| Mon 31 Aug |
1.1 |
Introduction to Differential Equations |
p10/5,7,11,15 |
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1.2 |
Separable Differential Equations |
p20/1-19(odd) |
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1.3 |
Linear Differential Equations |
p26/1,5,7,13,16 |
| Wed 2 Sep |
1.4 |
Exact Differential Equations |
p32/1,3,7,11,13,15 |
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1.5 |
Integrating Factors |
p37/3,5,9,14,15 |
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1.6 |
Special First Order DE's (Homogeneous) |
p46/5,7,8,10,12 |
| Mon 7 Sep |
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No class |
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| Wed 9 Sep |
1.7 |
Applications - Electrical Circuits, |
p55/19,23,25 |
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Orthogonal Trajectories |
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1.8 |
Existence and Uniqueness |
p60/1,5,6 |
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2.1 |
Introduction - Second Order Differential Equations |
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| Thu 10 Sep |
2.2 |
Theory of Solutions of Second Order DE's |
p69/3,5,8,10,11,13 |
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2.3 |
Reduction of Order |
p72/3,5,7,15 |
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2.4 |
Constant Coefficient Homogeneous Linear Equations |
p77/1,3,5,9,11,13,17,21 |
| Mon 14 Sep |
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No class |
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| Wed 16 Sep |
2.5 |
Euler's Equation |
p81/1,3,7,9,19 |
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2.6 |
Method of Variation of Parameters |
p93/1-6 |
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2.6 |
Method of Undetermined Coefficients |
p93/7,11,12,13,15, |
| Mon 21 Sep |
2.7 |
Models of Mechanical Systems |
p105/1,4,5,11,13 |
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Simple & Damped Harmonic Motion |
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| Wed 23 Sep |
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No class |
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| Mon 28 Sep |
2.7 |
Forced Motion |
p110/19,21,23 |
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2.7 |
Electrical Circuits |
p110/25,27 |
| Wed 30 Sep |
2.6 |
Higher Order DE's Summary of Second Order Linear DE's |
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matrix representation and geometrical interpretation. |
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6.1 |
Algebra and Geometry of Vectors |
p210/1,3,7,11,13,19 23,25,27,28,29,32,36 |
| Mon 5 Oct |
6.2 |
Dot Product |
p217/5,9,15,17,19 |
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6.3 |
Cross Product |
p222/1,5,9,15,17,23,31 |
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Review |
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| Wed 7 Oct |
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Exam 1 |
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| Mon 12 Oct |
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No class |
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| Wed 14 Oct |
6.4 |
Vector Space Rn |
p228/5,7,9,11,13,15 |
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6.5 |
Linear Independence and Dimension |
p235/1,5,9,17,19,25,27 |
| Mon 19 Oct |
7.1 |
Matrices |
p250/3,5,9,11,15,17,21,23,27 |
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7.2 |
Elementary Row Operations, Elementary Matrices |
p258/1,3,5,7,9,11 |
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7.3 |
The Row Echelon Form of a Matrix |
p265/3,5,7,11 |
| Wed 21 Oct |
7.4 |
The Rank and Row/Column Space of a Matrix |
p271/3,5,7,9,11,17 |
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7.5/7.6 |
Homogeneous Systems of Linear Equations |
p279/1,3,5,7,9,13,17 |
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7.7 |
Nonhomogeneous Systems of Linear Equations |
p292/3,5,7,11,13,15 |
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7.8 |
Matrix Inverse |
p298/3,5,7,9,13,15,17 |
| Mon 26 Oct |
8.1/8.2 |
Definition of the Determinant |
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8.3 |
Properties of Determinants |
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8.4/8.5 |
Evaluation of Determinants |
p313/1,3,7,9,11,13 |
| Wed 28 Oct |
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Using MATLAB for manipulating matrices: |
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(I) Input; size; determinant; inverse |
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(II) Solution of systems of equations. (HANDOUT) |
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| Mon 2 Nov |
8.7 |
Matrix Inverse |
p318/3,5,7,9 |
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8.8 |
Cramer's Rule |
p320/3,5,7,9 |
| Wed 4 Nov |
9.1 |
Eigenvalues and Eigenvectors |
p320/1,3,5,7,11,13,15,17,19,20 |
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9.2 |
Diagonalization |
p339/1,3,5,7,9,12,13 |
| Mon 9 Nov |
9.3 |
Orthogonal and Symmetric Matrices |
p347/1,3,5,9,11 |
| Wed 11 Nov |
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Diagonalization using MATLAB - extracting |
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|
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Eigensolutions (HANDOUT) |
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| Mon 16 Nov |
10.1 |
Theory of Systems of Linear DE's |
p373/1,3,5,7,9,17,19,21,25,31,33 |
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10.2 |
Solution of X'=AX When A is Constant |
p392/7,13,21,25,27,33, 35,41,43,47 |
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Review |
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| Wed 18 Nov |
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Exam 2 |
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| Mon 23 Nov |
10.3 |
Solution of X'=AX+G |
p401/15,17,19,23 |
| Wed 25 Nov |
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Using MATLAB to solve systems of |
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|
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Linear First Order DE - ODE23/ODE45 (HANDOUT) |
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| Mon 30 Nov |
3.1 |
Laplace and Inverse Laplace transforms |
p121/1,3,5,7,9,13,15,17,25,29 |
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3.2 |
Laplace Transform Solution of Initial Value Problem |
p126/1,3,5,8,10,13 |
| Wed 2 Dec |
3.3 |
Shifting Theorems and the Heaviside Function |
p139/1,3,5,7,9,11,15,17,19 |
| Mon 7 Dec |
3.3 |
Shifting Theorems (Cont'd) |
p139/23,25,27,31,35,37 |
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3.4 |
Convolution Theorem |
p146/1,5,7,9,13,19,21 |
| Wed 9 Dec |
3.5 |
Unit Impulses and the Dirac Delta Function |
p151/1,3,5 |
| Mon 14 Dec |
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Review |
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| Wed 16 Dec |
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Final |
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