Math 484 Applied Mathematics II Spring 2007

Instructor: Dr. J. Hou

Location:                    Brown Hall, Suite B183                   

Phone Number:         823 - 9135

E-mail:                        jhou@nsu.edu

Office Hours: Monday:        9:00 – 11:00

                                     Tuesday:       3:00 – 4:00

                                     Wednesday:  10:00 – 12:00

                         Thursday:     11:00 – 12:30

                                     Friday:          9:00 – 11:00, 2:00 – 3:00

Credits:             3 semester hours

Text: Advanced Engineering Mathematics, Sixth edition, Peter V. O’Neil

Prerequisite:     Math 384

Course Description:

This course is a continuation of Math 384, Introduction to Applied Mathematics I.  It is a senior level course containing advanced topics in mathematical and scientific applications. Topics vary, but may include partial differential equations, Fourier analysis and boundary value problems, with selected applications in mathematical physics and engineering. The course integrates some applications of partial differential equations with computer activities.

Course Rationale:

Differential equations provide a powerful tool for solving and analyzing many practical problems of mathematics, science, and engineering.  The applications to engineering, physics, and science generally are of the greatest importance.  This course is one of the required applied mathematics core courses and highly recommended course in both physics and engineering programs. 

Applied mathematics involves the relationships between mathematics and its applications.  The focus of this course is placed on partial differential equations in both finite and infinite domains to address the three fundamental aspects of applied mathematics:  modeling, analysis, and interpretation of results.  Special functions are introduced in relation to solving PDEs in different coordinate systems. 

Course Goals and Measurable Intended Student Learning Outcomes

The primary goals of this course are to study partial differential equations, their solutions with Fourier series and Fourier/Laplace transformations, as well as their applications in various areas of science and engineering.  Students, upon completion of this course, will be able to: 

Ø Find the Fourier series of a function and understand the convergence theorem.

Ø Solve the linear wave equations, heat equations and potential equations in finite rectangular region by separation of variables and Fourier series.

Ø Deal with non-homogeneous boundary conditions and equations.

Ø Apply the definition of the Fourier transform in deriving the Fourier transform of a function.

Ø Find the inverse Fourier transform.

Ø Utilize the Fourier transform and related theorems to solve a boundary-initial value problem in an infinite or semi-infinite domain.

Ø Use partial differential equations to model physics problems in wave, heat transfer, etc.

Ø Understand the origin and application of special function in solving boundary value problems involving PDEs.

Ø Use the solution (graphically) to interpret the models involving PDEs.

Course Requirements:

Each student should :

Ø Prepare for each lecture by reading the appropriate topic(s).

Ø Devote a minimum of 15 hours per week for preparation.

Ø Attend all lectures and keep a notebook of lecture notes and solved problems.

Ø Complete and turn in all assignments on time.

Available Supplements:

Solutions manual can be ordered through the bookstore.  The following computer software are available:  Maple, Mathcad, and Mathematica. 

Primary Methods of Instruction/Methods to Engage Students:

Ø Students will be required to complete four homework sets.

Ø There will be two hours of lecture and discussion and one hour of intense problem solving session every week.

Ø Students are required to complete a project and present their outcomes.  The project must incorporate at least one of the available computer software and be presented using Microsoft PowerPoint presentation. 

TOPICS OUTLINE

Text:

Topics:

Assignments to be collected:

Sec. 13.1-6 – Review of Fourier series                                            #

Sec. 17.1 – Wave Equation, Initial & Boundary Conditions          #1,3,4,5

Sec. 17.2 – Fourier Series Solutions of Wave Equations                 #1,3,4,7,9,11

Sec. 18.1 – Heat Equation, Initial & Boundary Conditions            #1,3

Sec. 18.2 – Fourier Series Solutions of Heat Equations                  #2,4,7,9,11,13,15

Sec. 19.1 – Harmonic Functions and the Dirichlet Problem            #1(f),3

Sec. 19.2 – Dirichlet Problem for a Rectangle                                 #1,4

Exam 1

Sec. 17.7 – Vibrations of a Rectangular Membrane                        #1

Sec. 18.5 – Heat Conduction in a Rectangular Membrane              #2

Sec. 14.7 – Complex Fourier Series                                                 #4,7

