NJIT: Mathematical Sciences: Courses: MATH 340

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Mathematical Sciences Info for Students > Undergraduate > Course Information > Course Syllabi

MATH 340 Course Syllabus - SPRING 2014

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 340: Applied Numerical Methods

Number of Credits: 3

Course Description: An iIntroduction to numerical methods with emphasis on mathematical models. Implements and investigates numerical techniques for the solution of linear and nonlinear systems of equations, eigenvalue problems, interpolation and approximation, techniques of optimization, Monte Carlo methods, and applications to ordinary differential equations and integration. Effective From: Spring 2009

Textbook: Elementary Numerical Analysis (3rd ed.), Kendall Atkinson & Weimin Han (John Wiley & Sons)..

Prerequisites: Math 211 with a grade of C or better or Math 213 with a grade of C or better, and CS 101 with a grade of C or better or CS 113 with a grade of C or better or CS 115 with a grade of C or better or Math 240 with a grade of C or better

Instructor: (for specific course-related information, follow the link below)

Math 340-002	Prof. Bukiet
Math 340-004	Prof. Bukiet

Course Learning Objectives:

Students will demonstrate the ability to apply numerical techniques to approximate solutions to rootfinding and nonlinear equations.
Students will demonstrate the ability to apply numerical techniques to approximate area under curves and integrals, as well as of derivatives.
Students will demonstrate the ability to apply numerical techniques to approximate and interpolete function values.
Students will demonstrate the ability to communicate advantages and disadvantages of various numerical techniques and evaluate appropriateness of methods for solving problems.
Students will demonstrate the ability to apply numerical techniques to approximate solutions to ordinary differential equations and analyze stability of these techniques.

Grading Policy: The final grade in this course will be determined as follows:

▪ Quizzes, Homework & Labwork:	30%
▪ 2 Midterm Exams:	20% each
▪ Final Exam:	30%

Drop Date: Please note that the University Drop Date March 31, 2014 deadline will be strictly enforced.

Homework Policy: It is vital that you complete and turn in all the homework assignments on time. The homework assignments will be assigned in class.

Attendance: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Department�s Attendance Policy. This policy will be strictly enforced.

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.

January 20, 2014	M	Dr. Martin Luther King, Jr. Day ~ University Closed
March 16-23, 2014	Su-Su	Spring Recess ~ No Classes Scheduled ~ University Open
March 31, 2014	M	Last Day to Withdraw from this course
April 18, 2014	F	Good Friday ~ University Closed
May 6, 2014	T	Classes follow a Friday Schedule
May 7, 2014	W	Reading Day
May 8-14, 2014	R-W	Final Exams

Course Outline and Homework Assignments:

Week Dates	Section	Topic of the Class

Week 1	1.1-1.2	Quiz on prerequisite material Review of Taylor Series, their Errors and Mean Value Theorem
Week 1	1.3-2.4	Numerical Methods Foundations: Operation counts and Sources of Error
Week 2	▪	LAB:
	1.3-2.4	Numerical Methods Foundations: Operation counts and Sources of Error
	3.1	Root Finding: Bisection Method
Week 3	▪	LAB:
	3.2	Root Finding: Newton's Method and its error
	3.3	Root Finding: Secant Method and Regula Falsi
Week 4	▪	LAB:
	3.4	Root Finding: Fixed Point Iteration
	3.5	Root Finding: Accelerating Convergence and Ill-behaved Rootfinding Problems
Week 5	▪	LAB:
	└►	REVIEW FOR Midterm EXAM
	└►	MIDTERM EXAM I:
Week 6	▪	LAB:
	4.1	Go over exam and start Interpolation: Polynomial Interpolation
	4.1-4.2	Interpolation: Polynomial Interpolation and its Error
Week 7	▪	LAB:
	4.3	Interpolation: Spline Interpolation
	5.1	Numerical Integration: Trapezoidal & Simpson�s Rule
Week 8	▪	LAB:
	5.2	Numerical Integration: Trapezoidal & Simpson�s Rule Error Formulas
	8.3.2	Numerical Integration: Richardson Extrapolation
Week 9	▪	LAB:
	5.3	Numerical Integration: Gaussian Quadrature
	5.4	Numerical Differentiation
Week 10	▪	LAB:
	5.4	Numerical Differentiation and Extrapolation
	└►	REVIEW FOR Midterm EXAM
Week 11	▪	LAB:
	└►	MIDTERM EXAM II:
	8.1	Go over exam and Review of Ordinary Differential Equations
	8.1	Review of Ordinary Differential Equations
Week 12	▪	LAB:
	8.2	Ordinary Differential Equations: Euler�s Method
	8.3-8.4	Ordinary Differential Equations: Euler�s Method, Convergence and Stability
Week 13	▪	LAB:
	8.4	Ordinary Differential Equations: Implicit methods and Stability
	8.5	Ordinary Differential Equations:Taylor and Runge-Kutta Methods
Week 14	▪	LAB:
	8.7	Ordinary Differential Equations: Systems of Differential Equations
	└►	REVIEW FOR FINAL EXAM
Week 15	▪	LAB:
Week 15	└►	REVIEW FOR FINAL EXAM

Finals	Final EXAM WEEK: MAY 8-14, 2014

Prepared By: Prof. Bruce Bukiet

Last revised: December 16, 2013

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