Advanced Numerical Analysis CH 7th Sem Syllabus for AKTU B.Tech 2019-20 Scheme (Departmental Elective-4)

Advanced Numerical Analysis detail syllabus for Chemical Engineering (CH), 2019-20 scheme is taken from AKTU official website and presented for AKTU students. The course code (RCH078), and for exam duration, Teaching Hr/Week, Practical Hr/Week, Total Marks, internal marks, theory marks, and credits do visit complete sem subjects post given below.

For all other ch 7th sem syllabus for b.tech 2019-20 scheme aktu you can visit CH 7th Sem syllabus for B.Tech 2019-20 Scheme AKTU Subjects. For all other Departmental Elective-4 subjects do refer to Departmental Elective-4. The detail syllabus for advanced numerical analysis is as follows.

Module 1:

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Module 2:

Fundamentals of Vector Spaces

1. Generalized concepts of vector space, sub-space, linear dependence 1,2
2. Concept of basis, dimension, norms defined on general vector spaces 2
3. Examples of norms defined on different vector spaces, Cauchy sequence and convergence, introduction to concept of completeness and Banach spaces 3
4. Inner product in a general vector space, Inner-product spaces and their examples, 4
5. Cauchy-Schwartz inequality and orthogonal sets 4
6. Gram-Schmidt process and generation of orthogonal basis, well known orthogonal basis 5
7. Matrix norms 6
8. Module 3: Problem Discretization Using Approximation Theory Sections
9. Transformations and unified view of problems through the concept of transformations, classification of problems in numerical analysis, Problem discretization using approximation theory 1,2
10. Weierstrass theorem and polynomial approximations, Taylor series approximation 2, 3.1
11. Finite difference method for solving ODE-BVPs with examples 3.2
12. Finite difference method for solving PDEs with examples 3.3
13. Newton’s Method for solving nonlinear algebraic equation as an application of multivariable Taylor series, Introduction to polynomial interpolation 3.4
14. Polynomial and function interpolations, Orthogonal Collocations method for solving ODE-
15. BVPs 4.1,4.2,4.3
16. Orthogonal Collocations method for solving ODE-BVPs with examples 4.4
17. Orthogonal Collocations method for solving PDEs with examples 4.5
18. Necessary and sufficient conditions for unconstrained multivariate optimization, Least square approximations 8
19. Formulation and derivation of weighted linear least square estimation, Geormtraic interpretation of least squares 5.1,5.2
20. Projections and least square solution, Function approximations and normal equation in any inner product space 5.3
21. Model Parameter Estimation using linear least squares method, Gauss Newton Method 5.4
22. Method of least squares for solving ODE-BVP 5.5
23. Gelarkin’s method and generic equation forms arising in problem discretization 5.5
24. Errors in Discretization, Generaic equation forms in transformed problems 6,7

Module 4:

Solving Linear Algebraic Equations Sections

1. System of linear algebraic equations, conditions for existence of solution – geometric interpretations (row picture and column picture), review of concepts of rank and fundamental theorem of linear algebra 1,2
2. Classification of solution approaches as direct and iterative, review of Gaussian elimination 3
3. Introduction to methods for solving sparse linear systems: Thomas algorithm for tridiagonal and block tridiagonal matrices 4
4. Block-diagonal, triangular and block-triangular systems, solution by matrix decomposition 4
5. Iterative methods: Derivation of Jacobi, Gauss-Siedel and successive over-relaxation methods 5.1
6. Convergence of iterative solution schemes: analysis of asymptotic behavior of linear difference equations using eigen values 9
7. Convergence of iterative solution schemes with examples 5.2
8. Convergence of iterative solution schemes, Optimization based solution of linear algebraic equations
9. Matrix conditioning, examples of well conditioned and ill-conditioned linear systems 7

Module 5:

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Module 6:

Solving Ordinary Differential Equations – Initial Value Problems (ODE-IVPs) Sections

1. Introduction, Existence of Solutions (optional topic),
2. Analytical Solutions of Linear ODE-IVPs. Analytical Solutions of Linear ODE-IVPs (contd.), Basic concepts in numerical solutions of
3. ODE-IVP: step size and marching, concept of implicit and explicit methods 4
4. Taylor series based and Runge-Kutta methods: derivation and examples 5
5. Runge-Kutta methods 5
6. Multi-step (predictor-corrector) approaches: derivations and examples 6.1
7. Multi-step (predictor-corrector) approaches: derivations and examples 6.1
8. Stability of ODE-IVP solvers, choice of step size and stability envelopes 7.1,7.2
9. Stability of ODE-IVP solvers (contd.), stiffness and variable step size implementation 7.3,7.4
10. Introduction to solution methods for differential algebraic equations (DAEs) 8
11. Single shooting method for solving ODE-BVPs 9
12. Review

Reference Books:

1. Gilbert Strang, Linear Algebra and Its Applications (4th Ed.), Wellesley Cambridge Press (2009).
2. Philips, G. M.,Taylor, P. J. ; Theory and Applications of Numerical Analysis (2nd Ed.), Academic Press, 1996.
3. Gourdin, A. and M Boumhrat; Applied Numerical Methods. Prentice Hall India, New Delhi, (2000).
4. Gupta, S. K.; Numerical Methods for Engineers. Wiley Eastern, New Delhi, 1995.

For detail syllabus of all other subjects of B.Tech Ch, 2019-20 regulation do visit Ch 7th Sem syllabus for 2019-20 Regulation.

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