数/
担当教員（複数担当の場合） 		テーマ
キーワード・文献・補足事項等
1

Introduction.

Basic mathematical models, direction fields, classification (textbook, chapter 1).
2

First-order differential equations.

Linear equations, method of integrating factor, separable equations, difference between linear and nonlinear equations (textbook, chapter 2).
3

First-order differential equations.

Autonomous differential equations; method of integrating factor, separable equations; exact equations and integrating factors (textbook, chapter 2) .
4

Second-order linear differential equations.

Homogeneous equations with constant coefficients and their solutions (textbook, chapter 3).
5

Second-order linear differential equations.

 Complex roots and repeated roots of the characteristic equation (textbook, chapter 3)
6

Second-order linear differential equations.

Non-homogeneous equations; method of undetermined coefficients; variations of parameters (textbook, chapter 3).
7

Higher-order linear differential equations.

General theory and homogeneous equations with constant coefficients and their solutions (textbook, chapter 4).
8

Higher-order linear differential equations.

Non-homogeneous equations; method of undetermined coefficients; variations of parameters (textbook, chapter 4).
9

Systems of linear differential equations of first order.

Preliminary concepts: matrices, linear independence, eigenvectors and eigenvalues (textbook, chapter 7).
10

Systems of linear differential equations of first order.

 General theory and characteristic equation (textbook, chapter 7).
11

Systems of linear differential equations of first order.

Complex roots and repeated roots of the characteristic equation (textbook, chapter 7).
12

Systems of linear differential equations of first order.

Fundamental matrices and non-homogeneous equations (textbook, chapter 7).
13

The Laplace transform.

Definition and examples (textbook, chapter 6).
14

The Laplace transform.

Solution of the initial value problem (textbook, chapter 6).
15

The Laplace transform.

Differential equation with discontinuous forcing function (textbook, chapter 6).

授業実施形態

授業外学習の指示

Students are strongly recommended to spend at least 2 hours every week to prepare for the class. Each class’ materials (the relevant sections of the textbook, self-preparation assignments, and optional slides in the PDF format provided by the instructor) should be reviewed both before and after the class. The meaning of all English technical words should be comprehended prior to class.

成績評価方法

種別 割合(%) 評価基準等
定期試験（筆記） 70

Demonstration of the ability to state and solve differential equations.
レポート試験
（統一締切日を締切とするレポート）

上記以外の試験・レポート、平常点評価
（日常的な授業における取組状況の評価）		 30

Includes evaluations of lecture quizzes, self-preparation assignments, attendance and activity in class. See also “Other Comments” below.

成績評価方法(備考)

受講および研究に関するアドバイス

See “Recommendations for Private Study” above.

教科書

書名 著者 出版社 ISBNコード 備考
Elementary Differential Equations and Boundary Value Problems W.E. Boyce, R.C. Diprima, D.B. Meade Wiley 978-1-119-04481-9 Electronic version of this book (epub) has ISBN code13 978-1-119-37792-4

教科書(使用頻度、その他補足)

Any edition of the main textbook, starting from 8th, can be used for studying

参考書

書名 著者 出版社 ISBNコード 備考
A First Course in Differential Equations with Modeling Applications Dennis G. Zill Brooks Cole, 10th edition 978-1111827052
Differential Equations and Linear Algebra G. Strang Wellesley-Cambridge 978-0980232790
Schaum's Outline of Differential Equations R. Bronson and G. Costa McGraw-Hill Education, 4th Edition 978-0071824859

参考書(使用頻度、その他補足)

参考になるwwwページ

授業内外における学生・教員間のコミュニケーションの方法

学生との直接対話,その他(教員より別途指示）

備考

Attendance.
Students are responsible for all material covered in this class. Students must attend at least 66% of the lectures.
Professional ethics.
The behavioral and ethical standards of Ritsumeikan University will be observed in all aspects of this course. Specifically, academic dishonesty (e.g. copying assignments or the like) will result in a grade F for the corresponding assignment, and in many cases - in a failing grade (F) for the course.