DifferentialEquations

Web Site for dfield and pplane [| http://math.rice.edu/~dfield/dfpp.html] This course plan may be modified during the semester. Such modifications will be announced in advance during class periods, and the students are responsible for keeping abreast of such changes. The WWW page for the course will also be used to list assignments and other notes, and students are responsible for checking this web page regularly.
 * __TOPICS TO BE COVERED AND HOMEWORK ASSIGNED__**

1.1: 5 7 __13 15__ __21__ 23 __33 35__ 45

1.2: 9 __11__ 15 __25 27__ __31 35__

1.3: 5 7 __23__ 24 __25 26__

1.4: 5 __17 20 35 47__ __49 51__ 65

1.5: __7 12 16__ 29 __34 37 41__ 42

2.1: __11 12__ __22__ __23__ 39

2.2: __13 15 17__ 20 __21 22 23__ 29

2.3: __2 4 11__

2.4: 5 26 30

2.5: 25 26 29

2.6: 25 26 27

3.1: 11 __13 19 20 24__ 25 __33 35 39__

3.2: __1 5 7__ 11 __15 19 21__ 29 33 __34__

3.3: 5 __9 11 12 23 31__ 41 52 55

3.4: __3__ 5 12(a-c) __15 17 18 22__

3.5: 5 11 __23 25 27 29 37__ 45

<span style="font-family: 'Times New Roman',serif;">3.6: __4 7 11__ 21 24

<span style="font-family: 'Times New Roman',serif;">4.1: 5 __10 18 19 21 22 24 25 26__ 30

<span style="font-family: 'Times New Roman',serif;">4.3: __9 11 13__ 19

<span style="font-family: 'Times New Roman',serif;">5.2: __3 6 9 11__ 15 __19__ 27 31

<span style="font-family: 'Times New Roman',serif;">5.3: __1 6 8 11 16 18 21 23 only find eigenvalues and eigenvectors and explain from pplane__

//<span style="font-family: 'Times New Roman',serif;">5.4: 3 7 9 13 14 15 optional section //

//<span style="font-family: 'Times New Roman',serif;">5.5: 7 11 15 19 20 21 optional section //

//<span style="font-family: 'Times New Roman',serif;">5.6: 4 6 7 23 27 29 33 34 37 optional section //

//<span style="font-family: 'Times New Roman',serif;">5.7: 1 15 26 28 29 31 33 34 optional section //

<span style="font-family: 'Times New Roman',serif;">6.1: use pplane in all problems 5 __9 11__ __13 15 19__ 23 25

<span style="font-family: 'Times New Roman',serif;">6.2: use pplane in all problems __19 23 25 27 29__ __32__ 34 36

<span style="font-family: 'Times New Roman',serif;">6.3: use pplane in all problems, but find eigenvalues yourself __4-25 27__

//<span style="font-family: 'Times New Roman',serif;">6.4: 2 __5 7 14 17__ 18 optional section //

// // //  // //  //

** TOURO **** COLLEGE **** COURSE SYLLABUS **

** LANDER **** COLLEGE **
 * DEPARTMENT: ** Mathematics


 * COURSE TITLE: ** Differential Equations


 * COURSE NUMBER: 512 **


 * PREREQUISITES: ** MAT 121, 122 (Calculus I and II)


 * CREDIT HOURS: ** 4


 * DEVELOPER: ** Dr. Kaganovskiy


 * LAST UPDATE: 1/17/2011 **


 * __ COURSE DESCRIPTION __**

This course focuses on Differential Equations and Computational Methods.

It is intended for Mathematics and Science students who are going to apply these techniques in

their coursework. Reflecting the shift in emphasis from traditional methods to new computer-

based methods, we focus on the mathematical modeling of real-world phenomena as the goal

and constant motivation for the study of differential equations. Topics covered include standard

methods for 1st order equations (separation of variables, integrating factor for linear equation

etc), population models, equilibrium and stability, acceleration-velocity models, numerical

methods Euler, Improved Euler, Runge-Kutta, linear equations of higher order, resonance in

mechanical and electrical systems, systems of ODEs eigenvalues and numerical methods,

nonlinear systems with applications to population modeling and nonlinear mechanics, chaos, and

Laplace transform techniques.

The student will:
 * __ COURSE/DEPARTMENTAL OBJECTIVES __**
 * Learn about ordinary differential equation of 1st and higher orders.
 * Learn about numerical methods for ODEs, nonlinear systems and population modeling.
 * Learn applications of the above in physics, biology, and engineering.


 * __ COURSE/INSTITUTIONAL OBJECTIVES __**

This course is intended to teach students the basic concepts of differential equations. This should further professional and pre-professional career interests for students in the fields of science and business. Goals include the fostering of analytical and quantitative thinking, and the ability to solve problems and interpret data.


 * __ HARDWARE/SOFTWARE/MATERIALS REQUIREMENTS: __**
 * Maxima Computer Algebra System ** . Dfield and pplane programs

Homework Assignments
 * __ COURSE REQUIREMENTS __**

Midterm and Final Examinations


 * __ GRADING GUIDELINES __**

Students must take all exams. Grades are to be based on the weighted average of the grades in the examinations.

**__ METHODOLOGY __** Classroom lectures and assigned homework problems. Differential Equations and Boundary Value Problems Computing and Modeling 5 th Edition
 * __ COURSE TEXT __**

EDWARDS & PENNEY Publisher: Prentice Hall

Bibliography:

1) A First Course in Differential Equations [|Dennis G. Zill]

Brooks Cole; 9 edition (May 14, 2008) **ISBN-13:** 978-0495108245

2) Linear Algebra and Differential Equations [|**Alexander Givental**],

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