numerical analysis assignment

Math 128A - Numerical Analysis

Uc berkeley, fall 2021, course website.

• The course is hosted on bCourses __________________________________________________________________________________________

Lecture Videos

• Pre-recorded Lecture Videos __________________________________________________________________________________________

Lecture Slides

• Chapter 1 - Mathematical Preliminaries and Error Analysis ( PDF , HTML )
• Chapter 2 - Solutions of Equations in One Variable ( PDF , HTML )
• Chapter 3 - Interpolation and Polynomial Approximation ( PDF , HTML )
• Chapter 4 - Numerical Differentiation and Integration ( PDF , HTML )
• Chapter 5 - Initial-Value Problems for Ordinary Differential Equations ( PDF , HTML )
• Chapter 6 - Direct Methods for Solving Linear Systems ( PDF , HTML ) __________________________________________________________________________________________

MATLAB Codes

All in-class MATLAB codes

Organized by textbook sections:

• Section 1.2: num2bin.m
• Section 2.1: bisection.m , bisection_table.m
• Section 2.2: fixedpoint.m , fixedpoint_table.m , fixedpoint_plot.m
• Section 2.3: newton.m , newton_table.m , newton_plot.m
• Section 2.5: steffensen.m , steffensen_table.m
• Section 2.6: horner.m , muller.m , muller_table.m , muller_plot.m
• Section 3.3: divideddifference.m
• Section 3.5: ncspline.m , ccspline.m , splineeval.m , diffsplineeval.m , splinedemo.m
• Section 4.1: diffdemo.m
• Section 4.2: richdemo.m
• Section 4.5: romberg.m
• Section 4.7: gaussquad.m
• Section 4.8: simpsondouble.m , gaussdouble_demo.m
• Section 4.9: laguerrequad.m
• Section 5.4: rk4.m
• Section 5.11: rk4stability.m
• Programming Assignment 3: pendplot.m
• Section 6.2: gausselim.m
• Section 6.5: lu_demo.m , mkM.m __________________________________________________________________________________________

Introduction to Numerical Analysis Spring 2012

Numerical analysis is the story of how functions, derivatives, integrals, and differential equations are handled as strings of numbers in the computer. At the heart of numerical analysis is an understanding of the speed of convergence of Taylor, Fourier, and other series expansions. Most scientists and engineers are sooner or later faced with computing tasks that require some knowledge of numerical analysis.

• Series expansions: from calculus to computation
• Integrals as sums and derivatives as differences
• Interpolation, splines, and a second look at numerical calculus
• Numerical methods for ODE, initial-value problems
• Root finding, Newton's method, boundary-value problems
• Fourier transform, Fourier series, Shannon sampling theory
• Bandlimited interpolation, spectral methods
• Least-squares approximation
• Principal component analysis

The class will NOT cover partial differential equations (see 18.303), and will contain much less linear aglebra than 18.06. Prerequisites: Calculus at the level of 18.01, 18.02, and 18.03. Some exposure to linear algebra (matrices) at the level of 18.06 helps, but is not required. The assignments will involve basic computer programming in the language of your choice (Matlab recommended; this class encourages you to learn Matlab if you don't already know it).

The material will be inspired from various sources. Current version of the typeset notes: Feb 14 version , Feb 23 version , Mar 2 version , Mar 15 version , Mar 21 version , Apr 2 version , Apr 29 version , May 14 version , April 2014 version .

• Burden and Faires, Numerical Analysis (more basic)
• Suli and Mayers, An Introduction to Numerical Analysis
• Stoer and Bulirsch, Introduction to Numerical Analysis (more advanced)
• Trefethen, Spectral methods in Matlab

See also the nice set of notes by John Neu.

Some code used in class:

Code for polynomial interpolation. Code for spline interpolation. Codes for ODE solvers: example 1 , example 2, stiff. Code for bandlimited interpolation.

Date and Time: Tu-Th, 1:00-2:30, room 2-135. Instructor: Laurent Demanet. Office hours: W-F, 2:00-4:00, room 2-392.

50% homework, 20% in-class midterm, 30% in-class final.

The homework problem sets will consist of both theoretical problems and numerical experiments. No late copy will be allowed. The lowest score will be dropped. Collaboration is allowed, but the codes and copies you turn in must be original and written by you.

The midterm and final are open-book. No calculators, phones, or computers are allowed.

