{"id":4201,"date":"2020-02-08T05:20:10","date_gmt":"2020-02-08T05:20:10","guid":{"rendered":"https:\/\/www.inspirenignite.com\/up\/advanced-numerical-analysis-ch-7th-sem-syllabus-for-aktu-b-tech-2019-20-scheme-departmental-elective-4\/"},"modified":"2020-07-05T03:28:34","modified_gmt":"2020-07-05T03:28:34","slug":"advanced-numerical-analysis-ch-7th-sem-syllabus-for-aktu-b-tech-2019-20-scheme-departmental-elective-4","status":"publish","type":"post","link":"https:\/\/www.inspirenignite.com\/up\/advanced-numerical-analysis-ch-7th-sem-syllabus-for-aktu-b-tech-2019-20-scheme-departmental-elective-4\/","title":{"rendered":"Advanced Numerical Analysis CH 7th Sem Syllabus for AKTU B.Tech 2019-20 Scheme (Departmental Elective-4)"},"content":{"rendered":"

Advanced Numerical Analysis detail syllabus for Chemical Engineering (CH), 2019-20 scheme is taken from AKTU<\/a> 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.<\/p>\n

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<\/a>. For all other Departmental Elective-4 subjects do refer to Departmental Elective-4<\/a>. The detail syllabus for advanced numerical analysis is as follows.<\/p>\n

Module 1:<\/h4>\n

For the complete syllabus, results, class timetable and more kindly download iStudy<\/a>. It’s a lightweight, easy to use, no images, no pdfs platform to make student’s life easier.<\/b><\/p>\n

Module 2:<\/h4>\n

Fundamentals of Vector Spaces<\/p>\n

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

    Module 4:<\/h4>\n

    Solving Linear Algebraic Equations Sections<\/p>\n

      \n
    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<\/li>\n
    2. Classification of solution approaches as direct and iterative, review of Gaussian elimination 3<\/li>\n
    3. Introduction to methods for solving sparse linear systems: Thomas algorithm for tridiagonal and block tridiagonal matrices 4<\/li>\n
    4. Block-diagonal, triangular and block-triangular systems, solution by matrix decomposition 4<\/li>\n
    5. Iterative methods: Derivation of Jacobi, Gauss-Siedel and successive over-relaxation methods 5.1<\/li>\n
    6. Convergence of iterative solution schemes: analysis of asymptotic behavior of linear difference equations using eigen values 9<\/li>\n
    7. Convergence of iterative solution schemes with examples 5.2<\/li>\n
    8. Convergence of iterative solution schemes, Optimization based solution of linear algebraic equations<\/li>\n
    9. Matrix conditioning, examples of well conditioned and ill-conditioned linear systems 7<\/li>\n<\/ol>\n

      Module 5:<\/h4>\n

      For the complete syllabus, results, class timetable and more kindly download iStudy<\/a>. It’s a lightweight, easy to use, no images, no pdfs platform to make student’s life easier.<\/b><\/p>\n

      Module 6:<\/h4>\n

      Solving Ordinary Differential Equations – Initial Value Problems (ODE-IVPs) Sections<\/p>\n

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

        Reference Books:<\/h4>\n
          \n
        1. Gilbert Strang, Linear Algebra and Its Applications (4th Ed.), Wellesley Cambridge Press (2009).<\/li>\n
        2. Philips, G. M.,Taylor, P. J. ; Theory and Applications of Numerical Analysis (2nd Ed.), Academic Press, 1996.<\/li>\n
        3. Gourdin, A. and M Boumhrat; Applied Numerical Methods. Prentice Hall India, New Delhi, (2000).<\/li>\n
        4. Gupta, S. K.; Numerical Methods for Engineers. Wiley Eastern, New Delhi, 1995.<\/li>\n<\/ol>\n

          For detail syllabus of all other subjects of B.Tech Ch, 2019-20 regulation do visit Ch 7th Sem syllabus for 2019-20 Regulation<\/a>.<\/p>\n

          Don’t forget to download iStudy<\/a> for the latest syllabus, results, class timetable and more.<\/p>\n","protected":false},"excerpt":{"rendered":"

          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, […]<\/p>\n","protected":false},"author":2300,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[47],"tags":[],"class_list":["post-4201","post","type-post","status-publish","format-standard","hentry","category-chemical-engineering"],"_links":{"self":[{"href":"https:\/\/www.inspirenignite.com\/up\/wp-json\/wp\/v2\/posts\/4201","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.inspirenignite.com\/up\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.inspirenignite.com\/up\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.inspirenignite.com\/up\/wp-json\/wp\/v2\/users\/2300"}],"replies":[{"embeddable":true,"href":"https:\/\/www.inspirenignite.com\/up\/wp-json\/wp\/v2\/comments?post=4201"}],"version-history":[{"count":0,"href":"https:\/\/www.inspirenignite.com\/up\/wp-json\/wp\/v2\/posts\/4201\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.inspirenignite.com\/up\/wp-json\/wp\/v2\/media?parent=4201"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/up\/wp-json\/wp\/v2\/categories?post=4201"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/up\/wp-json\/wp\/v2\/tags?post=4201"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}