Week(s) | Topics | Textbook | Exams |

1 | Introduction to Differential Equations | Midterm I | |

- Examples of Differential Equations | 1.1 | ||

- Definitions | 1.2 | ||

- Families of Solutions | 1.3 | ||

- Geometric Interpretation; Isoclines | 1.4, 1.5 | ||

- Existence and Uniqueness Theorem | 1.6 | ||

2, 3 | First Order O.D.E. | ||

- Separation of Variables | 2.1 | ||

- Exact Equations | 2.4 | ||

- Linear Equations of Order One | 2.5, 2.6 | ||

- Homogeneous Functions and Equations | 2.2, 2.3 | ||

- Integrating Factors | 5.1, 5.2 | ||

- Substitution | 5.3 | ||

- Bernoulli's Equation | 5.4 | ||

- Equations With Linear Coefficients | 5.5 | ||

4 | Applications of First Order O.D.E.* (***) | 4.1 - 4.4 | |

5 | Linear O.D.E. | 6.1 | Midterm II |

- The Existence and Uniqueness Theorem | 6.2 | ||

- Linear Independence of Solutions; Wronskian (****) | 6.3, 6.4 | ||

- Structure of the Solution Set | 6.5, 6.6 | ||

- The Operator Notation | 6.7 - 6.9 | ||

6** - 8 | Solving Linear O.D.E. | ||

- Reduction of Order | 9.2, 16.8, 16.9 | ||

- Homogeneous Linear Equations with Constant Coefficients | 7.1 - 7.6 | ||

- Constructing an Equation from a Solution | 8.1 | ||

- Nonhomogeneous Equations: Undetermined Coefficients | 8.2, 8.3 | ||

- Nonhomogeneous Equations: Variation of Parameters | 9.3 | ||

- The Equation y''+y=f(x) | 9.4 | ||

9, 10 | Applications of Second Order O.D.E.* | ||

- Examples of Harmonic Oscillators | 10.1 | ||

- Undamped Vibration | 10.2 | ||

- Resonance | 10.3 | ||

- Damped Vibration | 10.4 | ||

- The Simple Pendulum | 10.5 | ||

- Planetary Motion; Kepler's Laws | 10.6 - 10.9 | ||

11 - 12 | Power Series Solution | Final | |

- Introduction | 17.1 | ||

- Power Series | 17.2 | ||

- Linear Equation at an Ordinary Point | 17.3-17.5 | ||

- Regular Singular Points; The Indicial Equation | 18.1, 18.2 | ||

- Linear Equation at a Regular Singular Point | 18.3-18.9, 18.12 | ||

- Solution for Large x | 18.10 | ||

13 - 14 | The Laplace Transform | ||

- The Transform Concept; Application to O.D.E. | 14.1 | ||

- The Laplace Transform | 14.2 | ||

- Transforms of Elementary Functions | 14.3 | ||

- Functions of Class "A" | 14.4-14.6 | ||

- The Laplace Transform and The Derivatives | 14.7, 14.8 | ||

- The Gamma Function | 14.9 | ||

- The Inverse Transform: Partial Fractions | 15.1, 15.2 | ||

- A Step Function | 15.4 | ||

- A Confolution Theorem | 15.5 | ||

- Initial Value Problem | 15.3 | ||

15 | Review and Catch-Up |

* Only selected topics will be considered in class

** Short week.

*** Orthogonal trajectories

**** Wronskian