Series methods (power and/or Fourier) will be applied to appropriate differential equations. The evaluation scheme. Topics include logic, methods of mathematical proof, set theory, relations and functions. KEYWORDS: Electronic textbook, Ordinary differential equations Fourier analysis, Finite difference approximations, Accuracy, stability and convergence, Dissipation, dispersion, and group velocity, Boundary conditions,. Approximation theory a) Least square approximation 9. GBTU CBNST syllabus TAS-302. I Introduction. Topics will include root ﬁnding, discrete. Time Integration Schemes. This course is intended to be an introduction into numerical methods, and is designed to. There will be a number of programming assignments that emphasize important numerical methods in computational physics. Implement a range of numerical algorithms efﬁciently in a modern scientiﬁc comput- ing programming language. Ltd, New Delhi, Software Engineering – Syllabus. AP PGECET (Andhra Pradesh Post Graduate Engineering Common Entrance Test) exam is managed by the Jawaharlal Nehru Technological University, Kakinada on behalf of APSCHE. be able to develop computer programs to analyze real biomedical data or model biomedical systems. Numerical differentiation and Integration: Numberical differentiation, Numerical integration using Trapezoidal Rule, Simpson’s 1/3rd and 3/8th rules Numerical solution of 1st and 2nd order differential equations: Taylor series, Euler’s Method, Modified Euler’s Method, Runge-Kutta Method for 1st and 2 nd Order Differential Equations. Associate Professor. Interpolation Methods: Lagrange polynomials, finite differences, least square approximation. Numerical Methods by Germund Dahlquist and Ake Bjorck. The uses of numerical methods are summarized as follows: The roots of nonlinear (algebraic or transcendental) equations which arise in engineering applications can be obtained numerically where analytical methods fail to give solution. ISBN: 978-0-07-340110-2 • Supplemental. Contact Information. Title IX Indiana University of Pennsylvania and its faculty are committed to assuring a safe and productive. Objectives 1. ] on Amazon. Materials balance: Steady state conservation system, steady state system with non conservative pollutants, step function. name of experiment page no. numerical methods lab iv sem. Finance 550 Numerical Methods & Optimization in Finance Syllabus Phil Dybvig 314-398-3196 (cell) Washington University Olin School Focus: Optimization tools that are useful in finance. Learning objectives: describe general methods and principles for modelling and simulating a system. If the student applies for the exam fourth time he/she will be invited to take the oral exam regardless to the result of the written exam. Syllabus Throughout the course examples of real world problems will be mathematically modeled and computationally solved. BINF 690 - Numerical Methods for Bioinformatics Syllabus. Articles from classroom scratch of Numerical Methods for Engineering Students. Falling Object 4. In each case,. GATE Syllabus For ECE 2020: GATE 2020 syllabus for Electronics and Communication Engineering (ECE) branch will be released by the officials of IIT Delhi in the month of September 2019. Numerical Methods in Engineering and Science by Dr. Objective Oriented Programming. This course oﬀers students an in-depth exposure to the use of numerical methods and pro-gramming to solve engineering problems. Numerical solutions to the diffusion equations of multiple dimensions. It is the purpose of this course to introduce state-of-the-art numerical methods and provide an understanding of their performance through analysis and application. Introduction to the theory, architecture and application of artificial neural systems. SIO 239 SUGGESTED BOOKS: Textbooks: Numerical methods for engineers and scientists, J. Office: MCS 220J. MA8491 Numerical Methods Syllabus Notes Question Paper Question Banks with answers Anna University Anna University Numerical Methods - NM Syllabus Notes Question Bank Question Papers Regulation 2017 Anna University MA8491 Numerical Methods Notes are provided below. To introduce numerical methods used for the solution of engineering problems. Laws of probability, Bayes theorem. Convex envelope. The course covers the Fourier method, Energy method, normed vector spaces, bilinear forms, L p - and Sobolev spaces, weak derivatives, elliptic boundary value problems, hyperbolic and parabolic time-dependent initial value problems, linearisation for nonlinear problems, interpolants and finite elements, higher order methods and elements. Numerical algorithms do. Numerical solutions of ordinary differential equations : Single step methods, Taylor’s series method, Euler’s method, Picard’s method of successive approximations, Runge-Kutta method of 4 th order, Multi step methods, Milne’s and Adams-Bash forth Predictor-Corrector methods. Derive and analyze numerical methods for ODEs and PDEs. Fall, 2009. Systems of linear differential equations will be studied. Download link is provided for Students to download the Anna University MA6452 Statistics and Numerical Methods Lecture Notes, Syllabus Part A 2 marks with answers & Part B 16 marks Question, Question Bank with answers, All the materials are listed below for the students to make use of it and score good (maximum) marks with our study materials. 