| 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 |