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Course: Math 260 (Introduction to Differential Equations
and Linear Algebra) |
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Text Book: Differential Equations and Linear Algebra, C.
H. Edwards and D. E. Penny, Prentice Hall, Second Edition (2005). |
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Objectives: This course introduces elementary differential
equations and linear algebra to students of Computer Science, Computer
Engineering, System Engineering and Earth Sciences. |
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Course Description: Systems of linear equations. Rank of
matrices. Eigenvalues and eigenvectors. Vector spaces, subspaces, bases,
dimensions. Invertible matrices. Similar matrices. Diagonalizable
matrices. Block diagonal and Jordan forms. First order differential
equations: separable and exact. The homogeneous differential equations
with constant coefficients. Wronskian. Non-homogeneous differential
equations. Methods of undetermined coefficients and variation of
parameters. Systems of differential equations. Non-homogeneous systems. |
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Date |
Section |
Topic |
Homework |
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1 |
Feb 20-Feb 24 |
3.1 |
Introduction to Linear Systems |
2, 22, 24, 26 |
Part I: Linear Algebra |
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3.2 |
Matrices and Gaussian Elimination |
4, 8, 14, 28 |
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3.3 |
Reduced Row-Echelon Matrices |
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2 |
Feb 27-Mar 03 |
3.3 |
Reduced Row-Echelon Matrices |
3, 10, 24, 35 |
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3.4 |
Matrix Operations |
3, 10, 20, 24 |
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3.5 |
Inverse of Matrices |
4, 12, 20, 28 |
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3 |
Mar 06-10 |
3.6 |
Determinants |
2, 4, 12, 30, 40, 43 |
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4.1 |
The Vector Space R3 |
1, 6, 13, 16, 24, 26, 30 |
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4.2 |
The Vector Space Rn
& Subspaces |
3, 8, 16, 19 |
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4 |
Mar 13-17 |
4.3 |
Linear Combination & Independence of Vectors |
1, 6, 12, 17, 26 |
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4.4 |
Bases & Dimension for Vector Spaces |
3, 8, 13, 16, 22 |
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5 |
Mar 20-24 |
4.5 |
Row and Column Spaces |
1, 7, 13, 15, 17, 25, 26 |
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6.1 |
Introduction to Eigenvalues |
2, 15, 24, 28, 36 |
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Review (Exam-1) |
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6 |
Mar 27-31 |
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Review (Exam-1) |
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Exam -1 (Sund Mar 28) 6pm B54 ( 3.1 - 4.5 ) |
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6.2 |
Diagonalization of Matrices |
2, 14, 25, 28 |
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7 |
Apr 03- 07 |
6.3 |
Applications involving Powers of Matrices |
2, 10, 20, 26, 36 |
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7.5 |
Jordan form (pp 454-457) |
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8 |
Apr 10-14 |
7.5 |
Jordan form (pp 454-457) |
37, 38, 41, 43 |
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1.1 |
Differential Equations and Mathematical Models |
2, 12, 22, 30, 36, 40 |
PartII: Differential Equations |
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1.2 |
Integrals as General & Particular Solutions (page: 10-11) |
4, 6, 15, 18 |
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Apr 17-21 |
Midterm |
Midterm Vacation |
Midterm Vacation |
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9 |
Apr 24-28 |
1.4 |
Separable Equations & Applications |
1, 10, 24, 27, 33 |
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1.5 |
Linear First-Order Equations |
4, 12, 24, 28, 32 |
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Review (Exam-2) |
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10 |
May 01-05 |
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Review (Exam-2) |
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Exam -2 (Sund May 2) 6pm B54 ( 6.1 - 1.5 ) |
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1.6 |
Substitution Methods & Exact Equations |
2, 10, 22, 40, 60 |
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2.4 |
Euler's Method |
3, 7, 12 |
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11 |
May 08-12 |
5.1 |
Second-Order Linear Equations |
1, 11, 16, 19, 25, 28, 44 |
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5.2 |
General Solutions of Linear Equations |
2, 8, 13, 24, 26 |
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12 |
May 15-19 |
5.3 |
Homogeneous Equations with Constant Coefficients |
1, 4, 14, 22, 28, 33, 38 |
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5.5 |
Method of Undetermined Coefficients |
4, 12, 26, 32, 36 |
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13 |
May 22-26 |
7.1 |
First-Order Systems & Applications |
2, 8, 13, 18, 21 |
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7.2 |
Matrices & Linear Systems |
2, 4, 12, 16, 20, 25 |
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14 |
May 29-Jun2 |
7.3 |
The Eigenvalue Method for Linear Systems |
4, 9, 18, 24, 26 |
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7.5 |
Multiple Eigenvalue Solutions |
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15 |
Jun 5-9 |
7.5 |
Multiple Eigenvalue Solutions (contd.) |
4, 10, 16, 28, 30 |
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Review |
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Jun-19 |
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Final Exam (sat 7pm) comperhenxive |
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