Sec. 15.1 – The Fourier Integral                                                      #1,7,9

Sec. 15.2 – Fourier Cosine and Sine Integrals                                 #1,2,4,5,11

Sec. 15.3 – Complex Fourier integral and Transform                      #1,2,11,13,20,3

Sec. 15.4 – Properties & Applications of Fourier Transform           #1,2,3,7,10,11,12,14

Sec. 15.5 – Fourier Cosine and Sine Transforms                             #3,7,9,13

Exam 2

Sec. 17.3 – Wave along Infinite & Semi-infinite Strings                #1,3,7,10

Sec. 17.4 – Characteristics and d’Alembert’s Solution                   #1,5

Sec. 18.3 – Heat Conduction in Infinite Media                              #1,2,5,9,11

Sec. 16.1 – Legendre Polynomials                                                  #

Sec. 16.2 – Bessel Functions                                                           #

Sec. 16.3 – Sturm-Liouville Theory, Eigenfunction Expan.            #

Exam 3

Sec. 17.5 – Vibration of a Circular Elastic Membrane                    #

Sec. 17.6 – Continue from 16.5                                                      #

Sec. 18.3 – Heat Conduction in Infinite Media                              #

Sec. 18.4 – Heat Conduction in an Infinite Cylinder                      #

Sec. 19.3 – Dirichlet Problem for a Disk                                         #

Sec. 19.4 – Poisson’s Integral Formula for the Disk                       #

Related University-Wide and Course-Specific Requirements:

Ø Writing:  There are free-response questions where the student will write his/her explanation.

Ø Information Technology Literacy:  Students will explore various websites to gain a better understanding of math concepts and problems.  Each student is also required to use the available computer software in completing homework problems and a final project.  Students are encouraged to communicate with the professor and/or classmates through electronic means.

Ø Quantitative Reasoning:  Most of the math concepts have applications that require quantitative reasoning.

Ø Scientific Reasoning:  Most of the math applications require the use of scientific reasoning.

Ø Oral Communication:  Students demonstrate oral communication through classroom discussions and presentation of their final project.

Ø Critical Thinking:  Majority of the math concepts and applications require critical thinking.

Ø Other Requirements:  Students are required to illustrate the related applications to topics covered in the course by modeling, formulating, and presenting results of a real world problem of their choice in the field of mathematics, physics, chemistry, or engineering.

Evaluation:      Final grades are determined as follows:

                          Homework Sets:                                 20%

                          Project:                                              10%

                          3 Tests:                                               45%   

                          Final Exam:                                        25%

Grading Standards:

A         90 – 100,         A-        88-89

B+       86 – 87,           B         80 – 85,           B-        78 – 79

C+       76 – 77,           C         70 –75,            C-        68 –69

D+       66 –67,            D         60 – 65,           D-        58 – 59           

F          Below 58

Class Policies And Procedures:

Ø No Make-Ups except in cases of extreme emergencies.

Ø All tests will be announced.

Ø Cheating of any kind will not be tolerated and will result in an automatic grade of “F” for the semester (further disciplinary actions may be taken by the university).

Academic Integrity Policies:

Students are expected to attend all class sessions.  Information regarding academic or academically related misconduct, and disciplinary procedures and sanctions regarding such misconduct, may be obtained by consulting the NSU Student Handbook.

Americans With Disabilities Act (ADA) Statement:

In accordance with section 504 of the 1973 Rehabilitation Act and the Americans with Disabilities Act (ADA) of 1990, if you have a disability or think you have a disability please make contact with Supporting Students through Disability Services (SSDS) Office.

Location:                    2^nd floor/Lyman B. Brooks Library, Room 240

Contact Person:         Marin E. Shepherd, Disability Services Coordinator

Telephone:                   823-2014

University Assessment Statement:

As part of NSU’s commitment to provide the environment and resources needed for success, student may be required to participate in a number of university-wide assessment activities.  The activities may include tests, surveys, focus groups and interviews, and portfolio reviews.  The primary purpose of the assessment activities is to determine the extent to which the university’s programs and services maintain a high level of quality and meet the needs of the students.  Students will not be identified in the analysis of results.  Unless indicated otherwise by the instructor, results from University assessment activities will not be computed in the student grades.