This is an introductory course in ordinary differential equations with a particular emphasis on linear differential equations. A nuance of the present course is an early introduction of the Laplace transform into the theory, and then subsequently using the Laplace transform to extract much of the basic information about constant coefficient linear ordinary differential equations in an expedited manner. We will cover the following:

• Chapter 1: First Order Differential Equations. We will not cover all of this material.
• 1.1 An introduction to Differential Equations
• 1.2 Direction Fields
• 1.3 Separable Differential Equations
• 1.4 Linear First Order Equations
• 1.5 Substitutions; Homogeneous and Bernoulli Equations
• Chapter 2: The Laplace Transform
• 2.1 Laplace Transform Method: Introduction
• 2.2 Definitions, Basic Formulas, and Principles
• 2.3 Partial Fractions: A Recursive Method for Linear Terms
• 2.4 Partial Fractions: A Recursive Method for Irreducible Quadratics
• 2.5 Laplace Inversion
• 2.6 The Linear Spaces: Special Cases
• 2.7 The Linear Spaces: The General Case
• 2.8 Convolution
• Chapter 3: Second Order Constant Coefficient Linear Differential Equations
• 3.1 Notation, Definitions, and some Basic Results
• 3.2 Linear Independence
• 3.3 Linear Homogeneous Differential Equations
• 3.4 The Method of Undetermined Coefficients
• 3.6 Spring Systems or 3.7 RCL Circuits
• Chapter 4: Linear Constant Coefficient Differential Equations
• 4.1 Notation, Definitions, and Basic Results
• 4.2 Linear Homogeneous Differential Equations
• 4.3 Nonhomogeneous Differential Equations
• Chapter 5: Second Order Linear Differential Equations
• 5.1 The Existence and Uniqueness Theorem
• 5.2 The Homogeneous Case
• 5.3 The Cauchy-Euler Equations
• 5.5 Reduction of Order
• 5.6 Variation of Parameters
• Chapter 8: Matrices: This will only be a review and we will spend maximum of two hours on this material
• 8.1 Matrix Operations
• 8.2 Systems of Linear Equations
• 8.3 Invertible Matrices
• 8.4 Determinants
• 8.5 Eigenvectors and Eigenvalues
• Chapter 9: Linear Systems of Differential Equations
• 9.1 Introduction
• 9.2 Linear Systems of Differential Equations
• 9.3 The Matrix Exponential Function and its Laplace Transform
• 9.4 Fulmer's Method
• 9.5 Constant Coefficient Linear Systems

Homework is assigned daily for discussion during the following hour. Homework for grading will be assigned twice a week, mostly on Tuesday and Thursday. Doing the homework exercises as they are assigned is the best strategy for a successful completion of the course. I will work out some of the problems (2 or so) in class the next day after each section was covered in class.. Here is a list of probable homework (graded or not). The list of problems from Sections 8 and 9 will be added later.

Section	Homework
1.1	1, 5, 7, 9, 11, 13, 15, 17, 19, 21,25,27, 32, 36
1.2	5-15 (Odd)
1.3	11, 14, 15, 17, 19, 24, 27, 31, 33, 34
1.4	1, 3, 5, 9, 13, 16, 17, 21, 26, 29, 31
1.5	1, 3, 5, 9, 11, 13, 15
2.1	1 -35 (Odd)
2.2	12, 13, 15, 18, 19, 20, 23, 25, 27
2.3	7, 9, 11, 13
2.4	1, 3, 6, 9, 10, 13, 15, 19, 21, 23, 25, 27, 29, 31
2.5	1 -7, 15-39 (Odd)
2.6	1, 3, 5, 7, 9, 11, 15 -31 (Odd)
2.7	1, 3, 5, 7, 9, 11, 15, 19,
2.8	1, 3, 5, 7, 9, 15, 17, 19, 23-31 (odd). 33, 35, 37
3.1	1-15 (Odd)
3.2	1-17 (Odd)
3.3	1-15(Odd)
3.4	1-21 (Odd)
3.6	1-14
4.1	1-11 (Odd), 14, 18, 26, 29, 33
4.2	All odd problems.
4.3	1-15 (Odd)
4.6	1-15 (Odd)
5.1	1-8, 9-15 (Odd), 25, 28
5.2	1-23 (Odd), 28-42
5.3	1-11 (Odd)
5.5	1-11 (Odd)
5.6	1-15 (Odd)

The final takes place Tuesday, Tuesday, Dec. 7, 12:30-2:30, in the same room as class. The final counts 150 points.

Grading

• Tests: 100 each. Total: 200.
• Homework: 100
• Final: 150.
• Total points: 450.

Grades: A ≥ 405, B ≥ 360, C ≥ 315, D ≥ 270, and F<270.

Absence on a Test, or Final without excuse makes automatically 0 points. Please inform me before the test

Note: We are meeting 35 times. 2 of those days are reserved for tests. I am expecting that few days will be used for review of the material (for tests and for the final). There are 37 sections to be covered, so in average, we will be covering more than a sections per day!

Students are asked not to use their cell phone during the class. I do not want to see any cell phones during tests. Students are asked to arrive on time and not to leave before the class is over.

Important dates

1. Classes start Monday, June 8, 2015
2. First Test, Thursday, June 25, 2015
3. No class, Friday, July 3, 2015
4. Second Test, Tuesday, July 21, 2015
5. Last class, July 27, 2015
6. Final, Thursday, July 30, 4:00-6:00 PM, 2015