• Homework 1 , due on 02/23. Solutions: 1 , 2 , 3 , courtesy of Michael Tarczon
• Homework 2 , due on 03/01. Partial solutions .
• Homework 3 , due on 03/20 (changed from 03/15). Solution set , courtesy of Michael Tarczon
• Homework 4 , due on Tuesday 04/03. Solution set , courtesy of Ishika Kulatilaka
• Homework 5 , due on Thursday 04/12. Solution set , courtesy of Daisy Yuen
• Homework 6 , due on Thursday 04/26. Solution set , courtesy of Daisy Yuen
• Homework 7 , due on Thursday 05/03. Solution set , courtesy of Michael Tarczon
• "Homework 8" , not due.

The midterm is scheduled on March 6 in class (1:00PM to 2:30PM in 2-135). The final is scheduled on May 24 from 9:00AM (sharp) to 12:00PM in Walker. Please arrive sufficiently ahead of schedule.

Massachusetts Institute of Technology

• Department of Mathematics
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Numerical Analysis

Announcements.

• Computer arithmetics
• Interpolation and approximation
• Numerical differentiation and integration
• Numerical solution of nonlinear equations, systems of linear equations and ordinary differential equations

Optional readings

• Heath, Scientific Computing: An Introductory Survey, 2nd edition, McGraw-Hill, 2002, ISBN: 0-07-239910-4.
• Cheney and Kincaid, Numerical Mathematics and Computing, 4th edition, Brooks/Cole, 1999, ISBN: 0-534-35184-0.
• Gerald and Wheatley, Applied Numerical Analysis, 6th edition, Addison-Wesley, 1999, ISBN: 0-201-87072-X.
• Shampine, Allen, and Pruess, Fundamentals of Numerical Computing, John Wiley and Sons, 1997, ISBN: 0-471-16363-5.

Interesting links

• Numerical Analysis FAQ : Frequently asked questions about scientific computing and numerical analysis.
• Matlab primer for version 4: PDF file .
• GSL: The GNU Scientific Library A free open-source numerical library for C programmers.
• Numerical Recipes in C A popular collection of numerical algorithms.
• Netlib A huge collection of mathematical software.
• Gnuplot A free program for scientific plotting.

Assignments

Late assignments.

CS 4220/Math 4260: Numerical Analysis: Linear and Nonlinear Problems

Inclusiveness.

• CMS for managing coursework.
• VOD channel for lecture recordings.
• Ed Discussion for asking and answering questions.
• Jupyter notebooks and data for class demos.
• [B] Prof. David Bindel's CS4220 course notes from Spring 2020.
• [AG] A First Course in Numerical Methods. U. Ascher and C. Greif. Available online .
• [TB] Numerical Linear Algebra. L. N. Trefethen and D. Bau III. Available online (no direct link, need to search).
• [NW] Numerical Optimization. J. Nocedal and S. J. Wright. Available online .
• [BV] Convex Optimization. S. Boyd and L. Vandenberghe. Available online .
• Julia programming language documentation for linear algebra , sparse arrays , and iterative solvers .
• Latex typesetting wikibook : Basics and Mathematics .
• Homework 1 due Fri Feb 26 at 3:44pm ET (before class) [ source ]
• Homework 2 due Fri Mar 12 at 3:44pm ET (before class would normally start) [ source ]
• Homework 3 due Fri Mar 26 at 3:44pm ET (before class) [ source ]
• Homework 4 due Fri Apr 16 at 3:44pm ET (before class) [ source ]
• Homework 5 due Fri Apr 30 at 3:44pm ET (before class) [ source ]
• Homework 6 due Fri May 14 at 3:44pm ET (before class) [ source ]
• Homeworks (48%). There will be six homeworks that will have theoretical and/or coding components. Each is worth 8% of your grade. Submissions need to be typeset with latex.
• Midterm exam (16%). There will be a take-home midterm, released on March 29 and due April 5 before class starts. The format is just like the homework, except that you have to work on the problems on your own.
• Final exam (32%). There will be a take-home final, released on May 18 and due May 25. The format is the same as the midterm.
• Participation (4%). Showing up to virtual lectures, asking questions, coming to office hours, providing feedback, Ed Discussion involvement, and other engagement with the course will count towards participation.

Numerical Analysis

Numerical Analysis deals with the process of getting the numerical solution to complex problems. The majority of mathematical problems in science and engineering are difficult to answer precisely, and in some cases it is impossible. To make a tough Mathematical problem easier to solve, an approximation is essential. Numerical approximation has become more popular as a result of tremendous advances in computational technology. As a result, a great deal of scientific software is being developed to solve more complex challenges quickly and easily. Let us go through the definition of numerical analysis as well as the various concepts included, such as errors, interpolation and so on in this article.