001 Syllabus (PDF Format). Eigenvalue problems. It covers C programs on 15 frequently asked Numerical methods in a very easy and simple way. 7 Variable Step-Size Multistep Methods Chapter 6. Post a Comment Note: Share to Twitter Share to Facebook. Select and use appropriate methods for finding roots of equations as well as interpolation and approximation methods. Fluid-particle-wall interactions. E SOFTWARE ENGINEERING SYLLABUS FOR REGULATION 2013 AFFILIATED INSTITUTIONS ANNA UNIVERSITY, CHENNAI REGULATIONS - 2013 M. , 3rd edition, Cambridge University Press, 2007. Motteler Class Time: TuTh 2:30-3:45, CP 210 Office Hours: TuTh 3:45-5:00 Text: Scientific Computing: An Introductory Survey, by Michael T. Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson's rule, single and multi-step methods for differential equations. Course Objectives: This course provides an introduction to the use of computers to solve scientific problems. When we reach the end of the class, you should be able to:. Assessment: Problem sets will be due on Tuesdays before class. SYLLABUS MTH/CS 364/464 - Numerical Analysis Fall 2016 Numerical Methods: Design, Analysis, and Computer Implementation of Algo- An Introduction to Numerical. AP215 is designed to give practical training in numerical methods to physical scientists and engineers. Learning objectives: describe general methods and principles for modelling and simulating a system. Prior experience with numerical methods at the level of CS 4210/4220 or CS 6210/6220 will be highly useful, though not strictly required. Numerical methods for solving high order nonlinear equations. Convex envelope. But the following books are good references for reading: S. List of course names mentioned here is partial and are not comprehensive and the institution would be offering many other courses than those mentioned on this page. Programming Assignments. There will be six homework assignments, each counting for 5% of your ﬁnal numerical grade. Matrix and Numerical Methods in Systems Engineering, ESI 4327C, Spring 2018 Page 3 Panos M. We will cover classical topics in Numerical Analysis: The solution of linear and non-linear equations, conditioning, least squares, numerical computation of eigenvalues, interpolation, quadrature, and numerical methods for ODEs. GATE 2020 Syllabus for Petroleum Engineering. TI-83 or higher recommended. 001 Syllabus (PDF Format). This course is an advanced introduction to numerical linear algebra and related numerical methods. Introduction 1. Students will learn the concepts of order, stability, and convergence of a numerical method. 2 Autonomous Systems and Stability o 9. ma6459 syllabus numerical methods regulation 2013 anna university for students. Create and manipulate arrays (vectors and matrices) by using NumPy. These topics include: introduction and some background stuff, algorithms for polynomial interpolation, Spline, numerical integration, systems of linear equations, nonlinear equations, method of least squares, numerical methods for ordinary differential equations. Numerical Methods for Conservation Laws by LeVeque; Matrix Computations by Golub and Van Loan. Numerical (cont. Sample Exam 1 Sample Exam 2. Numerical Integration: Design and implementation of quadrature rules. This website is generated automatically by CE Coursesite Generator which is produced by Yasser Ganji Saffar and is under GNU GPL version 2. The changes given below are for GATE 2016 syllabus compared to 2015. Oscillationg minimizers. Finite Di erence & Volume Methods for Hyperbolic PDEs. Existence, uniqueness, and stability theory. This course contains methods to approximate the roots of equations, solving systems of linear equations. Instructor: Dr. And this is exactly what this course is about. This lecture discusses different numerical methods to solve ordinary differential equations, such as forward Euler, backward Euler, and central difference methods. Applied Linear Algebra. Most numerical analysts specialize in small subfields, but. SYLLABUS - MATH 373: INTRODUCTION TO NUMERICAL ANALYSIS (3-0) 3 credits. MA8452 STATISTICS AND NUMERICAL METHODS Syllabus 2017 Regulation. Candidates can check out the full syllabus of the Petroleum Engineering which is also called as PE here. Algorithm efficiency and analysis, time and space analysis of algorithms – order notations. Approximating Eigenvalues. NUMERICAL SOLUTION OF HYPERBOLIC PDEs 3 hrs. Cal State LA Department of Mathematics Syllabus for MS