Nagle, Saff, and Snider, p. 5.

2. Type of equation, variables, linearity.
3. Type of equation, variables, linearity.
5. Type of equation, variables, linearity.
6. Type of equation, variables, linearity.
8. Type of equation, variables, linearity.

5. Check an explicit solution (failure).
8. Check an explicit solution (success).
11. Check an implicit solution.
13. Check an implicit solution to second order differential equation (success).
17. Plotting a family of solutions.
20. a) Find m so that exp(m*x) is a solution.
22. a) Initial value problem.

4. Use of DEplot for direction fields.
6. Second derivative of solution curve from first order equation.
10. c) Use of DEplot for direction fields.

Nagle, Saff, and Snider, p. 28.

5. Euler's Method via dsolve/numeric.
8. Euler's Method via dsolve/numeric.
9. Plotting Euler method output with specified stepsize.

23. Separable initial value problem.
26. Separable initial value problem.

Nagle, Saff, and Snider, p. 59.

14. First order linear equation, not in standard form.
22. First order linear initial value problem, not in standard form.
25. First order initial value problem, general solution.
30. Bernoulli equation.
32. Discontinuous forcing term using dsolve, piecewise, plot.

21. Exact initial value problem.
29. Integrating factors for exact equations. Check for solution.

15. Homogeneous equation to separable equation, substitution techniques.
21. Bernoulli equation to first order linear equation, substitution techniques.

Nagle, Saff, and Snider, p. 104.

1. Salt solution problem with dsolve.
15. Logistic growth in alligator populations.
17. Forward difference derivative, least squares logistic curve fit.
25. Radiocarbon dating.
26. Sensitivity analysis of radiocarbon dating.

4. Cooling problem.
11. Cooling: a car with air conditioner.
15. Stefan's law of radiation. Separation of variables.

7. Parachutist, classical approach to discontinuity.
9. Free fall in a fluid.
18. Friction on an inclined plane.
25. Escape velocity.

8. Heun or improved Euler method vs. forward Euler.
19. Heun or improved Euler method for logistic models.

Nagle, Saff, and Snider, p. 143.

5. Taylor approximation methods of order 2 and 4.
9. Runge Kutta approximation for differential equation in #5.
12. Tabular output for Runge Kutta.

19-22. Linear second order equation or not? Theorem 2: existence and uniqueness of solutions for second order initial value problems.
30. Boundary value problem solution possibilities.
31. Initial value problem and derivatives of solutions.

7. Independent solutions for initial value problem.
13. Linear combinations from fundamental solution sets.
15. b) Properties of the Wronskian determinant.
18. Linearly independent functions for which the Wronskian determinant is identically zero.
19. Wronskian from the equation.
20. Derivation of Abel's Identity.
21. Simultaneous zeros of independent solutions.

Nagle, Saff, and Snider, p. 181.

5. Reduction of order, long version.
10. Reduction of order, reduction of order formula.

19. Second order linear constant coefficient initial value problem.
26. Third order linear constant coefficient equation.
46. From Cauchy-Euler equation to constant coefficient equation.
49. a) Numerical approximation to eigenvalues.
50. Repeated roots and reduction of order.

22. Complex eigenvalue initial value problem.
29. a) Third order equation, complex eigenvalues.
41. a) Repeated complex eigenvalues.

Nagle, Saff, and Snider, p. 203.

4. Superposition.
11 c). Superposition.
18. Reduction of order for nonhomogeneous equations. DESol.

10. Linear independence of functions.
17. Independence of solutions of a differential equation.
19. Third order initial value problem.

29. Fourth order general solution, approximate eigenvalues. No annotations on assume.

15. General solution, second order, undetermined coefficients.
31. Initial value problem, second order, undetermined coefficients.
51. Nonhomogeneous Cauchy-Euler.

18. Annihilate a function.
21. Form of a particular solution by annihilators.

10. Variation of parameters, long form.
21. Nonhomogeneous Cauchy-Euler.
22 Nonhomogeneous Bessel equation of order one half.
24. Variation of parameters, with Wronskian.
27. Nonhomogeneous solutions with definite integrals. Numerical integration.

3. Variation of parameters, third order.

Nagle, Saff, and Snider, p. 214.

3. Conversion of third order initial value problem to system.
5. Conversion of system to higher order equations.
22. Conversion of system to higher order equations.
29. Two tank mixing problem.

6. Harmonic motion.

7. Damped harmonic motion.

3. Forced vibrations and resonance.
10. Variation of parameters, long form.
21. Nonhomogeneous Cauchy-Euler.
22. Nonhomogeneous Bessel equation of order one half.
24. Variation of parameters, with Wronskian.
27. Nonhomogeneous solutions with definite integrals. Numerical integration.