Introduction to Numerical Analysis

Numerical analysis is a discipline of mathematics concerned with the development of efficient methods for getting numerical solutions to complex mathematical problems. There are three sections to the numerical analysis. The first section of the subject deals with the creation of a problem-solving approach. The analysis of methods, which includes error analysis and efficiency analysis, is covered in the second section. The efficiency analysis shows us how fast we can compute the result, while the error analysis informs us how correct the result will be if we utilize the approach. The construction of an efficient algorithm to implement the approach as a computer code is the subject’s third part. All three elements must be familiar to have a thorough understanding of the numerical analysis.

Meanwhile, there are at least three reasons to learn the theoretical foundations of numerical methods:

• Learning various numerical methods and analyzing them will familiarize a person with the process of inventing new numerical methods. When the existing approaches are insufficient or inefficient to handle a certain problem, this is critical.
• In many cases, there are multiple solutions to a problem. As a result, using the right procedure is critical for getting a precise answer in less time.
• With a solid foundation, one can effectively apply methods (especially when a technique has its own restrictions and/or drawbacks in certain instances) and, more significantly, analyze what went wrong when results did not meet expectations.

Let’s have a look at some of the key topics in numerical analysis.

Different Types of Errors

The disparity between the approximate representation of a real number and the actual value is termed an error .

Error = True Value – Approximate Value , is the formula for calculating the error in a computed amount.

The absolute error is defined as the absolute value of the error defined above.

Relative Error = Error / True Value is a measurement of the error in respect to the magnitude of the true value.

The relative error is multiplied by 100 to get the percentage error .

The phrase “ truncation error ” refers to the error that occurs when a smooth function is approximated by reducing its Taylor series representation to a limited number of terms.

Significant Digits

If x A is an approximation to x, so we can conclude that x A approximates x to r significant β-digits if |x − x A | ≤ (½)β s−r+1 with “s” the greatest integer such that β s ≤ |x|.

As an example, the approximate value x A = 0.333 includes three significant digits for x = ⅓, since |x − x A | ≈ .00033 < 0.0005 = 0.5 × 10 −3 .

But 10−1 < 0.333 · · · = x.

Hence, in this case s = −1 and and therefore r = 3.

Propagation of Errors

When an error is committed, it has an impact on subsequent outcomes because it propagates through subsequent calculations. We’ll look at how utilizing approximate numbers rather than actual numbers affects the outcomes before moving on to function evaluation. We’ll now explore how error propagates in four basic arithmetic operations .

• In addition and subtraction, the total of the error bounds for the terms provides an error bound for the results .
• In multiplication and division, The sum of the bounds for the relative errors of the given integers gives a limitation for the relative error of the results.

Finite Difference Operators

Now, let us discuss the various finite difference operators in brief.

Forward Operator

Assume that “h” be the finite difference, then

Δf(x) = f(x+h) – f(x)

Δ 2 f(x) = f(x+2h)-2f(x+h) + f(x)

Δ 3 f(x)= f(x+3h) – 3f(x+2h) + 2f(x+h) – f(x)

Shift Operator

Assume that h be the finite difference.

Then, E f(x) = f(x+h)

E n f(x) = f(x+nh)

Backward Difference

Suppose h be the finite difference.

Central Difference Operator

Averaging operator, factorial notation, relation between different finite operators.

Relationship Between Δ and E

E ≡ 1 + Δ and Δ ≡ E-1

Hence, E n ≡ (1+Δ) n and Δ n ≡ (E-1) n

Interpolation

Interpolation is the process of determining the approximate value of a function f(x) for an x between multiple x values x 0, x 1 , …, x n for which the value of f(x) is known.

I.e., f(x i ) = f i (i = 0, 1, 2, …, n)

If the real-valued function f(x) has (n+1) different values, then x 0 x 1 , ..x n . A polynomial of degree n or less is P n (x i ) = f(x). It indicates that there can only be one polynomial with a degree less than or equal to n that interpolates f(x) at (n+1) unique points x 0 , x 1 , x 2 , …x n .