Comprehensive Examinations NUMERICAL ANALYSIS 1. By the end of the course, you should have a good gut-level. Math 504 (Fall 2018) - Numerical Methods I Syllabus Description Majority of the numerical algorithms rely on the solutions of linear algebra problems. Numerical methods are used frequently in all areas of science, such as fluid dynamics, meteorology and financial risk management. Again, some engineering courses need their students to have seen some Laplace transforms. Exams: There will be two exams, one at midterm and a final exam. 3 Computer Oriented Numerical Methods Second Year Part III Group A Fourth Semester Subject Cod Syllabus - AS4 : Numerical Methods AS4 : Numerical Methods ( 4 Hours – 5 Credits) UNIT I Errors in computer Arithmetic –Empirical relations and Curve Fitting &. Math 4311: Numerical Analysis Course Syllabus. The attention is given to sources and. Grewal, Khanna Publishers. Recent questions and answers in Numerical Methods out-of-syllabus-now. Course objectives: This course is a graduate-level course in numerical methods for ordinary and. General Information. NPTEL Syllabus Numerical methods and programing - Video course I. Included are methods for the solution of algebraic and transcendental equations, simultaneous linear equations, ordinary and partial differential equations, and curve fitting techniques. The GATE Petroleum Engineering Syllabus 2020 is given by the IIT Delhi this year as it is the exam conducting authority. ma 415 - intro numerical methods Semester Hours: 3 Derivation and analysis of approximate methods for the solution of nonlinear equations, interpolation and integration of functions, and techniques for the solution of systems of linear equations and for approximating solutions of elementary differential equations. The tool is capable of handling large system of equations, non-linearities and complicated geometries that are not uncommon in engineering practice and that are often impossible to solve analytically. REQUIRED TEXT(S)/MATERIALS: John H. Resource: Scientific calculator with statistical functions and access to a computer with MS Excel, MATLAB and R software. Lecture 5: The Bisection Method and Locating Roots: mybisect. Ma Numerical Methods – Download as Text File. pdf provides the msbte model answer paper pdf format for the use of students. Important concepts such as accuracy, stability, efficiency and convergence are discussed. Nonlinear models. Candidates can check out the full syllabus of the Petroleum Engineering which is also called as PE here. a) Direct methods for solving linear systems, numerical factorizations. COURSE DESCRIPTION:. The course material will assume some familiarity with linear algebra and calculus. Approximation and Errors in computation 1. GATE Syllabus for Mechanical Engineering stream. py Euler's method: orbit-euler. numerical integration methods. Understand Statistical Methods for Data Analysis and sampling techniques. for the numerical solution of two-point boundary value problems. Syllabus MAE 384 Numerical Methods for Engineers Tu/Thu 12:00-1:15 PM SCOB 152 Instructor: Huei-Ping Huang Office hours: Tuesday & Thursday 3:30-5:00PM ISTB2 Room 219A Textbook: Numerical Methods for Engineers and Scientists: An Introduction with Applications Using MATLAB, Gilat and Subramaniam, Wiley 2007. There will be a number of programming assignments that emphasize important numerical methods in computational physics. Lecture Time: MWF 1:25 PM - 2:15 PM A Friendly Introduction to Numerical. Matrix and Vector norms 1. Mathews & Kurtis D. Compute integrals using appropriate quadrature, Monte Carlo, or Quasi-Monte Carlo methods. General Information. COURSE DESCRIPTION:. Grading: ﬁnal exam 40%, midterm exam 30%, homework 30%. pdf) or read UT Dallas Syllabus for physf taught by Roy Chaney (chaneyr ). Topics include solving linear systems and eigenvalue problems, numerical methods for ordinary di erential equations, and nite di erence methods for partial di erential equations. GATE 2020 exam is scheduled for 1st, 2nd, 8th, and 9th February 2020. Numerical Methods, NM Study Materials, Engineering Class handwritten notes, exam notes, previous year questions, PDF free download. Aitken acceleration. – Solutions are in numerical form. The course will have a focus on the analysis of numerical methods, but also require you to use numerical soft-. 1 Linear Systems of Equations (Optional) 6. to an introduction to numerical methods. 