Course Name Year Term Period Faculty / Graduate School All Instructors Credits
34758:Introduction to Differential Equations (G1) 2019 Spring Tue3 College of Information Science and Engineering SVININ MIKHAIL 2

Campus

BKC

Class Venue

Forest106

Language

English

Course Outline and Method

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.

Student Attainment Objectives

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.

Recommended Preparatory Course

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

Course Schedule

Lecture/Instructor（When there are multiple instructors) Theme
Keyword, References and Supplementary Information
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).

Class Format

Recommendations for Private Study

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.

Grade Evaluation Method

Kind Percentage Grading Criteria etc.
Final Examination (Written) 70

Demonstration of the ability to state and solve differential equations.
Report Examination
(A report to be submitted by the unified deadline)

Exams and/or Reports other than those stated above, and Continuous Assessment　
(Evaluation of Everyday Performance in Class)		 30

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

Grade Evaluation Method （Note）

Advice to Students on Study and Research Methods

See “Recommendations for Private Study” above.

Textbooks

Title Author Publisher ISBN Code Comment
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

Textbooks （Frequency of Use, Note）

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

Reference Books

Title Author Publisher ISBN Code Comment
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

Reference Books （Frequency of Use, Note）

Web Pages for Reference

How to Communicate with the Instructor In and Out of Class(Including Instructor Contact Information)

Talk with Students,Other (Separate instructions will be provided)

Other Comments

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.