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Scientific Computing Lab - II 2022
Subject Code: MAT222
Credits: 2
Scientific Computing Lab II
ReviewofPythoncommands,Pythonvariables,SymbolicVariables,Firstcom- putations; Elementary functions and Usual constants; Auto completion; Sim- ple plotting.
SymbolicExpressionsandSimplification;Transformingexpressions;UsualMath- ematical functions; Assumptions and pitfalls; Explicit solving of Equations; Equa- tion with no explicit solution; Sums; Limits; Sequences; Power Series Expan- sions; Series; Derivaties; Partial Derivatives; Integrals; Solving linear systems; Vector Computations; Matrix Computations; Reduction of a Square Matrix
Programming with Sage; Python language keywords; Sage Keywords; Special symbols in Sage and their uses; Function Calls; Algorithms - Loops; Approxi- mation of Sequence Limits; Conditionals; Procedures and functions; Iterative and recursive methods; Input and Output
Lists and Othere Data Structures; List creation and access; Global list opera- tions; Main methods on lists; Examples of list manipulations; Character Strings; Shared or Duplicated Data Structures; Mutable and Immutable Data Structures; Finite sets; Dictionaries;
2DGraphics-Graphicalrepresentationofafunction;ParametricCurve;Curves in Polar Coordinateds; Curve Defined by an implicit function; Data Plot; Dis- playing solutions of differential equations; Evolute of a curve; 3D Graphics
StatisticswithSagemath:Basicfunctions-random,mean,median,mode,mov-
ing average, std, variance; C Int Stats - stats.IntList, min, max, plot, histogram, product, sum; Distributions - norm, uniform, expon, bernoulli, poisson; Statis-
tical functions - stats.gmean, stats.hmean, stats.skew, stats.histogram2, stats.kurtosis, stats.linregress; Statistical model - linear fit - stats.glm
References.
P. Zimmermann et.al., Mathematical Computation with Sage, SIAM, Philadel- phia, 2018. (http://sagebook.gforge.inria.fr/english.html)
R.A.Mezei,AnIntroductiontoSAGEProgramming:WithApplicationstoSAGE Interacts for Numerical Methods, John Wiley & Sons, 2015.
G.A.Anastassiou,R.A.Mezei,NumericalAnalysisUsingSage,Springer,2015.
R.A.Beezer,AFirstCourseinLinearAlgebra,UniversityPressofFlorida,2009.
A.Kumar&S.G.Lee,LinearAlgebrawithSage,KyoboBooks,2015. (http://matrix.skku.ac.kr/2015-Album/Big-Book-LinearAlgebra-Eng-2015.pdf )
https://docs.scipy.org/doc/scipy/reference/stats.html