Week  Topic  Reading  Homework (ANSWERS at back of book)  Lecture Notes  

Aug 21  I. Introduction: what is a DE, order, linear and nonlinear, solutions, direction fields. II. First Order Equations: solution of linear ODE, separable equations, integrating factors. 
Chap. 1, 2.12.2. 
10th Edition: 1.1: 5, 9, 13, 1520, 21, 23 1.3: 1, 3, 5, 7, 12, 17, 19 2.1: 4, 11, 13, 16, 20, 24, 31, 33 2.2: 7, 17, 19, 21, 24, 27, 30, 31, 33 
11th Edition: 1.1: 4, 6, 9, 1116, 17, 19 1.3: 1, 3, 4, 5, 9, 12, 14 2.1: 4, 7, 9, 11, 12, 15, 21, 23 2.2: 5, 15, 16, 17, 20, 21, 25, 26, 28 
Lecture 1
Lecture 2 Lecture 3 Lecture 4 
Aug 28  II. First Order Equations: integrating factors, modeling and applications, linear vs nonlinear equations / existence & uniqueness, autonomous equations & population dynamics  2.3  2.5, 2.8. 
2.3: 5, 9, 13, 27
2.4: 5, 11, 13, 25, 27, 29 2.5: 5, 7, 13, 15, 17, 21, 23 Enrichment problems, not required: The Brachistochrone: 2.3.32 More bifurcations: 2.5.25, 27 
2.3: 3, 7, 9, 21
2.4: 3, 8, 9, 21, 23, 24 2.5: 4, 5, 9, 15, 17, 20, 22 Enrichment problems, not required: The Brachistochrone: 2.3.24 More bifurcations: 2.5.24, 26 
Lecture 5
Lecture 6 Lecture 7 Lecture 8 
Sep 4  II. First Order Equations: Exact equations & integrating factors. III. Second order linear equations: Homogeneous equations, the Wronskian. 
2.6, 3.1  3.2 
2.6: 5, 6, 9, 15, 19, 27, 28, 32
3.1: 5, 8, 15, 19, 21, 23, 26 3.2: 9, 13, 15 Enrichment problems, not required: Exact equations: 3.2.41,45 
2.6: 4, 5, 6, 11, 15, 20, 21, 22
3.1: 4, 6, 11, 14, 16, 17, 19 3.2: 7, 10, 12 Enrichment problems, not required: Exact equations: 3.2.31, 34 
Lecture 9
Lecture 10 
Sep 11  III. Second order linear equations: The Wronskian, characteristic equations, real, complex, an repeated roots, reduction of order.  3.2  3.4 
3.2: 17, 28, 29
3.3: 11, 17, 19, 22, 25 3.4: 7, 11, 14, 17, 23, 27, 37, 38 Enrichment problems, not required: Euler equations: 3.4.41, 43 Try also the substitution y(t)=t^{r}, solve for r, then write down the general solution. This is the usual sub for Euler eqs. 
3.2: 14, 22, 23
3.3: 8, 12, 13, 15, 18 3.4: 6, 9, 11, 13, 18, 21, 28, 29 Enrichment problems, not required: Euler equations: 3.4.32, 33 Try also the substitution y(t)=t^{r}, solve for r, then write down the general solution. This is the usual sub for Euler eqs. 
Lecture 12
Lecture 13 Lecture 14 Lecture 15 
Sep 18  III. Second order linear equations: vibrations, nonhomogeneous equations, method of undetermined coefficients, variation of parameters.  3.53.7 
3.5: 5, 6, 11, 13, 17, 19, 23a, 27a, 29, 31
3.6: 1, 7, 17, 29 3.7: 1, 7, 11, 13, 19, 21, 24 Note: 3.5.13 involves hyperbolic functions. If these are new to you, see the note on hyperbolic functions in 'Documents'. 
3.5: 4, 5, 8, 10, 13, 14, 17a, 20a, 22, 24
3.6: 1, 6, 13, 24 3.7: 1, 4, 6, 8, 13, 15, 17 Note: 3.5.10 involves hyperbolic functions. If these are new to you, see the note on hyperbolic functions in 'Documents'. 
Lecture 16
Lecture 17 Lecture 18 Lecture 19 
Sep 25 
III. Second order linear equations: forced vibrations, application: mechanical and electrical vibrations. IV. Higher order linear equations: Existence & uniqueness of solutions, solving constantcoefficient higherorder linear equations. 
3.8, 4.1, 4.2 
3.7: 12
3.8: 6, 8, 13, 15, 16, 18, 19, 24 4.1: 5, 9, 15, 19, 23, 27 (don't have to show #26) 4.2: 5, 7, 24, 35, 39 
3.7: 7
3.8: 4, 5, 9, 11, 12, 13, 14, 19 4.1: 3, 7, 10, 14, 17, 20 (don't have to show #19) 4.2: 4, 5, 17, 25, 29 
Lecture 20
Lecture 21 Lecture 22 Lecture 23 
Oct 2  VI. Laplace Transform: definition, initial value problems.
MIDTERM I 
6.1, 6.2 
6.1: 3, 7, 19, 23, 27
6.2: 1, 9, 11, 17, 22, 27, 29 Enrichment problems, not required: Gamma functions: 6.1.30, 31 
6.1: 3, 6, 15, 17, 21
6.2: 1, 7, 8, 13, 16, 19, 21 Enrichment problems, not required: Gamma functions: 6.1.23, 24 
Lecture 24