3. Variation of parameters, third order.

Nagle, Saff, and Snider, p. 266.

6. From systems to higher order equations, undetermined coefficients.

5. Frequency response curve for LRC series circuit.

1. Runge-Kutta for higher order equations.

2. Verify a solution pair in a system.
3. Critical point set for a system.
7. Integral curves for an autonomous system, separable.
9. Integral curves for an autonomous system, exact.
13. Phase plane diagram, phaseportrait.
15. Phase plane diagram, phaseportrait.

Week10.mw

Nagle, Saff and Snider, p. 531.

11. System of scalar differential equations to matrix differential equation.

Nagle, Saff and Snider, p. 536.

Nagle, Saff, and Snider, p. 545.

6. a) Matrix product.
13. Matrix inverse.
15. d) Complete solution to a system with multiple solutions.
16. Singular matrix. No solutions, many solutions.
19. Inverse of a matrix with expression entries.
25. Determinant of a square matrix.
29. Forming the identity matrix. Characteristic equation.
30. Gauss Jordan reduction for inverses.
34. Derivative of a matrix.
38. Verifying that a matrix solves a differential equation.
39. Integrating a matrix.

1. System to matrix, genmatrix.
8. Higher order equation to matrix equation, companion matrix.
12. Matrix to system.
18. Linear dependence of vector valued functions.
22. Fundamental solution sets.
23. Superposition.

Nagle, Saff, and Snider, p. 565.

8. Eigenvalues and eigenvectors.
10. Eigenvalues and eigenvectors, complex.
17. Trajectories of solutions.
23. Fundamental matrix.
24. Fundamental matrix and verification.
29. Fundamental matrix, floating point decimals.
30. Fundamental matrix, matrix exponential.
33. Initial value problem with matrices.
35. Generalized eigenector solution.
42. Cauchy-Euler first order system.
43. Cauchy-Euler system.
47. Approximate solutions.
49. Stability.

1. General solution, complex eigenvalues.
7. Fundamental matrix, complex eigenvalues.
9. Fundamental matrix, complex eigenvalues.
13. a) Initial value problem, complex eigenvalues.
17. Cauchy-Euler with complex eigenvalues. Additionally, evalc.
21. RLC network.

11. Gauss-Jordan solution of systems of linear equations.

8. Nonhomogeneous matrix equation, undetermined coefficients.
13. Nonhomogeneous matrix equation, undetermined coefficients.
13.(bis) Nonhomogeneous matrix equation, variation of parameters.
21. a) Nonhomogeneous initial value problem, &* ".
35. Two tank mixing problem.

24. Matrix exponential solution to initial value problem.

Nagle, Saff, and Snider, p. 363.

7. Definition of Laplace transform.
12. Definition of Laplace transform. Piecewise,convert( ,Heaviside).
23. Piecewise, discont, plot.

9. Multiplication by t, multiplication by exp(c*t).
12. sin(3*x)*cos(3*x), Combine(  ,trig).
29. Transfer function, alias.
31. Translation in t.

3. Inverse Laplace transform, shifting.
11. Partial fractions.
19. Partial fractions.
24. Inverse Laplace transform from partial fractions.
33. Inverse Laplace, derivative by s.

Nagle, Saff, and Snider, p. 387.

7. Initial value problem by Laplace transform.
25. Initial value problem by Laplace transform.
29. General solution via Laplace transform.
37. Initial value problem via Laplace transform, non-constant coefficients.

5. Inverse Laplace transform, convolution.
13. Laplace transform of a convolution.
23. Transfer function, impulse response.

3. Dirac delta.
11. Laplace transform of Dirac delta.
21. Initial value problem with impulse, plot.
31. Stability.

10. Simultaneous differential equations and Laplace transforms.

Nagle, Saff, and Snider, p. 750.

7. Classification of a critical point for stability.
11. Classification of a critical point for stability.
15. Classification of a critical point for stability.
17. Classification of a critical point for stability.

1. Almost linear point at origin, stability.
11. Almost linear point, stability.
15. Almost linear point, stability.

Nagle, Saff, and Snider, p. 440.

6. Radius and interval of convergence of power series.
13. Product of power series.
16. Quotients of series.
20. Derivatives of power series.
34. Taylor series.
47. Series solution to Duffing's equation using dsolve.

11. Differential equation, power series solution.
25. Differential equation, power series solution, general term.

17. Differential equation, series solution, centered at Pi.