1 Linear Systems of Equations (Optional) 6. Topics include logic, methods of mathematical proof, set theory, relations and functions. Learn Computers, Waves, Simulations: A Practical Introduction to Numerical Methods using Python from Ludwig-Maximilians-Universität München (LMU). I Introduction. Provide doctoral students the basics of the numerical techniques which will be employed in their • to understand the methods and algorithms which are employed by the accessible routines in common statistical packages such as SAS, R, and Splus, and to be able to construct similar algorithms for the development of new methods. RECENT UPDATE The final exam (due on May 4th) is posted on Blackboard under course content. We will cover several topics in high order numerical methods for convection dominated problems, including methods for solving Boltzmann type equations, methods for solving unsteady and steady Hamilton-Jacobi equations, and methods for solving moment models in semi-conductor device simulations. Penny, Academic Press Midterm exam: There will be one theoretical midterm exam on Friday, March 18th. GATE syllabus 2020 for Civil Engineering consists of the subjects and topics that the candidates will have to study. The course code of Numerical Methods is BCA-S304. The main topics include computer arithmetic, nonlinear algebraic equations, polynomial interpolation, numerical differentiation and integration, initial-value problems for ordinary differential equations, and. Approximation theory a) Least square approximation 9. Solution of boundary value problem by finite difference. The sensitivity of the computed results to errors in the data, as well as to round-off errors introduced during the computations, will be discussed. The covered topics are listed in the syllabus. Theoretical, numerical, and experimental methods. SYLLABUS COMPUTER PROGRAMMING & NUMERICAL METHODS Course Plan Module Contents Sem. First introduction to numerical methods for PDEs, mainly based on finite difference methods. 001 Syllabus (Web Format) CSC 335. Bau, III, SIAM The following lectures from the text (and other sources) will be covered: Part I: Fundamentals Lecture 1 Matrix-Vector Multiplication Lecture 2 Orthogonal Vectors and Matrices Lecture 3 Norms. 5 Numerical Prediction Models. The GATE Petroleum Engineering Syllabus 2020 is given by the IIT Delhi this year as it is the exam conducting authority. IOE SYLLABUS - Numerical Methods (NM) _ IOE NOTES - IOE The course emphasizes algorithm development and programming and application to realistic engineering problems. In the end whether these algorithms are worthy for common use translates into whether the associated linear algebra problems can be solved eﬃciently and accurately. Solution of boundary value problem by finite difference. An equation f(x) = 0 may or may not have solutions. MATH2089 Numerical Methods and Statistics MATH2089 is a Level II course which is available only to students for whom it is specifically required as part of their program. Course is part of a two course sequence (660 and 661), but can be taken independently. Note of Numerical Methods can be accessed from HERE. Numerical errors, absolute and relative errors, stability and convergence of numerical algorithms. With respect to engineering issues, the student will: 1. Syllabus Course Description This is a practical programming course focused on the basic theory and efficient implementation of a broad sampling of common numerical methods. Taylor and MacLauren Series 3. 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The primary goal is to provide students with a basic knowledge of numerical methods including: root-finding, interpolation, numerical differentiation and integration, and numerical solution to ordinary differential equations. Study and application of numerical methods in solving problems commonly encountered in engineering. ASSESSMENT The evaluation is composed of a final exam, problem sets, and class participation. Eigenvalue problems. Numerical Analysis I teaches this analysis associated with direct methods of solution of linear systems, zeros of non-linear equations, approximation and interpolation, numerical integration, initial value problem for ordinary diﬀerential equations, with attention to generation and propagation of numerical errors and to computational speed. Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations ADD. This GATE lecture of engineering mathematics on topic "Numerical Methods Part 1 (Basics)" will help the GATE aspirants engineering students to understand following topic: Introduction Analytical. Numerical solutions to the diffusion equations of multiple dimensions. Theoretical, numerical, and experimental methods. NPTEL Syllabus Numerical methods and programing - Video course I. Evaluation scheme: The questions will cover all the chapters of the syllabus. The course emphasizes algorithm development and programming and application to realistic engineering problems. (B) Develop an understanding of the mathematical principles of numerical methods. • Numerical methods for approximating deﬁnite integrals: the Midpoint, Trapezoidal, and Simpson’s rules. Chapra, Published by McGraw Hill. Syllabus Change Policy. ] on Amazon. to an introduction to numerical methods. Numerical differentiation and Integration: Numberical differentiation, Numerical integration using Trapezoidal