May 25th
May 25th
Pre-Calculus for Non-Science Majors
+Sbow all row ops, and use only elementary row ops; Sections 3.5,3.6 optional
(in italics)
| Time |
Section |
Topic |
Problems |
| 1.5 |
2.1 |
Linear Differential Equations |
2, 3, 10, 15, 18, 29, 33, 43, 44 |
| 1.5 |
2.2 |
First Order Linear Differential Eqs |
3, 15, 18, 19, 23, 26, 29, 35 |
| 2.5 |
2.4 |
Linear Models : Mixing and Cooling |
4, 6, 7, 8, 10, 16, 17, 21 |
| 1 |
2.5 |
Logistic Differential Equation |
11, 14, 15, 17, 29, 31 |
| 1.5 |
3.1 |
Matrices: Sums and Products |
8, 11, 14, 18, 23, 44, 46, 61, 62, 68, 73 |
| 2 |
3.2 |
Systems of Linear Equations |
14, 19, 20+* ,25+, 32+ , 39, 52, 53+, 63, 79 [Write system in form A x =
0 ] *Find and state both a REF and the RREF |
| 1.5 |
3.3 |
Matrix Inverse |
2, 5+, 6+, 10+,
11, 15,21,27,28, 39,46 |
| 2 |
3.4 |
De terminants and Cramer ' s Rule |
1, 6, 12, 17, 20, 24, 29, 31, 33; 36, 40, 41 |
| 1.5 |
3.5
3.6 |
Vector Spaces and Subspaces (omit spaces Mmn and Pn,)
Span and Basis |
To be announced |
| 1.5 |
4.1 |
Second Order Linear Differential Equations |
4, 9, 13, 24, 25, 26, 28, 34, 45, 46, 49 |
| 2 |
4.2 |
Real Roots of the Characteristic Equation |
5, 6, 11, 16, 20, 49, 51, 52, 56, 58, 63, 64 |
| 2.5 |
4.3 |
Complex Roots of the Characteristic
Equation |
5, 11*, 12*, 13*, 22, 25, 26, 44, 50a, 52 [See eq.
(19) on p. 241], 63 [*Also write solutions in amplitude -phase form] |
| 2.5 |
4.4 |
Undetermined Coefficients |
10, 16, 20, 25, 26, 32, 34, 43, 49 |
| 1.5 |
4.5 |
Variation of Parameters |
3, 4, 5, 8, 13, 14 |
| 2.5 |
4.6 |
Forced Oscillations |
3, 6, 7, 8, 9, 10, 13, 14, 21, 22, 23, 33, 34 |
| 1.5 |
8.1 |
Laplace Transform and its Inverse |
3, 8, 12, 15, 24a, 33, 34, 41, 44, 47, 52 |
| 2 |
8.2 |
Solving DE 's by Laplace Transform |
3, 7, 8 [ change cos (3t) to cos(2t)], 10, 12, 13 |
| 2 |
8.3 |
Step Function and Delta "Function" |
1, 2, 11, 12, 20, 23, 28, 34, 35, 40, 47, 52 |
| 1.5 |
8.4 |
Convolution Integrals and Transfer Functions |
7, 10 (Hint: consider separately the cases a=O,
a≠0],
14, 15, 16, 21, 26, 27, 38 |
| 1 |
2.6 |
Theory of Linear DE Systems |
3abd, 6abd, 10, 11, 18abd |
| 2 |
6.1 |
Systems of Linear Differential Equations |
3, 7, 8, 11, 20, 22 |
| 2.5 |
5.3 |
Eigen values and Eigenvectors |
5, 6, 10, 15, 19, 21, 22, 30, 37, 38, 40, 55, 73 |
| 2 |
6.2 |
Real Eigenvalues |
11, 16, 23, 28, 29, 32, 43, 51 |
| 2 |
5.4 |
Diagonalization (omit " coordinates " on pp. 327-332) |
25, 28, 31, 43, 44, 49abd, 55, 56 |
| 0.5 |
6.5 |
Decoupling |
1, 4, 13 |
| 44.5 |
Total |
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