## Math 420 (Differential Equations) - Spring 2015

**Course Documents**

- Syllabus
- Course Calendar
- WinPlot (download below)

wp32z.exe | |

File Size: | 874 kb |

File Type: | exe |

**First-Order ODEs**

**Section 1.1 -**

**Definitions and Terminology**

**:**3, 5, 9, 13, 17, 19, 23, 27, 33, 41

**Section 1.2 -**

**Initial Value Problems**

**:**5, 9, 13, 15, 21, 27, 33, 37, 41

**Section 2.2 - Separable Equations:**13, 19, 21, 25, 27, 33, 49, 55

**and**3.1.1, 3.1.5, 3.1.9

**Section 2.3 - Linear Equations:**5, 11, 17, 23, 24, 29, 33, 39, 47

**and**3.1.17, 3.1.21, 3.1.27

**Section 2.4 - Exact Equations:**5, 10, 15, 19, 25, 27, 29, 31, 35, 37, 45

**Section 2.5 - Solutions by Substitutions:**5, 11, 15, 21, 25, 29, 36, 38

**Section 2.6 - A Numerical Method:**1, 3, 7, 11, 12

**Higher-Order ODEs**

**Section 4.1.1 -**

**Initial-Value and Boundary-Value Problems**

**:**1, 3, 9, 13

**Section 4.1.2 - Homogeneous Equations:**17, 21, 25, 29

**Section 4.1.3 - Non-homogeneous Equations:**35, 38, 40

**Section 4.2 - Reduction of Order:**5, 9, 13, 17, 19, 21

**Section 4.3 - Homogeneous Linear Equations with Constant Coefficients:**1, 17, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61

**Section 5.1.1 - Spring/Mass Systems: Free Undamped Motion:**6, 7, 11 (this is a great review of trig)

**Section 5.1.2 - Spring/Mass Systems: Free Damped Motion:**20, 23, 25, 27

**Section 4.5 - Undetermined Coefficients - Annihilator Approach:**22, 30, 42, 48, 54, 70

- Suggested Practice Problems (do not turn in): Any of the odd-numbered problems

**Section 5.1.3 - Spring/Mass Systems: Driven Motion:**32

- Suggested Practice Problems (do not turn in): 29, 31, 33, 37

**Section 4.6 - Variation of Parameters:**4, 9, 17, 22, 28

- Suggested Practice Problems (do not turn in): 1, 3, 5, 6, 11, 13, 15, 19, 21, 25, 27

**Section 4.7 - Cauchy-Euler Equation:**7, 11, 13, 15, 21, 29, 37, 41

- Suggested Practice Problems (do not turn in): 1, 3, 5, 9, 17, 19, 23, 25, 27

**Series Solutions and Laplace Transforms**

**Section 6.1 - Review of Power Series:**5, 13, 17, 19, 21, 29, 33, 37

- Suggested Practice Problems (do not turn in): Any of the odd-numbered problems

**Section 6.2 - Solutions About Ordinary Points:**1, 9, 15, 21, 23

**Section 7.1 - Definition of the Laplace Transform:**17, 25, 31, 35, 39

- Suggested Practice Problems (do not turn in): 11 - 39 odd

**Section 7.2.1 - Inverse Transforms:**7, 15, 21, 27

- Suggested Practice Problems (do not turn in): 1 - 29 odd

**Section 7.2.2 - Transforms of Derivatives:**33, 37, 39

- Suggested Practice Problems (do not turn in): 31 - 39 odd

**Section 7.3.1 - Translation on the s-Axis:**10, 19, 29, 33

- Suggested Practice Problems (do not turn in): 1 - 29 odd

**Section 7.3.2 - Translation on the t-Axis:**41, 45, 51, 57, 67, 71

- Suggested Practice Problems (do not turn in): 37 - 71 odd

**Section 7.4.1 - Derivatives of a Transform:**5, 13, 17

- Suggested Practice Problems (do not turn in): 1 - 13 odd

**Section 7.4.2 - Transforms of Integrals:**25, 29, 33, 39, 45

- Suggested Practice Problems (do not turn in): 19 - 33 odd, and 37 - 45 odd

**Section 7.4.3 - Transform of a Periodic Function:**51, 53

- Suggested Practice Problems (do not turn in): 49

**Systems of Differential Equations**

**Section A.II.1 - Matrices: Basic Definitions and Theory**

- Suggested Practice Problems (do not turn in): 1 - 29 odd

**Section A.II.2 - Matrices: Gaussian and Gauss-Jordan Elimination**

- Suggested Practice Problems (do not turn in): 31 - 45 odd

**Section A.II.3 - Matrices: The Eigenvalue Problem**

- Suggested Practice Problems (do not turn in): 47 - 55 odd

**Section 8.1 - Preliminary Theory - Linear Systems:**5, 9, 15, 19, 21

- Suggested Practice Problems (do not turn in): 1 - 23 odd

**Section 8.2.1 - Homogeneous Linear Systems: Distinct Real Eigenvalues:**11, 13

- Suggested Practice Problems (do not turn in): 1 - 13 odd

**Section 8.2.2 - Homogeneous Linear Systems: Repeated Eigenvalues:**23, 29

- Suggest Practice Problems (do not turn in): 19 - 29 odd

**Section 8.2.3 - Homogeneous Linear Systems: Complex Eigenvalues:**37, 45

- Suggested Practice Problems (do not turn in): 33 - 45 odd

**Section 8.3.1 - Nonhomogeneous Linear Systems: Undetermined Coefficients:**3, 9

- Suggested Practice Problems (do not turn in): 1 - 9 odd

**Section 8.3.2 - Nonhomogeneous Linear Systems: Variation of Parameters:**17, 27, 31

- Suggested Practice Problems (do not turn in): 11 - 31 odd