Solved Example on Numerical Analysis

Show that μ 4 = μ 3 + Δμ 2 + Δ 2 μ 1 + Δ 3 μ 1

As we know that

Δμ x = μ x+h – μ x

Hence, μ 4 – μ 3 = Δμ 3

μ 3 – μ 2 = Δμ 2

μ 2 – μ 1 = Δμ 1

μ 4 = μ 3 + Δμ 3

μ 4 = μ 3 + Δμ 2 – Δ 2 μ 2

μ 4 = μ 3 + Δμ 2 + Δ 2 μ 1 + Δ 3 μ 1

Hence, proved.

Stay tuned to BYJU’S – The Learning App and download the app all the Maths-related concepts easily by exploring more videos.

Frequently Asked Questions on Numerical Analysis

What is numerical analysis.

Numerical analysis is a branch of mathematics concerned with the development of efficient methods for solving complicated mathematical problems numerically.

What are the different types of numerical analysis?

The different types of numerical analysis are finite difference methods, propagation of errors, interpolation methods, and so on.

Is calculus required for learning numerical analysis?

Yes, calculus is required for learning numerical analysis, as we should know differential integration.

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Numerical Analysis II

Table of contents.

• General information

Programming problems

Testate condition.

• Assignment sheets
• Exercise groups
• Previous exams
• Previous midterms and endterms
• Prof. Habib Ammari's Lecture Recordings and Notes in 2021

Prof. Habib Ammari's Lecture Recordings in 2020

General information, remote teaching arrangements.

The course will be held remotely in Zoom under the following arrangements.

Prof. Ammari will inform the students of the URL of the meeting in Zoom. He will also record his lectures for students to view in their own time. Links to these recordings, as well as the lecture notes and the slides from the lectures, can be found below.

Exercise classes will be hosted on Zoom. Your tutor will contact you with details. We strongly encourage you to take part in these classes, as they will be the most effective way to have any questions answered.

Assignments will be published each week. You should submit all your solutions using the SAM Upload Tool , including scans or photos of any handwritten solutions. Students are strongly enocuraged to complete the assignments, particularly since the Python programming skills they develop will form a large part of the final exam.

As last year, bonus points can be earnt by completing the "Mid-term summary assignment" and "End-term summary assignment". These replace the mid-tem and end-term tests of previous years. See below for details.

Prof. Habib Ammari's Lecture Recordings in 2021

Here, you can find the recordings of Prof. Ammari's lectures. The titles correspond to the slides, given below.

22 February 2021: Lecture 1, part i: Some basics

26 February 2021: Lecture 1, part ii: Some basics

1 March 2021: Lecture 2: Existence, uniqueness, and regularity in the Lipschitz case

5 March 2021: Lecture 3, part i: Linear systems

8 March 2021: Lecture 3, part ii: Linear systems

12 March 2021: Lecture 4, part i: Numerical solution of ordinary differential equations

15 March 2021: Lecture 4, part ii: Numerical solution of ordinary differential equations

19 March 2021: Lecture 4, part iii: Numerical solution of ordinary differential equations

22 March 2021: Lecture 4, parti iv: Numerical solution of ordinary differential equations

26 March 2021: Lecture 4, part v: Numerical solution of ordinary differential equations

29 March 2021: Lecture 4, part vi: Numerical solution of ordinary differential equations

16 April 2021: Lecture 5, part i: Geometrical numerical integration methods for differential equations

23 April 2021: Lecture 5, part ii: Geometrical numerical integration methods for differential equations

26 April 2021: Lecture 5, part iii: Geometrical numerical integration methods for differential equations

30 April 2021: Lecture 5, part iv: Geometrical numerical integration methods for differential equations

3 May 2021: Lecture 5, part v: Geometrical numerical integration methods for differential equations

7 May 2021: Lecture 5, part vi: Geometrical numerical integration methods for differential equations // Lecture 6, part i: Finite difference methods

10 May 2021: Lecture 6, part ii: Finite difference methods

14 May 2021: Lecture 6, part iii: Finite difference methods

17 May 2021: Lecture 6, part iv: Finite difference method

18 May 2020: Lecture 5, slides 49-78: geometrical numerical integration methods

Lecture Notes

Here, you can find the lecture notes:

Here are the slides used in the lectures:

Introduction

Assignments

There will be weekly homework assignments available for download from the course web page each Wednesday afternoon . Homework will include theoretical problems and programming problems, which are to be prepared using Python 3 (available at the student computer pools at ETH).

All solutions (both codes and scans or photos of written solutions) should be submitted using the SAM Upload Tool . Since we are not using a server for permanent storage, everything on the server might disappear after several weeks so please don't rely on it for storing files. Instructions on how to use the upload tool can be found in the User Guide.

