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MATH 225 LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS
Spring 2006, Fall 2018, Spring 2020
Math225 : Linear Algebra and Differential Equations.
Text book :
"Differential Equations and Linear Algebra" by
C.H.Edwards and D.E. Penney, Prenticel Hall
Other Books :
" Linear Algebra and Differential equations" ,
by A.C. Baker and H.L. Porteus, Ellis Horwood.
System DEs ,
Modelling ,
Differential
Equations>,
First Order Differential
Equations ,
Fourier
Series ,
Modelling with Differential
equations ,
Modelling with First Order DEs
Subjects covered
1. January 30:
Differential Equations and Mathematical Models
Integrals as General and Particular Solutions
I. Homework set:
Section 1.2. Problems 36,42
Section 1.3. Problems 12,15,19,29,33.
Section 1.4. Problems 20,30,32.
2. Feb. 06:
Slope and Solution Curves
Separable Equations and Applications
Linear First Order Equations
Substition Method and Exact Equations
II. Homework set: (due February 15)
Section 1.5. Problems 20,25,31,32
Section 1.6. Problems 15,30,33,57,58,59.
3. Feb. 13:
Exact Differential Equations
Second order DEs reducible to first order DEs
Mathematical Modelling (Newton's cooling law, Toricalli's law and
Population growth)
Stability
III. Homework set: (due February 22)
Section 2.2. Problems 10,11,21,23,24
4. Feb. 20
Introduction to Linear Systems
Matrices and Gauss Eliminiation
Reduced Row-Echolon Matrices
IV. Homework set: (due March 1)
Section 3.2 Problems (page 162) 9,10,17,21,27,28
Section 3.2 Problem 20. Solve this problem by using
Maple.
You print the output and attach it to the
homework.
5. Feb 27
Matrix Operations
Inverses of Matrices
Determinants
V. Homework set: (due March 8)
Section 3.4 Problems (page 182) 10,21,23,27,29,42
Page 172 Problem 5. Solve this problem by using Maple
You print the output and attach it to the
homework.
6. March 6
Determinants
Cramer's rule
VI. Homework set: (due March 15)
1. Section 3.5. Page 195
Problems 28,32,33
2. Section 3.6. Page 212
Problems 32,51,52,53
3. Page 196. Solve the linear system
3 x1+2 x2-x3+4 x4=-1
2 x1+3 x2-2 x3+5 x4=0
x1-2 x2+x3+ x4=-4
-x1+x2+x3-3 x4=0
by the use of Maple
7. March 13
Curve fitting
Vector space R^3
first midterm with solutions
VII. Homework set: (due March 22)
1. Section 4.1 (page 233) Problems: 28,32,35,41
2. Section 4.2 (page 241) Problems: 22,27,31
8. March 20
Vector space R^3
Vector space R^n
Bases and Dimension
VIII. Homework set: (due April 5)
1. Section 4.3 (page 248) Problems: 16,19,27,28,29
2. Section 4.4 (page 255) Problems: 13,18,25,29,31.
9. April 3
Bases and Dimension
Row and Column spaces
Orthogonal Vectors in R^n
IX. Homework set: (due April 12)
1. Section 4.5 (page 263) Problems: 17,21,23,24,30
2. Section 4.6 (page 271) Problems: 20,28,30.
10. April 10
Orthogonal Vectors in R^n
General Vector spaces
Higher Order Linear Differential Equations
11. April 17
Higher Order Linear Differential Equations (5.1)
Second order Linear Equations (5.1,5.2)
General solutions of Linear Equations (5.2,5.3)
Homogeneous equations with constant coefficients (5.3)
X. Homework set: (due April 26 )
1. Section 5.1 (page 294) Problems: 30,32,51,52
2. Section 4.6 (page 306) Problems: 17,18,37,38.
12. April 24
Homogeneous equations with constant coefficients (5.3)
Nonhomogeneous equations and undetermined coefficients (5.5)
second midterm with solutions
13. May 1
Nonhomogeneous equations and undetermined coefficients (5.5)
Sections 5.4 and 5.6 are exluded
Introduction to Eigenvalues (6.1)
Diagonalization of Matrices (6.2)
XI. Homework set: (due May 10)
1. Section 5.5 (page 346) Problems: 36,37,38,41
2. Section 5.5 (page 347) Problems: 47,51,58,59
14. May 8
Diagonalization of Matrices, Powers of Matrices (6.2,6.3)
Matrices and Linear Systems (7.1-7.2)
The Eigenvalue Method for Linear Systems (7.3,7.5)
(Section 7.4 is excluded)
15. May 15
Multiple Eigenvalue Solutions (7.3,7.5)
In the Final Exam You will be responsible from
Chaper 1, Section 1 to Chapter 7, Section 5.
Final exam with solutions
Course Schedule
Monday 13.40-15.30 , BZ08
Wednesday 15.40-17.30 , BZ-08
Exams :
(25%) First Midterm Exam
March 13, 2006 (17.40) at BZ01 and BZ02
(25 %) Second Midterm Exam
April 25, 2006 (17.40) at BZ01 and BZ02
(35 %) Final Exam
May 24, 2006 (9.00 at EB201 and EB202)
(15%) Attendance+ Homework :
ORTALAMA NOTUNUZ ICIN BAKINIZ
ortalama notunuz
Final exam with solutions
Course Syllabus
1. Introduction, First order Differential equations
2. First Order ODes, Integrating Factot
3. Homogeneous Differential Equations. Mathematical Models.
4. Systems of Linear equations. Matrix Form
5. Echelon matrices. Matrix Operations
6. Inverse Matrices. Determinant.
7. Vector Space R^3.
8. Multidimensional spaces, subspaces, linear combinations.
9. Linear independence, basis and dimension
10. General vector spaces.
11. Second order linear differential equations, its space of solutions.
12. Method of undetermined coefficients. Variation of parameters.
13. Higher order linear differential equations.
14. Eigenvales and eigenvectors.
15. Diagonalization of matrices and systems of linear ODEs
Last update January 2006
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