Oct 9  VI. Laplace Transform: step functions, IVPs with discontinuous functions, impulse functions.  6.3  6.5 
6.3: 3, 12, 15, 17, 21, 33, 34, 35
6.4: 10, 13, 15, 19 6.5: 7, 11, 13, 18, 23 
6.3: 2, 8, 10, 12, 15, 23, 24, 25
6.4: 6, 8, 10, 15 6.5: 5, 7, 9, 14, 17 
Lecture 27
Lecture 28 Lecture 29 Lecture 30 
Oct 16 
VI. Laplace Transform: Convolution integrals.
VII. Systems of first order linear equations: 2x2 matrices, linear systems of differential equations. 
6.6, 7.17.5 
6.6: 1, 7, 9, 15, 18, 22
7.1: 1, 11, 18, 23 7.2: 1, 8, 23 7.3: 13, 17, 20, 29 7.5: 15, 27, 33 Enrichment problems, not required: The Tautochrone: 6.6.29 
6.6: 1, 6, 8, 12, 14, 17
7.1: 1, 9, 15, 20 7.2: 1, 7, 17 7.3: 11, 15, 17, 24 7.5: 10, 19, 25 Enrichment problems, not required: The Tautochrone: 6.6.22 
Lecture 31
Lecture 32 Lecture 33 Lecture 34 
Oct 23  VII. Systems of first order linear equations: Linear systems of differential equations.  7.5  7.9 
7.5: 3, 19, 20, 25
7.6: 5, 13, 21, 26, 28 7.8: 3, 7, 13, 16 7.9: 1, 3, 7, 13 Enrichment problems, not required: Variation of parameters: 7.9.5, 15 Laplace transforms: 7.9.18 
7.5: 3, 13, 14, 18
7.6: 3, 11, 16, 21, 23 7.8: 3, 6, 11, 14 7.9: 1, 2, 5, 9 Enrichment problems, not required: Variation of parameters: 7.9.4, 11 Laplace transforms: 7.9.17 
Lecture 35
Lecture 36 Lecture 37 Lecture 38 
Oct 30  VII. Systems of first order linear equations: Inhomogeneous systems.
IX. Nonlinear Systems: Nonlinear systems of equations and stability. 
9.1  9.4 
DUE MONDAY NOV 13; TAKE HOME Quiz 11 DUE NOV 13
9.1: 7 (omit (d)), 13, 18, 20, 21 9.2: 7, 13, 15, 17, 24 (715 use pplane, don't need to turn in graph) 9.3: 13, 15, 17, 23 9.4: 5, 12, 17 Enrichment problems, not required: Bifurcations: 9.4.13, 15 
DUE MONDAY NOV 13; QUIZ 11 is TAKEHOME
9.1: 7 (omit (d)), 11, 15, 17, 18 9.2: 6, 10, 12, 14, 20 (612 use pplane, don't need to turn in graph) 9.3: 10, 12, 14, 20 9.4: 3, 10, 15 Enrichment problems, not required: Bifurcations: 9.4.11, 13 
Lecture 39
Example from Lecture 39. Lecture 40 Lecture 41 Lecture 42 
Nov 6  IX. Nonlinear Systems: Nonlinear systems of equations and stability.
X. PDEs and Fourier Series: Twopoint boundary value problem, Fourier Series and convergence MIDTERM II MONDAY 
9.39.4, 10.1  10.3 
Lecture 43
Lecture 44 Lecture 45 

Nov 13  X. PDEs and Fourier Series: even & odd functions, separation of variables, heat conduction.  10.4  10.6 
10.1: 16, 19
10.2: 3, 7, 11, 21 10.3: 3, 7, 14, 17 10.4: 5, 6, 11, 19, 37 10.5: 3, 5, 12, 17 (omit (d)), 18 10.6: 9, 13, 21, 23 Sample Mathematica script to help you plot partial sums and errors. Enrichment problems, not required: 10.1: 11, 13, 21 10.4: 35, 36 
10.1: 16, 19
10.2: 3, 7, 11, 21 10.3: 3, 7, 14, 17 10.4: 5, 6, 11, 19, 37 10.5: 3, 5, 12, 17 (omit (d)), 18 10.6: 9, 13, 21, 23 Sample Mathematica script to help you plot partial sums and errors. Enrichment problems, not required: 10.1: 11, 13, 21 10.4: 35, 36 
Lecture 46
Lectures 45/46 MATLAB demo script. Lecture 47 Lecture 48 Lecture 48 MATLAB demo script. Lecture 49 
Nov 20  THANKSGIVING BREAK  
Nov 27  X. PDEs and Fourier Series: Laplace equation.  10.8  10.8: 3, 5, 7, 9, 11, 14, 16  10.8: 3, 5, 7, 9, 11, 14, 16 
Lecture 50
Lecture 51 Lecture 52 
Dec 4  X. PDEs and Fourier Series: Wave equations, d'Alembert solution of the wave equation in an infinite string.
FINAL EXAM REVIEW 
10.7 
10.7: 7 (omit (d)), 9, 11 (omit (d)), 15, 16, 21
Enrichment: 10.7.22, 23 
10.7: 7 (omit (d)), 9, 11 (omit (d)), 15, 16, 21
Enrichment: 10.7.22, 23 
Lecture 53
Lecture 5355 MATLAB demo script. Lecture 54 Lecture 55 