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

Jan 8  I. Introduction: what is a DE, order, linear and nonlinear, solutions, direction fields. II. First Order Differential Equations: separable equations, integrating factors. 
1.11.3, 2.12.3. 
1.1: 7, 15
1.2: 7, 21, 27, 31 1.3: 1, 7, 10cd, 17 2.2: 3, 5, 15, 17, 25, 29, 33, 39 2.3: 3, 5, 7, 15, 19, 21, 23 Enrichment, not for credit: 1.2.19, 2.3.29 
Lecture 1
Lecture 2 Lecture 3 Lecture 4 
Jan 15  II. First Order Differential Equations: exact equations, special integrating factors, substitutions and transformations  2.4  2.6. 
2.4: 1, 3, 5, 13, 17, 23, 25, 27
2.5: 1, 3, 5, 9, 11, 13, 20 2.6: 11, 15 Enrichment, not for credit: 2.4.32, 2.6.47 
Lecture 5
Lecture 6 Lecture 7 
Jan 22  II. First Order Differential Equations: substitutions and transformations
III. Modeling with Firstorder equations 
2.6, 3.13.5 
2.6: 1, 3, 7, 17, 27, 31, 42
3.2: 7, 14, 15, 21, 25 3.3: 5, 12 3.5: 1, 5 Enrichment, not for credit: 2.6.47, 3.3.15, 3.4.20 
Lecture 8 and examples.
Lecture 9 Lecture 10 Lecture 11 
Jan 29  IV. Second order linear equations: homogeneous equations: general solution, auxiliary equations, real, complex, an repeated roots. Nonhomogeneous equations: method of undetermined coefficients.  4.14.4 
3.4: 9, 19, 25
4.1: 2 4.2: 7, 11, 17, 19, 27, 29, 46 4.3: 17, 23, 25, 31 (do not solve), 32, 33 Enrichment, not for credit: 4.2.21, 23, 35ab, 37; 4.3.19, 27 
Lecture 12
Lecture 13 Lecture 14 Lecture 15 
Feb 5  IV. Second order linear equations: Nonhomogeneous equations: method of undetermined coefficients, variation of parameters. Variablecoefficient equations.  4.44.8 
4.4: 1, 3, 5, 7, 15, 21, 23, 27, 29, 31
4.5: 1, 9, 15, 29, 35, 43 4.6: 5, 15 4.7: 1, 5,37 Enrichment, not for credit: 4.4.35, 4.8.15 (good intuition building!) 
Lecture 16
Lecture 17 
Feb 12 
IV. Second order linear equations: forced vibrations and free vibrations. 
4.94.10 
4.7: 11, 13, 15, 45, 47
4.8: 11 (selfstudy) 4.9: 3, 5, 7, 11 4.10: 1, 3, 5, 9, 11 Enrichment, not for credit: 4.8.6 (conservation of energy!) 
Lecture 19 Lecture 20 Lecture 21 Lecture 22 
Feb 19 
V. Higher order linear equations: Solving constantcoefficient higherorder linear equations. VII. Laplace transforms: Definitions, properties. MIDTERM I THURSDAY 
6.16.2, 7.17.3 
6.1: 5, 7, 8, 21
6.2: 1, 5, 9, 13, 19, 31 7.2: 3, 11, 13, 19, 23, 25, 27, 29 
Lecture 25

Feb 26  VII. Laplace transforms: inverse, initial value problems, discontinuous functions.  7.37.6 
7.3: 1, 7, 17, 21, 24, 31
7.4: 11, 19, 29, 35 7.5: 11, 13, 21, 27, 31, 37 7.6: 3, 5, 7 (step fns only) Enrichment, not for credit: 7.3.22, 7.3.37, 7.4.37, 7.4.42, 7.4.43 
Lecture 26
Lecture 27 Lecture 28 Lecture 29 
Mar 5  SPRING BREAK  
Mar 12  VII. Laplace transforms: convolution, impulses.  7.67.8 
7.6: 11, 17, 19, 21, 27, 33, 39, 59
7.7: 3, 9, 13, 19, 21, 25, 27, 29, 31 (solve IVP only for 25, 27) 7.8: 3, 5, 9, 11, 17, 19, 23, 29 Enrichment, not for credit: 7.8.35 
Lecture 30
Lecture 31 Lecture 32 Lecture 33 
Mar 19  VI. Systems of differential equations: phase plane analysis and applications; solving homogeneous linear systems, linear algebra review. 
5.1, 5.4, 9.39.5 
5.4: 11, 18, 19, 27, 28, 33
9.3: 5, 9, 21, 27, 35 9.4: 1, 9, 15, 25 9.5: 3, 11, 17, 19, 31, 45 
Lecture 34
Lecture 35 Lecture 36 Lecture 37 
Mar 26  VI. Systems of differential equations: Solving linear systems, analysis of nonlinear systems.  9.59.8; 12.2. 
9.6: 1, 13ab, 19
9.7: 9.7.1, 7, 25, 26a 12.2: 5, 13, 14, 15, 16, 19, 20 (1320: find general solution too, and try to sketch by hand), 21 Enrichment, not for credit: 9.6.21, 9.8.17 
Lecture 38
Lecture 39 
Apr 2 
VII. Nonlinear systems of ODEs.
MIDTERM II WEDNESDAY 
12.3, 10.1  10.3  12.3: 11, 13, 15, 17, 19, 21 (also check nullclines for 13, 15) 
Lecture 42
Lecture 43 Lecture 44 Comp model phase plane 
Apr 9 
VIII. PDEs and Fourier Series: Separation of variables, Fourier series, Fourier sine and cosine series  10.110.4 
10.2: 5, 13, 17, 21, 24., 27, 28., 30., 31, 33
10.3: 1, 3, 5, 7, 11, 15, 19, 23, 25a, 28, 37 Enrichment, not for credit: 10.3.29, 10.3.3139 To plot partial sums and errors: Mathematica file. Free access to Mathematica via WebApps. 
Lecture 45
Lecture 46 Lecture 47 Lecture 48 Matlab Fourier series demo 
Apr 16  VIII. PDEs and Fourier Series: Fourier sine and cosine series, Heat equation, Wave equation.  10.410.6 
10.4: 3, 9, 15, 17
10.5: 9, 11, 13, 15, 19 10.6: 5, 7, 9, 11, 19 Enrichment, not for credit: 10.6.2021 
Lecture 49
Lecture 50 Lecture 51 Lecture 52 Matlab heat eq. demo Matlab wave eq. demo 
Apr 23  VIII. PDEs and Fourier Series: Laplace equation.
FINAL EXAM REVIEW 
10.7 
10.6: 15, 17
10.7: 3, 9, 11, 17, 23 
Lecture 53
Lecture 54 Lecture 55 