# Detailed weekly schedule

### (subject to minor fluctuations)

 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.   Have a good bayram!
*** Orthogonal trajectories
**** Wronskian

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