This is a course about differential equations (equations that involve functions and their derivatives) and how to solve such equations.

The equations show often as models for natural phenomena like motion of wave, distribution of heat, motion of pendulums and springs.

We also would be interested in the qualitative behavior of solutions which for example would tell us what happen for the motion of waves and springs after long time.

It turns out that linear algebra and calculus are the main tools to solve differential equation and understand their behavior.

Thus we spend a portion of class to learn about basic concepts and tools of linear algebra. We will roughly cover chapters 10, 3, 11, 12, 13 and some selected topics from our textbook.

Our emphasize would be on examples, solving problems and application, although understanding of the basic concepts would be crucial for solving problems.

Prerequisite: MAT 307 or MAT 205 and MAT 211.

MW 4-5:20 pm,

Earth&Space 069.

Office hours: M 1-2pm, W 11am-noon MLC: W 6-7pm,

Email: babak.modami@stonybrook.edu.

Office: MATH Tower S-240A,

Office hours: Tu 4-5pm, MLC: W 5-7pm,

Email: jared.krandel@stonybrook.edu.

No late homework will be accepted except under very exceptional circumstances.

No make-up exams will be given. If a midterm exam is missed because of a serious (documented) illness or emergency, your semester grade will be determined on the basis of other work done in the course. Exams missed for other reasons will be counted as failures.

Also new announcements and various documents like lecture notes and sample exams will be posted on the blackboard.

Week of | Topics | Problems due | Due date |
---|---|---|---|

Jan 27 | First-order differential equations: 10.1: Direction fields 10.2: Separation of variables 10.3: linear equations, integrating factors |
10.1A: 2, 3, 7, 9, 11, 12, 19, 20 10.2: 3, 9, 18, 19, 21 10.3: 3, 4, 6 ,7, 11, 19 |
Feb 5 |

Feb 3 | Vector spaces and linearity: 3.1: Linear Maps/Euclidean spaces 3.2: Vector Spaces 3.3: Linear Maps/Vector spaces |
the exercise was given in the class, 3.1: 4, 6, 8, 13, 16 |
Feb 12 |

Feb 10 | 3.4 Image and Null Space 3.5 Coordinates and Dimension 3.6 Eigenvalues and Eigenvectors |
3.2 : 6, 7, 11(a), 16, 20, 23 3.3: 13, 17(a) 3.4: 16, 18. |
Feb 19 |

Feb 17 | 3.6 Eigenvalues and Eigenvectors 3.7 Inner Products |
3.5AB : 4, 8, 15, 24 3.5C: 4 3.6A: 4, 6 3.7A:1, 4 |
Feb 26 |

Feb 24 | Ch.3/Ch.10/Midterm Review 1 Midterm 1, Wed. Feb 26 |
no homework | NA |

March 2 | Second-order differential equations: 11.1 Differential Operators 11.2 Complex Solutions |
3.7B: 2,3, 4 11.1: 8, 13, 11.2A: 16, 21, 22, 31 |
March 11 |

March 9 |
11.2 Higher Order Equations 11.3 Non-homogeneous Equations 11.4 Oscillations |
11.2BC: 3,9 11.3AB: 1, 2, 5,10 11.3CD: 2, 9 11.4: 4,5, 9. |
March 30 |

March 16 | Spring break (have fun) | ||

March 23 | 11.5 Laplace Transform 11.6 Convolution |
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March 30 |
12.1 Vector Fields 12.2 Linear Systems |
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April 6 | 13.1 Eigenvalues/vectors 13.2 Matrix exponentials |
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April 13 | -- Midterm Review 2 Midterm 2 April 15 |
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April 20 | 13.4 Equilibrium and Stability 13.4 Nonlinear Systems |
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April 27 | 14.6 Differential Equations 14.7 Power Series Solutions |
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May 4 | Final Review | ||

May 11 | Final exam on May 12 | ||