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Paper Code
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Paper Title
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Course outcome
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MATH101TH
CORE COURSE-1
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Differential calculus
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· Use
of e - δ definition to find the limits and continuity of functions.
· Study
relationship between continuation and differentiation.
· Able
to understand the idea of limits of functions by L- hospitals rule
· Learn
the proofs of general theorem and their geometrical consequences.
· Learns
the notation of concavity convexity asymptotes.
· Are
able to trace the curves in polar and rectangular coordinates.
· Understands
the concepts of limit and continuity of functions of several variables.
· Are
able to convert Cartesian to polar coordinates and vice versa.
· Learn
the proof and applications of Euler’s theorem on homogeneous functions
· Are
able to calculate Jacobeans’.
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Ability Enhancement
Compulsory Course -I
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English/Hindi(Communication)/Environmental Science
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These courses are the courses based upon the content that leads to Knowledge enhancement.
And are value-based and/or skill-based and are aimed at providing hands-on-training,
competencies, skills etc. in English and/Hindi and Environment science.
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MATH201TH
CORE COURSE -2
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Differential equations
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· Understands
basic definitions and terminology associated with ordinary differential equations.
· Learn
rules to find integrating factors.
· Distinguish
between linear and non linear, ordinary and partial differential equations.
· Recognize
and solve homogeneous and non homogeneous equations by different methods
· Students
are able to apply the methods of variation of parameters and reduction of order.
· Use
working to determine linear dependence and linear independent of functions.
· Learns
to solve Cauchy Euler’s equations.
· Learn
the concepts of total differential equations.
· Can
form partial differential equations of first order and use Langrange’s methods to
solve partial differential equations.
· Are
able to find solutions of partial differential equations by Charpit’s method.
· Learn
to classify second order partial differential equation through lustration only.
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Ability Enhancement
Compulsory Course -II
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English/Hindi(Communication)/Environmental Science
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These courses are the courses based upon the content that leads to Knowledge enhancement.
And are value-based and/or skill-based and are aimed at providing hands-on-training,
competencies, skills etc. in English and/Hindi and Environment science.
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MATH301TH CORE COURSE -3
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REAL ANALYSIS
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· Define
and recognize sequence and series of real numbers and their conversions and uniform
conversions
· Recognize
the difference between point wise conversions and uniform conversions of sequence
of function.
· Use
comparison, condensation, ratio, root condensation and Leibnitz’s test for conversion
of series.
· Construct
mathematical proofs of basic results in real analysis
· are
able to comprehend bounded sets ,Archimedean properties and Bolzano-Weierstrass
theorem
· Students
can produce proofs of results of real analysis.
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Skill Enhancement Course-1
MATH302TH
OR
MATH303T
OR
MATH304TH
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Analytical Geometry
OR
Integral Calculus
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Integral Calculus, (MATH304TH)
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Learns integration by partial functions and properties of the definite
integrals
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Establish various reduction formulae
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Are able to connect to integrals (smaller index+1)
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Learn to find area and length of curves in planes.
· Evaluate
double and triple integrals.;
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MATH401TH CORE COURSE-4
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Algebra
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· Study
the definition of groups rings and fields.
· Are
able to understand concept if subgroups, normal subgroups and quotient groups.
· Use
concepts of homomorphism isomorphism and endomorphism for group sand rings.
· Use
canonical types of groups like cyclic groups ,permutation groups and rings such
as polynomial rings and quotient rings
· Are
able to find cossets and related theorem.
· Produce
groups of theorem on algebra.
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Skill Enhancement Course-2
MATH402TH
OR
MATH403TH
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Vector Calculus
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Theory of Equations
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Number Theory
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VECTOR CALCULUS(MATH402TH
· Study
differentiation & partial differentiation of a vector sum.
· Learn
the concept of the dot product.
· To
study to find gradient, divergence and curl of vectors.
(Theory of Equations MATH403TH)
· Students
will be familiar with general properties of polynomials and their graphical representation.
· Will
be able to compute maximum and minimum values of polynomials.
· Will
gain the ability to use Descartes role of science for positive and negative roots.
· Will
come to know about the concept of symmetric functions.
· Will
use transformation of equations and will be able to find solutions of binomial and
reciprocal equations.
· Students
will gain the ability to find algebraic solutions of cubic and biquadrate’s.
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DSE-Course-1
MATH501TH
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MATH502TH
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MATH503TH
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Matrices
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Mechanics
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Linear Algebra
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Linear Algebra(MATH503TH)
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Analysis vectors in Rn algebraically
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Learn the concepts of linear independence and dependence, linear span
basis and dimensions.
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Study vector spaces and subspaces.
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Use matrix algebra and relate matrices to linear transformations.
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Study inner product spaces and Cauchy Schwarz’s in equality.
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Skill Enhancement Course -3
MATH504TH
OR
MATH505TH
OR
MATH506TH
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Probability and Statistics
OR
Mathematical Finance
OR
Mathematical Modeling
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DSE Course- 2
MATH601TH
OR
MATH602TH
OR
MATH603TH
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Numerical analysis
OR
Complex methods
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Analysis
Linear programming
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Numerical Analysis,(MATH601th)
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Study to find the approximate rules of non linear equation s by using
different methods such as bisection, secant and Newton Repson method.
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How to find missing numbers from the available data and the estimate
value of known quantity between the two known quantities.
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To find the value of definite integral from set of tabulated values
of the integrand by using trapezoidal and Simpsons rule.
Complex Methods (MATH602TH)
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Define functions in their complex domains
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Study relation between points in Cartesian plane and complex planes
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Study the complex integration of functions, limit and continuity of
complex functions, Cauchy Riemann equation harmonic functions.
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Skill Enhancement Course--IV
MATH604TH
Or
MATH605TH
Or
MATH606TH
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Boolean Algebra
Or
Transportation And
Game Theory
Or
Graph Theory
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Boolean algebra (MATH604TH)
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Study the definition, examples of ordered sets, maps between
the ordered sets, maximal and minimal elements,l attices, sublattices and homomorphisms.
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Definition and properties of modular and distributive lattices,
boolian polynomials , minimal form of boolian polynomials.
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