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MATH 225 LINEAR ALGEBRA AND DIFFERENTIAL EQUATIONS

Spring 2006


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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