NJIT Academic Integrity CODE: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.
Math 712: Numerical Methods II
Number of Credits: 3
Course Description: Numerical methods for the solution of initial- and boundary-value problems for partial differential equations, with emphasis on finite difference methods. Consistency, stability, convergence, and implementation are considered.
Prerequisites: Math 614, Math 331, or departmental approval, and proficiency in a computer programming language (FORTRAN, C, or C++).
Textbook: Finite Difference Schemes and Partial Differential Equations by J. Strikwerda, SIAM (Philadelphia © 2004); ISBN-10: 0898715679.
Instructor: (for specific course-related information, follow the link below)
Math 712-001 |
Grading Policy: The final grade in this course will be determined as follows:
▪ Homework: |
50% |
▪ Midterm: |
20% |
▪ Final Exam: |
30% |
Drop Date: Please note that the University Drop Date November 6, 2012 deadline will be strictly enforced.
Attendance Policy: Students must attend all classes. Absences from class will inhibit your ability to fully participate in class discussions. Tardiness to class is very disruptive to the instructor and students and will not be tolerated.
Makeup Exam Policy: There will be No make-up EXAMS during the semester. In the event the Final Exam is not taken, under rare circumstances where the student has a legitimate reason for missing the final exam, a makeup exam will be administered by the math department. In any case the student must notify the Math Department Office and the Instructor that the exam will be missed and present written verifiable proof of the reason for missing the exam, e.g., a doctors note, police report, court notice, etc., clearly stating the date AND time of the mitigating problem.
Further Assistance: For further questions, students should contact their Instructor. All Instructors have regular office hours during the week. These office hours are listed at the link above by clicking on the Instructor’s name. Teaching Assistants are also available in the math learning center.
Cellular Phones: All cellular phones and beepers must be switched off during all class times.
MATH DEPARTMENT CLASS POLICIES LINK
All DMS students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.
M |
Labor Day ~ No classes |
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T |
Last Day to Withdraw from this course |
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T |
Classes follow a Thursday Schedule |
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W |
Classes follow a Friday Schedule |
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R-Su |
Thanksgiving Recess |
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R |
Reading Day |
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F- R |
Final Exams |
Course Topics:
Weeks & Dates & Lecture |
Course Topics |
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Week 1 |
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1-2 |
Hyperbolic PDE’s (Chapters 1-5): ▪ Truncation Error, Convergence And Consistency ▪ Stability, Von Neumann Analysis, Cfl Condition ▪ Lax-Wendroff Scheme, Leapfrog Scheme, More General Multi-Step Schemes ▪ Difference Notation And Difference Calculus
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Dissipation And Dispersion Parabolic Pde’s (Chapters 6, 7, 10): ▪ Finite Difference Schemes ▪ Advection-Diffusion Equation ▪ Higher Dimensional Equations, Adi Scheme
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Stability And Convergence, Lax Equivalence Theorem
Elliptic Equations (Chapters 12-14): ▪ Maximum Principles ▪ Finite Difference Schemes For Poisson’s Equation ▪ Jacobi, Gauss-Seidel, Sor Methods
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Conjugate Gradient And Gmres Other Topics (Time Permitting): ▪ Spectral Methods
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Integro-Differential Equations |
Week 2 |
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3-4 | |
Week 3 |
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5-6 | |
Week 4 |
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7-8 | |
Week 5 |
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9-10 | |
Week 6 |
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11-12 | |
Week 7 |
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13-14 | |
Week 8 |
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15-16 | |
Week 9 |
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17-18 | |
Week 10 |
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19-20 | |
Week 11 |
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21-22 | |
Week 12 |
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23-24 | |
Week 13 |
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25 | |
Week 14 |
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26-27 | |
Week 15 |
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28 | |
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Final EXAM WEEK: December 14-20, 2012 |
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Prepared By: Prof. Shidong Jiang
Last revised: July 5, 2012