## Course Syllabus

Department of Mathematics and Computer Science, Lincoln University

 COURSE ID: MAT-313 COURSE NAME: Numerical Methods CREDITS: 3

TEXT BOOK:

John H. Mathews & Kurtis D. Fink, Numerical Methods Using Matlab, Fourth Edition (& Higher). Upper Saddle River: Pearson Prentice Hall, 2004.

INSTRUCTOR INFORMATION:

***To be provided for each section***

COURSE DESCRIPTION:

Modern computational algorithms for the numerical solution of a variety of applied mathematics problems are considered. Topics include numerical solution of polynomial and transcendental equations, acceleration of convergence, Lagrangian interpolation and least-squares approximation, numerical differentiation and integration.

PREREQUISITE:         MAT-122 (Calculus II) and CSC-158 (Programming I)

COURSE GOALS- STUDENT LEARNER OUTCOMES:

The student should
• To write programs using any software tool (Maple, Octave, R or Matlab) that involve loops, logical block constructs (if. . . else), plotting, and simple file input/output.
• To write programs using any software tool (Maple, Octave, R or Matlab) that evaluate and plot analytical functions.
• To translate numerical algorithms into using any software tool (Maple, Octave, R or Matlab).
• To distinguish between the effects of truncation error and roundoff error in evaluating a finite number of terms in an infinite series.
• To use machine precision to construct absolute and relative tolerances for the convergence of iterative computations.
• To set up and solve linear systems of equations manually as well as perform Gaussian elimination on small systems.
• To use using any software tool (Maple, Octave, R or Matlab) to correctly compute the solution to a system of linear equations.
• To use any software tool (Maple, Octave, R or Matlab) to perform curve fits of data to polynomials and linear combinations of arbitrary functions, as well as use a residual plot from a curvefit as an indicator of whether a better curve fit might be obtainable.
• To manually apply Eulers method, the Runge-Kutta methods to advance a single ordinary differential equation for one or two steps of the independent variable.
• To use any software tool (Maple, Octave, R or Matlab) programs to obtain numerical solutions to ordinary differential equations.

TENTATIVE SCHEDULE OF WEEKLY ASSIGNMENTS:

Chapter 1: Preliminaries, Sections 1.1 - 1.3
1.1 Review of Calculus
1.2 Binary Numbers
1.3 Error Analysis

Chapter 2: The Solution of Nonlinear Equations f(x) = 0, Sections 2.1 - 2.4
2.1 Iteration for Solving x = g(x)
2.2 Bracketing Methods for Location a Root
2.3 Initial Approximation and Convergence Criteria
2.4 Newton-Raphson And Secant Methods

Chapter 3: The Solution of Linear Systems AX = B, Sections 3.1 - 3.7
3.1 Introduction to Vectors and matrices
3.2 Properties of Vectors and Matrices
3.3 Upper-Triangular Linear Systems
3.4 Gaussian Elimination and Pivoting
3.5 Triangular Factorization
3.6 Iterative Methods for Linear Systems
3.7 Newton's Methods

Chapter 4: Interpolation and Polynomial Approximation, Sections 4.1 - 4.6
4.1 Taylor Series and Calculation of Functions
4.2 Introduction to Interpolation
4.3 Langrage Approximation
4.4 Newton Polynomials

Chapter 5: Curve Fitting, Sections 5.1 - 5.4
5.1 Least-Squares Line
5.2 Methods of Curve Fitting
5.3 Interpolation by Spline Functions

Chapter 6: Numerical Differentiation, Sections 6.1 – 6.2
6.1 Approximating the Derivation
6.2 Numerical Differentiation Formulas

Chapter 7: Numerical Integration, Sections 7.1 - 7.5
7.2 Composite Trapezoidal and Simpson's Rule

(Optional) Chapter 9: Solution of Differential Equations, Sections 9.1 – 9.7
9.1 Introduction to Differential Equations
9.2 Eulers Method
9.3 Runge-Kutta Methods
9.6 Predictor-Corrector Methods

COURSE ASSESSMENT- LEARNING OPPORTUNITIES*

• Homework

Daily homework will be given on material covered in class, reviewed the next day, and may be collected and graded on an unannounced basis. On all assignments, all work must be shown for credit.