Rule, Simpson's 1/3rd and 3/8th rules Numerical solution of 1st and 2nd order differential equations: Taylor series, Euler's Method, Modified Euler's Method, Runge-Kutta Method for 1st and 2 nd Order Differential Equations. In order to accomplish these goals, students are to develop the following skills:. In addition, the course contains methods of interpolation, using series to approximate real numbers and functions, and methods for fitting curves to data. The various scientific phenomena in nature and man-made events can be mathematically modeled using equations and expressions. To enhance the problem solving skills of engineering students using an extremely powerful problem solving tool namely numerical methods. To teach the fundamentals of numerical methods, with emphasis on the most essential methods. Introduction to complex numbers and proof strategies using ideas of vector algebra. course emphasizes algorithm development and programming and application to. Syllabus for Math 818. Numerical errors, absolute and relative errors, stability and convergence of numerical algorithms. Numerical methods-solution of Algebraic and transcendental Equations, Interpolation. Between 100 and 200. Probability distribution functions, cumulative pdfs, transformation of probabilities. A large class of problems cannot be analyzed with analytical tools, and numerical methods. Gaussian quadratures. You will be required to arrange a time to do your Matlab laboratory test through the School of. Numerical Methods for Physics is an upper-division/graduate level textbook on computational physics. Civil subject is the one of the papers in GATE 2020 Exam. Appropriate papers and links will be posted on the course website. Course number and name 0941301: Engineering Numerical Methods 2. 4 Numerical Methods. 231 Ordinary Differential Equations, Math 01. GATE CSE 2020 syllabus remains the same as GATE CSE 2016 (no change for last 5 years). Syllabus for Numerical Methods Topics of the Ph. Canale, McGraw Hill International Editions. Interpolation Methods: Lagrange polynomials, finite differences, least square approximation. Exam 2 (Numerical Methods & MathCAD Programming, accumulative, closed book and closed notes) during the 8 th ~10 th period on Wednesday, Mar. txt) or read online for free. MA6459 Numerical Methods (NM) Question bank , Notes Syllabus 2 marks with answers Part A Question Bank with answers Key, Important Part B Questions & MA6459 Numerical Methods ANNA UNIVERSITY Question Papers Collection Reviewed by EasyEngineering on 05:40 Rating: 5. the course page. Second edition (revised) is now available in two versions: Matlab and C++ version for $19: Amazon. 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Computational%component:% (1)%Finite%difference%based%methods%for%solving%linear%and%nonlinearelliptic% problems;% (2)%Boundary%integral%methods%for%solving%linear. Syllabus MAD 4401. GATE 2020 Syllabus for Civil Engineering - Candidates can check the syllabus of GATE 2020 for Civil Engineering to prepare for the upcoming examination. In order to accomplish these goals, students are to develop the following skills:. • Convergence of numerical algorithms – practical considerations. In addition, the course contains methods of interpolation, using series to approximate real numbers and functions, and methods for fitting curves to data. Numerical Methods and Optimization Techniques Semester 4 (SE Second Year) BE Electrical Engineering University of Mumbai Topics and Syllabus. Topics covered include: solution of nonlinear scalar equations, direct and iterative algorithms for the. IOE SYLLABUS – Numerical Methods (NM) The course aims to introduce numerical methods used for the solution of engineering problems. Ordinary Differential Equations. To introduce various techniques to solve problems in mathematics, computer science, engineering, and physical science. Numerical integration: One-dimensional quadrature (midpoint, trapezoidal, Simpson, Newton-Cotes, Hermite methods, etc. A numerical method to solve equations may be a long process in some cases. The covered topics are listed in the syllabus. The project is optional for undergraduates and required for graduate students. Numerical Differentiation Taylor Series Methods Richardson Extrapolation Lagrange methods Numerical errors Ascher and Greif 14. It is the purpose of this course to introduce state-of-the-art numerical methods and provide an understanding of their performance through analysis and application. AP215 is designed to give practical training in numerical methods to physical scientists and engineers. Learn Computers, Waves, Simulations: A Practical Introduction to Numerical Methods using Python from Ludwig-Maximilians-Universität München (LMU). Examination: _70___% (duration: 3 hrs , if applicable) Examination questions are designed to see how far students have achieved their intended learning outcomes. Dover Books on