Differential Equations โ 2009 Course Outline
Week Dates Sections
1Jan 12 - 16
1.1: Definitions and Terminology
1.2: Initial Value Problems
1.3: Mathematical Models
2.1: Direction Fields
2Jan 19 - 23
No class January 19
2.1: Phase Portraits
2.2: Separable Equations
3Jan 26 โ 30 2.3: First Order Linear Equations
3.1: Modeling with First Order Linear Equations
4Feb 2 - 6
2.4: Exact Equations
2.5: Solutions by Substitution
Group Work 1
5Feb 9 - 13
Exam 1
4.1.1: Existence/Uniqueness Theorem
4.1.2: Linear Independence and the Wronskian, Fundamental
Set
6Feb 16 - 20
4.3: Homogeneous Linear Equations with Constant Coefficients
(Distinct Real Roots)
4.3: Homogeneous Linear Equations with Constant Coefficients
(Repeated Real Roots)
4.2: Reduction of Order
7Feb 23 - 27
4.3: Homogeneous Linear Equations with Constant Coefficients
(Conjugate Complex Roots)
4.3: Higher-Order (H) Linear Equations with Constant
Coefficients
4.1.3: Theory: Nonhomogeneous Equations
8Mar 2 - 6 4.4: Method of Undetermined Coefficients - Superposition
4.6: Variation of Parameters
9Mar 9 - 13
4.7: Cauchy-Euler Equations (H) and (NH)
Group Work 2
Exam 2
10 Mar 16 - 20
5.1.1: Spring/Mass Systems: Free Undamped Motion
5.1.2: Spring/Mass Systems: Free Damped Motion
5.1.3: Spring/Mass Systems: Driven Motion
March 23 - 27 S p r i n g B r e a k W e e k
11 Mar 30 โ Apr 3
5.2: Eigenvalues; Deflection of a Beam
6.1.1: Review of Power Series
6.1.2: Power Series Solutions About Ordinary Points
12 Apr 6 - 10
6.1.2: Power Series Solutions About Ordinary Points
7.1: Definition of the Laplace Transform
7.2: Solving Linear IVPs Using Laplace Transforms
13 Apr 13 - 17
7.3.1: First Translation Theorem
Group Work 3
Exam 3
14 Apr 20 - 24 3.3: Modeling with Systems of Linear Equations
4.8: Solving Systems of Linear Equations by Elimination
15 Apr 27
May 1
Group Work 4
Comprehensive Final Exam (Friday, 12:30 โ 2:30)
