Numerical Analsysis-I

The course has been designed to teach the students about construction of numerical methods, their analysis and applications. It provides necessary background needed for numerical computing in various mathematical and engineering disciplines. The students are expected to know computer programming tobe able to write programs for numerical methods.

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Created by Muhammad Usman Last updated Wed, 10-Jan-2024 English
What will i learn?
  • Knowledge and Understanding: During the lecture the student understands the nature and operations of Numerical Analysis, demonstrates familiarity with theories and concepts used in Numerical Analysis, and identifies the steps required to carry out a piece of research on a topic in Numerical Analysis.
  • Intellectual Skills: By the end of the course the student is expected to recognize and apply appropriate theories, principles and concepts relevant to Numerical Analysis, critically assess and evaluate the literature within the field of Numerical Analysis, analyze and interpret information from a variety of sources relevant to Numerical Analysis.
  • Practical Skills: By the end of the course student will have the ability to compare the computational methods for advantages and drawbacks, choose the suitable computational method among several existing methods.
  • Transferable Skills: Within the lectures the student is able to transfer ideas and experience, work effectively as a part of a group and independently.

Curriculum for this course
6 Topics
Nonlinear equations
0 Sub Topics
Interpolation with equally spaced data
0 Sub Topics
Interpolation with non-equally spaced data
0 Sub Topics
Numerical differentiation
0 Sub Topics
Numerical integration and error estimates
0 Sub Topics
System of linear equations
0 Sub Topics
Title Lectures Price
Inquiry Based Session-1 lesson 1 20$
Regular Package/ 4 lesson 4 75$
Standard Package/8 Lesson 8 140$
Premium Package/12 12 225$
Fast Track/16 Lesson 16 300$
  • Calculus
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Introduction and some significant concepts.

Nonlinear equations: Bisection-, Fixed point iteration-, Newton-Raphson-, Secant and Regula-Falsi methods and convergence orders of these methods.

Interpolation with equally spaced data: Gregory- Newton forward difference and backward difference formulae, Bessel’s and Everett’s Formulae, Gauss forward difference and backward difference formulae, Hermite interpolating Formulae and Error estimation of these Formulae.

Interpolation with non-equally spaced data: Lagrange and Newton divided difference formulae, and their error estimation and Cubic Spline Formulae.

Numerical differentiation: in one dimension based on interpolation formulas.

Numerical integration and error estimates: Rectangular rule, Trapezoidal rule, Simpson’s one-three and three-eight rules.

System of linear equations: Factorization methods, Jacobi-, Gauss-Seidel and SOR methods with their error formulae.

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About the instructor
  • 1 Reviews
  • 1 Students
  • 6 Courses
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Hi, I am Dr. Muhammad Usman graduated from Peking University in the field of applied and computational mathematics with distinguished student. I also completed my postdoc in field of computational mathematics. I have numerous research articles published in well-reputed international journals. Therefore, I have rich experience in research and supervise project students. As for as my teaching career is concerned, I have 14 years’ experience in teaching. I have taught various courses at A-level, O-level, graduate and postgraduate level. In the recent past years, I involve extensively in teaching online at A-level and O-level. Positive feedback of my past students always encourage me to deliver more in the better way. I look forward to working together with you as partners in your child’s educational growth and development!!

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  • 6 Topics , 0 Sub Topics
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