Mathematics, 2003. Understand and apply basic numerical methods for solving ODEs. Lecture 5: The Bisection Method and Locating Roots: mybisect. Most numerical analysts specialize in small subfields, but. Numerical Analysis: Numerical Methods for Engineers, Chapra & Canale, McGraw Hill. , have applied. Students completing this course will be able to: 1) employ numerical techniques to diﬁerentiate and integrate functions; 2) solve numerically system of equations; 3) solve numerically the static and dynamic optimization problems commonly discussed in almost all ﬂelds of economics; 4) employ numerical methods to solve functional equations. Of course, you may also sharpen your coding skills. Gate 2020 syllabus for civil engineering gate syllabus for ce civil syllabus full pdf download, civil gate exam pattern, download pdf Numerical Methods: Accuracy. Group discussions about the homework are encouraged, but each student must write his/her own solutions and not copy them from anyone else. Program the numerical methods to create simple and efficient Python codes that output the numerical solutions at the required degree of accuracy. Recent questions and answers in Numerical Methods. Applied Numerical Methods with MATLAB is written for students who want to learn and apply numerical methods in order to solve problems in engineering and science. Download link is provided and students can download the Anna University MA6459 Numerical Methods (NM) Syllabus Question bank Lecture Notes Syllabus Part A 2 marks with answers Part B 16 marks Question Bank with answer, All the materials are listed below for the students to make use of it and score good (maximum) marks with our study materials. Mathematics. January 10, 2012. • Numerical Methods for Ordinary Differential Equations • Numerical Linear Algebra • Fast Fourier Transform • An Introduction to Partial Differential Equations, Wavelets and Kalman Filtering Course Ingredients • Lectures • Problem Sessions • Homework Assignments • Presentation/Project Syllabus. Tech MA202 Probability distributions, Transforms and Numerical Methods Sixth Module Notes Given Below MA202 Note Module-6 MA202 Note Module-5. Visitors are advised to contact the University directly for the official, detailed and accurate Syllabus, Transcripts and other information. Numerical Methods – Syllabus. A large class of problems cannot be analyzed with analytical tools, and numerical methods. For other time, please make an. Lee Office MH 182 E MWF 10AM-11AM Phone 657-278-2726 E-mail
These topics include: introduction and some background stuff, algorithms for polynomial interpolation, Spline, numerical integration, systems of linear equations, nonlinear equations, method of least squares, numerical methods for ordinary differential equations. The evaluation scheme will be as indicated in the table below. If the student applies for the exam fourth time he/she will be invited to take the oral exam regardless to the result of the written exam. Self-organizing maps. Civil subject is the one of the papers in GATE 2020 Exam. Yang, Wenwu Cao, Tae-Sang Chung, John Morris, Wiley Numerical Computing with MATLAB by Cleve Moler (available online). by using numerical techniques, and through methods of qualitative analysis. CFL Criterion. In this course, the educator deals with complete syllabus for NUMERICAL methods covering GATE, engineering curriculum and syllabus for different competitive exams also. It covers C programs on 15 frequently asked Numerical methods in a very easy and simple way. Students will understand the concepts of order, stability, and convergence of a numerical method. Solution of partial differential equations. Programming, round-off error, solutions of equations in one variable, interpolation and polynomial approximation, approximation theory, direct solvers for linear systems, numerical differentiation and integration, initial-value problems for ordinary. The Newton- Raphson method is applied once to get a new estimate and then the Secant method is applied once using the initial guess and this new estimate. Students should have learned what Numerical Methods/Analysis is about:. Methods and computation are the focus of this course. - The first book on the FEM by Zienkiewicz and Chung was published in 1967. This class will introduce computational methods for numerical solution of non-linear equations, di erential equations, approximations, iterations, methods of least squares, and other topics. course emphasizes algorithm development and programming and application to. Numerical analysis is the story of how functions, derivatives, integrals, and differential equations are handled as strings of numbers in the computer. Numerical Analysis Approximations and round off errors, Truncation errors and Taylor Series, Determination of roots of polynomials and transcendental equations by Newton-Raphson, Secant and Bairstow's method. Numerical Analysis.