Students are encouraged to work cooperatively. The objective of group work is to develop individual skills while learning to work effectively as a team, to think and talk about problem solving and the underlying mathematical concepts, and to develop the ability to ask and answer questions as they arise. However, each student is responsible for all the assigned material, in other words, students can work on their together, but should not simply copy work from each other.

Students are encouraged to make regular visits during office hours, to meet in study groups, and to use the Math Lab or the Math Tutors from the School of Natural Sciences.

• Quizzes, Tests and Final Exam

Short quizzes will be given on an unannounced basis. One hour in- class exams will be announced at least a week in advance. A cumulative two hour Final Exam will be given as scheduled by the Registrar. NO CALCULATORS are allowed during quizzes and exams, and all work must be shown for full credit.

• Late Work And Make-Ups: All graded assignments, quizzes and exams must be completed when scheduled. Late assignments or make-up tests or quizzes will only be allowed with official documentation and grades may be lowered. To qualify for a make-up, a student must have notified the professor and rescheduled in a timely manner.

 Participation 30% Tests 50% Final 20%

 A 92-100% A- 88-91% B+ 85-87% B 82-84% B- 78-81% C+ 75-77% C 72-74% C- 68-71% D+ 65-67% D 58-64% F 0-57%

UNIVERSITY POLICY

1) Attendance:

Lincoln University uses the class method of teaching, which assumes that each student has something to contribute and something to gain by attending class. It further assumes that there is much more instruction absorbed in the classroom than can be tested on examinations. Therefore, students are expected to attend all regularly scheduled class meetings and should exhibit good faith in this regard. For the control of absences, the faculty adopted the following regulations:

• Four absences may result in an automatic failure in the course.
• Three tardy arrivals may be counted as one absence.
• Absences will be counted starting with whatever day is specified by the instructor but not later than the deadline for adding or dropping courses.
• In case of illness, death in the family, or other extenuating circumstances, the student must present documented evidence of inability to attend classes to the Vice President for Student Affairs and Enrollment Management. However, in such cases the student is responsible for all work missed during those absences.
• Students representing the University in athletic events or other University sanctioned activities will be excused from class (es) with the responsibility of making up all work and examinations. The Registrar will issue the excused format to the faculty member in charge of the off- or on-campus activity for delivery by the student(s) to their instructors.

Students are responsible for proper conduct and integrity in all of their scholastic work. They must follow a professor's instructions when completing tests, homework, and laboratory reports, and must ask for clarification if the instructions are not clear. In general, students should not give or receive aid when taking exams, or exceed the time limitations specified by the professor. In seeking the truth, in learning to think critically, and in preparing for a life of constructive service, honesty is imperative. Honesty in the classroom and in the preparation of papers is therefore expected of all students. Each student has the responsibility to submit work that is uniquely his or her own. All of this work must be done in accordance with established principles of academic integrity.

An act of academic dishonesty or plagiarism may result in failure for a project or in a course. Plagiarism involves representing another person's ideas or scholarship, including material from the Internet, as your own. Cheating or acts of academic dishonesty include (but are not limited to) fabricating data, tampering with grades, copying, and offering or receiving unauthorized assistance or information.

3) The Student Conduct Code:

Students will be held to the rules and regulations of the Student Conduct Code as described in the Lincoln University Student Handbook. In particular, excessive talking, leaving and reentering class, phones or pagers, or other means of disrupting the class will not be tolerated and students may be asked to leave. Students who constantly disrupt class may be asked to leave permanently and will receive an F.

4) The Core Curriculum Learner Competencies:

All courses offered through the Department of Mathematics and Computer Science require students to meet at least the following out of the 8 Core Curriculum Learner Competencies:

(1) Listen and effectively communicate ideas through written, spoken, and visual means;
(2) Think critically via classifying, analyzing, comparing, contrasting, hypothesizing, synthesizing, extrapolating, and evaluating ideas;

(6) Apply and evaluate quantitative reasoning through the disciplines of mathematics, computational science, laboratory science, selected social sciences and other like-minded approaches that require precision of thought;

(8) Demonstrate positive interpersonal skills by adhering to the principles of freedom, justice, equality, fairness, tolerance, open dialogue and concern for the common good.

Note:

* The instructor of a given section of the course may make some modifications to the evaluation as well as to the rest of the syllabi including but not limited to; the grade weights, number of tests, and test total points.

**The grading scale guideline includes a 2-point flexibility.

Please consult with the department chairperson for any program updates or corrections which may not be yet reflected on this page _ last updated 9/10/2007.

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