Course Title
Mathematics IA: Ordinary Differential Equations
授業科目名
Course Category
授業科目区分
Students Admitted
授業対象学生
Course Code
授業科目コード
Course Description
This course is a first introduction to differential equations. Many real
講義題目
world problems in science and engineering can be expressed as
differential equations. We must know how to model these problems as
differential equations, and how to solve them and interpret their
solutions. In this course we will focus on linear ordinary differential
equations and the following four main topics:
1. First order differential equations
2. Second order differential equations
3. Systems of differential equations
4. The Laplace transform
Course Type and Schedule
授業方法及び開講学期
Credits
単位数
Instructor
Craig Pastro
担当教員名
Prerequisite
Calculus B
履修条件
Course Outline
授業の概要
1. Definition and classification of DEs and basic notions 1.1-1.3
2. First order DEs
a. Linear equations and integrating factors 2.1
b. Separation of variables 2.2
c. Modeling 2.3
d. Linear vs. non-linear equations 2.4
e. Autonomous equations 2.5
f.
Exact equations 2.6
3. Second order linear DEs
a. Homogeneous equation with constant coefficients 3.1
b. Fundamental solutions; the Wronskian 3.2
c. Complex roots 3.3
d. Repeated roots and reduction of order 3.4
e. Nonhomogeneous equations; method of
undetermined coefficients and variation of
parameters 3.5-3.6
4. Systems of first order linear equations
a. Introduction (How to convert higher order equations
into linear first order systems) 7.1
b. Basic theory of first order linear systems 7.4
c. Homogeneous linear systems with constant
coefficients 7.5
d. Complex eigenvalues 7.6
e. Fundamental matrices 7.7
f.
Repeated eigenvalues 7.8
g. Nonhomogeneous linear systems 7.9
5. Laplace transform
a. Definition and examples 6.1
b. Solution of initial value problems 6.2
c. Discontinuities 6.3-6.4
d. Impulses 6.5
e. Convolution 6.6
General Course Objectives
全体の教育目標
To learn how to set up, solve, and interpret ordinary differential
equations.
Specific Course Objectives
個別の学習目標
Course Plan
See course outline
授業計画
Keywords
キーワード
First order linear ordinary differential equations, second order linear
ordinary differential equations, systems of first order ordinary
differential equations, Wronskian, Laplace transform
Method of Instruction
授業の進め方
Text and References
教科書及び参考図書
Office Hours
学習相談
15 hours of lectures. (Almost) weekly homework, a midterm exam, and a
final exam.
Elementary Differential Equations and Boundary Value Problems 9th
edition by William E. Boyce and Richard C. DiPrima
To be decided. Also anytime by appointment (email me at
craig@artsci.kyushu-u.ac.jp).
Grading
Homework 20% (worst score dropped), Midterm exam 30%, Final
試験・成績評価の方法
exam 50%. You must pass the final exam (greater than or equal to 60%)
to pass the course. Your final grade = max{overall grade, grade on final}.
Notes
その他
Course webpage is at: http://goo.gl/yuNRKa