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Annexure ‘CD – 01’ FORMAT FOR COURSE CURRICULUMLTP/SSW/FWTOTAL CREDIT UNITS 31004Course Title: MATHEMATICS – I- SUBSIDIARYCredit Units: 4Course Level: UG Course Code: MATH123Course Objectives: The objective of this course is to lay the Foundations of Mathematics required for the study of behavioral, physical and natural Sciences. The emphasis is on introducing mathematical concepts using examples from various science domainsPre-requisites: Students must have basic knowledge of some elementary mathematics.Course Contents/Syllabus:Weightage (%)Module I Sets & Functions 20Descriptors/Topics :Introduction to Sets: Methods of describing a set, Types, Venn diagram, Operations on sets, De-Morgan’s lawAlgebra of sets Ordered pair and Cartesian Product of setsApplications of setsRelations and Properties of relationsBinary RelationsSingle-Valued FunctionsDifferent types of functionsComposition of functionsInvertible functionsModule II Introduction to Differential Calculus 30Descriptors/Topics:Overview of Limit, Continuity and Differentiability: Limit of a function, Methods of Evaluating limit of a function, Continuity at a point, Continuity on a set, Derivative of a function, Derivative at a point, Rules for differentiation (Sum, product, Quotient and Chain rule) Tangents and NormalMaxima and Minima of one variableRolle’s TheoremLagrange’s Mean Value Theorems Taylor’s seriesMaclaurin’s series of sin x, Cos x, ex , log(1 + x), (1 + x)mSuccessive differentiationLeibnitz theoremModule III Theory of EquationsDescriptors/Topics:Roots of a Polynomial equation in one variableRelation between roots and coefficients of a polynomial equationSum of powers of rootsSymmetric functionsTransformation of equationsCardan’s solution of a cubic polynomialDiscartes’ solution of a biquadratic equation25Module IV : StatisticsMeasures of central tendency: Mean, Median and Mode, Measures of Dispersion: Range, Quartile deviation, Mean deviation, Standard deviation, Skewness and Kurtosis Elementary probability theory and simple problemsConditional Probability and Baye’s Theorem (without proof)Fitting a straight line, parabola and exponential curve using Principle of least square25Student Learning Outcomes: After the completion of the course students familiar with the fundamentals laws of mathematics and .Further they can apply mathematical formulas in solving physics problem. Pedagogy for Course Delivery: Reviewing relevant, previously-learned topics.Presenting the new information by linking it to previous topics.Providing learning guidance and assignments.Providing time for practice, problem solving sessions and feedback.Taking tests and quiz on regular basis.Extra sessions for revision will be undertaken.Lab/ Practicals details, if applicable: NA List of Experiments:Assessment/ Examination Scheme:Theory L/T (%)Lab/Practical/Studio (%)End Term Examination30NA70Theory Assessment (L&T):Continuous Assessment/Internal AssessmentEnd Term ExaminationComponents (Drop down)MID TERMHOME ASSIGNMENTVIVAATTENDANCEWeightage (%)1078570Lab/ Practical/ Studio Assessment: NAContinuous Assessment/Internal AssessmentEnd Term ExaminationComponents (Drop downWeightage (%)Text Books:Karel Hrbá?ek and Thomas Jech, Introduction to Set Theory, Marcel Dekker Inc., New York H Anton, I Bivens and S Davis, Calculus, John Wiley and Sons, 2002 G B Thomas and R L Finney, Calculus, Pearson Education, 2007 Robert V Hogg, Joseph W McKean and Allen T Kraig, Introduction to Mathematical Statistics, Pearson Education, 2012. Kenneth Kunen, Set theory: An introduction to independence Proof, North-Holland Publishing?Company (1980).Reference Books: ................
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