Here is a Python cheat sheet , it contains instructions on how to install Python 3 and gives some useful commands. We also recommend these scipy lecture notes and Python for Scientists by John Stewart (available as a pdf on the ETH network) as other resources for learning Python.

Please upload your codes via the SAM Upload Tool . TAs will also upload the correction to your codes. Since we are not using a server for permanent storage, everything on the server might disappear after several weeks so please don't rely on it for storing files. Instructions on how to use the upload tool can be found in the User Guide.

As testate conditions are not in place anymore, it is not compulsory to hand in the assignments for correction. It is, however, recommended to submit the assignments as this will develop your understanding of the material and help you be better prepared for the exams.

You can download the assignments (with templates) and solutions here:

Exercise Groups

All registered students will receive an email with the registration link (for MyStudies) to exercise groups before the starting of the first exercise class (25th February).

Summary Assignments

Students will have the opportunity to earn bonus points by completing the "Mid-term summary assignment" and "End-term summary assignment" . These will be two additional assignments consisting of simple and routine problems. Completing these assignments is not compulsory but doing so to a good standard will earn a student bonus points. Suppose a student gets x points (out of 60 points) in the mid-term summary assignment and y points (out of 60 points) in the end-term summary assignment, then they will get 0.25 bonus points added to their final grade if x+y > 80 .

No programming problems will be involved in the mid-term and end-term summary assignments. The problems will focus on the important definitions and theorems from the course, with some examples.

The mid-term summary assignment will take place on 12th, April (Monday) and the end-term summary assignment will take place on 31th, May (Monday) . In both cases, the assignments will be published here at 9am (Zurich time) and students will need to submit solutions via the SAM Upload Tool within 24 hours (i.e. by 9am on Tuesday). You will need to take photos or scans of your handwritten solutions. You can either fill in the white boxes or use your own paper. The assignments are designed to take around an hour to complete and will be similar to the mid-term and end-term tests of previous years (see below).

Mid-term summary assignment - please submit via the SAM Upload Tool by 9am on Tuesday, 13 April .

End-term summary assignment - please submit via the SAM Upload Tool by 9am on Tuesday, 1 June .

End-term summary assignment - please submit via the SAM Upload Tool by 9am on Tuesday, 26 May .

There will be two short, 60-min tests during semester called "Mid-term test" and "End-term test". Both of the tests will consist of only simple and routine problems. One doesn't have to take part in these exams, but those who take part in and do well in these two exams can get bonus in final grade. Suppose a student gets x points (out of 60 points) in the Mid-term exam and y points (out of 60 points) in the End-term exam, then they will get 0.25 bonus points in the final grade if x+y > 80 .

No programming problems will be involved in the midterm exam. Simple examples given in class, important definitions and simple calculations are the possible choices of test problems. No books or notes related to this course are allowed to be used during tests.

The midterm exam will take place on 27th, April (Monday) , in room HG G 5 . The endterm exam will take place on 25th, May (Monday) , in room HG G 5 . Both the midterm and the endterm will be at 13:15 , instead of the usual Monday lecture.

The final exam will be a (computer-aided) written exam. Programming with Python will be involved. Spyder will be available as the default editor. The lecture notes (in the form of the pdf, as given above) will be available during the exam. August 10th, 2019 , in room HG G1 . The exam will start at 9:0 and end at 12:00 . Please arrive 15 mins early. -->

The exam will take place on Friday 7th August, starting at 14:30. Registered students have been emailed details of the room allocation as well as relevant safety measures.

Previous Exams

Previous mid-term and end-term exams.

Here, you can find the previous recordings of Prof. Ammari's lectures. The titles correspond to the slides, see above.

16 March 2020: Lecture 4, slides 1-17: explicit one-step method

20 March 2020: Lecture 4, slides 18-21: explicit Euler scheme

23 March 2020: Lecture 4, slides 22-39: high-order methods

27 March 2020: Lecture 4, slides 40-46: linear systems

30 March 2020: Lecture 4, slides 47-64: Runge-Kutta methods

3 April 2020: Lecture 4, slides 65-83: Runge-Kutta methods as collocation methods

6 April 2020: Lecture 4, slides 84-103: multistep methods

4 May 2020: Lecture 5, slides 1-24: geometrical numerical integration methods

11 May 2020: Lecture 5, slides 25-48: geometrical numerical integration methods

Here you can find the lecture notes.

