Math 2650 is a service course for a variety of programs as

well as an introductory course in Differential Equations for

students majoring in Mathematics. Because of this,

instructors may emphasize different topics depending on the

composition of individual sections. The following syllabus

attempts to take this in account by providing a variety of

optional sections to choose from. Suggested times for each

block are listed.

It is assumed that there will be 45 class periods. The

following outline uses between 36 and 38 days depending on the

chosen emphasis. Assuming that 4 days are set aside for

testing one is left with between 3 and 5 days that can be

used, e.g., for covering optional material.

At least five class days should be set aside for lab sessions

or computer presentations in order to satisfy the state

articulation agreement. The following sections are well suited

for this purpose: 1.4, 1.5, 3.2, 4.3, 4.7, and 5.1.

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Textbook: Introduction to Ordinary Differential Equations

Author: Stephen H. Saperstone

Chapters 1, 2, and 3: Introduction and First Order Equations

(1.1) Examples of ODEs ............................... 1 day

(1.2) Solutions of ODEs .............................. 1 day

(1.3) Separable Equations ............................ 2 days

(2.1) Linear Equations ............................... 2 days

(2.3) Exact Equations and Implicit Solutions.......... 1 day

(up to 7 Lectures)

(2.2) Reducible Equations........................ (Optional)

(2.4) Integrating Factors........................ (Optional)

(2.5) Reduction of Order (Optional)

(1.4) The Geometry of First-Order ODEs................ 2 days

(1.5) Numerical Estimation of Solutions............... 2 days

(1.6) Modeling with ODEs.............................. 3 days

(up to 7 Lectures)

(3.1) Solutions - Theoretical Matters................. 1 day

(3.2) Graphical Analysis.............................. 1 day

(up to 4 Lectures)

Chapters 4 and 5: Linear Second Order ODEs

(4.1) Introduction.................................... 1 day

(4.2) Homogenous Equations with Constant Coefficients 2 days

(4.3) Free Motion..................................... 1 day

(4.4) The Method of Undetermined Coefficients......... 3 days

(4.5) The Method of Variation of Parameters........... 2 days

(4.7) Forced Motion................................... 2 days

(5.1) Geometry of Second-Order ODEs.............. (Optional)

(5.4) Higher-Order Equations......... (See Note Below) 1 day

(up to 12 Lectures)

Remarks: In order to be in compliance with state articulation

you we must cover higher order equations with constant

coefficients. You can comply with requirement by assigning

the problems in Section (4.2) that involve higher order

equations, by covering higher order equations during coverage

of Laplace transforms, or by covering section (5.4). Allow at

least 1 day for this.

Chapter 6: Laplace Transforms

(6.1) Definition and Illustration..................... 1 day

(6.2) Operational Properties.......................... 1 day

(6.3) Discontinuous and Periodic Forcing Functions.... 1 day

(6.4) Solving Intitial Value Problems................. 2 days

(6.5) Convolution................................ (Optional)

(6.6) The Delta Fuction.......................... (Optional)

(up to 5 Lectures)

Remark: Section (6.4) needs to be covered. Since Sections

(6.1), (6.2), and (6.3) are rather long winded, you might

prefer to look for a quick way to get to (6.4).

Chapter 7: Series Solution of Linear Second-Order ODEs

(7.1) Power Series Methods............................ 2 days

(7.2) Solutions at an Ordinary Point.................. 1 day

(7.4) Solutions at a Regular Singular Point, Part I (Optional)

(7.5) Solutions at a Regular Singular Point, Part II(Optional)

(up to 3 Lectures)