Section # | My Lecture Notes | Solutions | Assignment | Description / Hints / Mathematica helps |
Sec. 2.2 | [13-23] | PH-[1-3] | 9, 11, 15, 21, 25, 35* | separation of variables |
Sec. 2.3 | [24-28] | PH-[4-6] | 7, 9, 11, 15, 21, 23* | integrating factor method |
Sec. 2.4 | [24-28] | PH-[7-9] | 11, 13, 17, 23, 29 | exact equations |
Sec. 2.5 | [29-37] | PH-[10-13] | 7, 9, 11, 13 | special integrating factors |
Sec. 2.6 | [29-37] | PH-[14-16] | 9, 15, 17, 41 | transformation tricks |
Sec. 3.4 | [41-45] | PH-[17-21] | 1*, 5*, 19*, 23*, 33*, 35* | Newtonian Mechanics |
Sec. 4.2 | [46-55] | PH-[22-23] | 1, 5, 13, 17, 27, 29 | homogeneous constant coefficient ordinary differential equations with real roots |
Sec. 4.3 | [46-55] | PH-[24-26] | 1, 5, 13, 21, 32*, 33*, 35* | homogeneous constant coefficient ordinary differential equations with complex roots |
Sec. 6.2 | [46-55] | PH-[27-30] | 1, 9, 13, 15, 17, 35* | higher order homogeneous constant coefficient ODEs. |
Event | Test I | Sept. 8 | Sections 2.2, 2.3, 2.4, 2.5, 2.6, 3.4, 4.2, 4.3, 6.2 | solutions of first order differential equations and homogeneous constant coefficient ODEs. |
Sec. 6.1 | [56-65] | PH-[31-33] | 1, 5, 7, 9, 17, 23 | theory of linear ODEs. |
Sec. 6.3 | [75-88] | PH-[34-37] | 5, 11, 13, 15, 17, 21, 23, 25, 27 | annihilators; a way to find the particular solution. |
Sec. 4.4 | [75-88] | PH-[38-39] | 9, 11, 15, 17, 21, 23, 27, 31 | undetermined coefficients ( section 6.3 justifies where the guess for the particular solution comes from). |
Sec. 4.5 | [91-93] | PH-[40-43] | 1, 3, 17, 21, 25, 29, 43* | superposition principle. |
Sec. 4.6 | [89-90] | PH-[44-48] | 1, 5, 15 | variation of parameters ( for things not covered by undetermined coefficients) |
Sec. 4.7 | [94-101] | PH-[49-50] | 45, 47 | variable coeffcients. |
Sec. 4.9 | [102-108] | PH-[51-52] | 3, 5, 9*, 11* [use math software for #3 and 5] | springs and vibrations. |
Sec. 4.10 | [102-108] | PH-[53-58] | 9*, 11* | forced vibrations. |
Sec. 5.7 | [102-108] | PH-[59-62] | 3*, 5*, 7*, 9*, 11*, 13* | RLC circuits and the analogy to springs with forced vibrations |
Event | Test II | Sept. 29 | Sections 6.1, 6.3, 4.4, 4.5, 4.6, 4.7, 4.9, 4.10, 5.7 | solutions of nonhomogeneous constant coefficient ODEs and select applications to springs and RLC circuits, variable coefficient DEqns. |
Sec. 7.2 | [109-114] | PH-[63-64] | 9, 13, 15, 17, 19, 21, 23 | Laplace Transformations |
Sec. 7.3 | [115-121] | PH-[65-66] | 5, 7, 11, 13, 15, 17, 19, 25 | Properties of Laplace Transformations |
Sec. 7.4 | [122-126] | PH-[67-71] | 1, 3, 21, 23, 27, 33, 35 | Inverse Laplace Transformations |
Sec. 7.5 | [127-133] | PH-[72-76] | 3, 9, 11, 35 | How to solve differential equations via Laplace Transformations |
Sec. 7.6 | [134-140] | PH-[77-81] | 5, 7, 9, 11, 17, 19, 33, 39, 59 | discontinuous functions (this is most interesting feature of the Laplace method in my opinion) |
Sec. 7.8 | [145-154] | PH-[82-84] | 1, 5, 29 | Dirac Delta "functions" |
Sec. 8.2 | [155-160] | PH-[85-89] | 1, 5, 9, 11, 15, 25, 29, 31, 33 | power series refresher |
Sec. 8.3 | [161-165] | PH-[90-97] | 1, 9, 13, 17, 19, 21, 27 | power series solutions to DEqns |
Sec. 8.4 | [166-170] | PH-[98-103] | 7, 11, 13, 17, 21, 31* | analytic coefficients |
Sec. 8.5 | [94-101] | PH-[104-105] | 1, 5, 13 | Cauchy-Euler Problem |
Sec. 8.6 | [171-178] | PH-[106-114] | 1, 17, 21, 23, 25, 27, 33, 41 | Frobenius method |
Sec. 8.7 | [171-178] | PH-[106-114] | 5, 11, 15 (note to self, find Ginny solution) | finding a second linearly independent solution |
Event | Test III | Nov. 3 | Sections 7.2, 7.3, 7.4, 7.5, 7.6, 7.8, 8.2, 8.3, 8.4, 8.6, 8.7 | Laplace transform and series solutions to ODEs |
Sec. 10.2 | . | PH-[118-126] | 1, 5, 9, 13, 15, 21, 23, 29, 33 | separation of variables for PDEs with nice boundary conditions |
Sec. 10.3 | . | PH-[127-132] | 1, 5, 7, 9, 11, 13, 19, 21, 29 | Fourier series |
Sec. 10.4 | . | PH-[133-134] | 5, 13, 17 | Fourier cosine and sine series |
Sec. 10.5 | . | PH-[135-144] | 3, 7, 15 | the heat equation |
Sec. 10.6 | . | PH-[145-149] | 1, 13, 15 | the wave equation |
Sec. 10.7 | . | PH-[150-161] | 1, 3, 7, 9, 11 | Laplace's equation |
Event | Test IV | take-home | Sections 10.2, 10.3, 10.4, 10.5, 10.6, 10.7 | PDEs with nice solutions. |