Here are the slides used in the lectures.

Matlab links:

• K. Sigmon: MATLAB Primer (2on1) (.pdf), Matlab Primer (single), (.pdf) 3rd edition, Gainesville Florida 1993.
• Ch. Mehl and A. Steinbrecher: Learning MATLAB by doing MATLAB (.pdf), four-page tutorial.
• Cleve Moler: Numerical Computing with Matlab, (in particular chapter (.pdf) on ordinary differential equations).
• The MathWorks: MATLAB Online Documentation
• Numerical Recipes: http://www.nr.com/
• Differential Equations in MATLAB 7 by Jaywan Chung(KAIST)
• Aitken-Neville Algorithm

Note: Extra reading is not considered important for understanding the course subjects.

• Deuflhard and Bornemann: Numerische Mathematik II - Integration gewohnlicher Differentialgleichungen, Walter de Gruyter & Co., 1994.
• Hairer and Wanner: Solving ordinary differential equations II - Stiff and differential-algebraic problems, Springer-Verlag, 1996.
• Hairer, Lubich and Wanner: Geometric numerical integration - Structure-preserving algorithms for ordinary differential equations}, Springer-Verlag, Berlin, 2002.
• L. Gruene, O. Junge "Gewoehnliche Differentialgleichungen", Vieweg+Teubner, 2009.
• Hairer, Norsett and Wanner: Solving ordinary differential equations I - Nonstiff problems, Springer-Verlag, Berlin, 1993.
• Walter: Gewöhnliche Differentialgleichungen - Eine Einuhrung, Springer-Verlag, Berlin, 1972.
• Walter: Ordinary differential equations, Springer-Verlag, New York, 1998.

Numerical Analysis

Department of Mathematics Thapar Institute of Engg. & Tech. Patiala

Spring 2024

Course description.

Numerical Analysis (MATH UMA011) is a one semester, upper-level module that emphasizes the mathematics used to design numerical methods, and to analyse their properties. Students also experiment with implementing algorithms in Matlab/Octave. Course credit are 4.0. For details please see Course Policies .

Instructor : Dr. Paramjeet Singh                                      

Lecture Time and Place :

MT 1-2 + CHE : Tuesday  12:10, Wednesday 02:40, Friday 11:20 in F210. 

Extra Classes: Announced Later. 

Notes and Assignment

Lecture Notes (Chapter-Wise):   ch1         ch2           ch3     ch4       ch5     ch6   ch7

C lass PDF Notes ( o ld):     ch1_class         ch2_class         ch3_class         ch4_class           ch5_class         ch6_class           ch7_class              

Lecture Videos ( pre-recorded ):   Visit YouTube  Numerical_Analysis .

Assignments :  Solve all the Exercises given at the end of each chapter. 

Sol ution of  E xercises:    ch_1_sol ch_2_sol   ch_3_sol  

Lab:   See Lab Assignments on LMS. 

Announcements (EXAMS)

  MATLAB EXAM: The lab evaluation will be during the week (April 24-29, 2023) on the allotted time schedule of Lab. The duration of the exam is 90 minutes and will have two numerical methods to write Matlab programs. The questions will have a weight of 15 marks (8+7). The students are advised to revise ALL the programs. The combined weight of Lab  is 20 Marks ( 15+5 ). 

Q uiz 2 will be conducted  on  April 17, 2023 (Monday) at 5:20 PM. The syllabus of exam include: Chapter 4 (Eigenvalues and Eigenvector: Power Method, QR factorization and QR Algorithm) and Chapter 5 (Interpolation:  Lagrange and Newton's Divided Difference interpolation including forward and backward difference operator).  Th ere are no makeup quizzes during the semester . The Questions may involve Multiple Choice  and S hort A nswer type questions.

 Quiz 1 will be conducted on February 17,  2023 (Friday) at 5:30 PM.  The syllabus will be Chapter 1 ( Floating Point Arithmetic, Errors, Condition and Stability ) and Chapter 2 (Roots of Nonlinear Equations) . T here are no makeup quizzes during the semester . The Questions may include Multiple Choice  and S hort A nswer type questions.

 An advise to develop good study habits can be found here .

You should check this page daily and begin working the assignments immediately after they are posted.

You are expected to do all assigned problems. You may need to do additional problems for practice.

You are expected to read the textbook as we cover the material. 

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Introduction to numerical analysis, assignments.

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