Your roadmap · आपका रोडमैप
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Admission & first meetingप्रवेश और पहली मुलाकातEnquire at your nearest NDSS centre, meet the teacher, fix the batch time and get your study material.
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Semester 6 — subject classesसेमेस्टर 6 — विषयवार कक्षाएँEvery theory subject of the term, unit by unit, with notes, numericals and doubt classes.
Metric Spaces and Complex AnalysisNumerical Analysis and Operations Research
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Labs, practicals & project workलैब, प्रैक्टिकल और प्रोजेक्टExperiments / jobs / project work as in the syllabus, with practical file and viva preparation.
Mathematics Practical-VI
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Unit tests & mid-termयूनिट टेस्ट और मिड-टर्मA test after every unit and a mid-term in the university / board pattern.
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Semester 6 mock testमॉक टेस्टA full mock test of all subjects before the exam, with analysis.
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Semester 6 exam (university / board)सेमेस्टर / वार्षिक परीक्षाPrevious papers, important questions and full revision.
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Online tests & resultऑनलाइन टेस्ट और रिज़ल्टTake the tests online; your marks and result show in your student login and at the centre.
सिलेबस · पाठ्यक्रम
3 subjects · 14 chapters · 70 topics
Metric Spaces and Complex Analysis5 chapters · 6 Months
Subject page →+
01Unit 1: Metric Spaces
6 टॉपिक+
- Definition and examples of metric spaces
- Open and closed balls
- Open and closed sets, interior, closure and boundary
- Limit points and dense sets
- Convergent and Cauchy sequences
- Subspaces
02Unit 2: Completeness, Compactness and Connectedness
6 टॉपिक+
- Complete metric spaces
- Cantor's intersection theorem
- Banach contraction principle
- Continuity and uniform continuity
- Compactness and Heine-Borel theorem
- Connectedness
03Unit 3: Analytic Functions
6 टॉपिक+
- Limits, continuity and differentiability of complex functions
- Cauchy-Riemann equations
- Analytic and harmonic functions
- Harmonic conjugates
- Elementary functions
- Mobius transformations and conformal mapping
04Unit 4: Complex Integration
5 टॉपिक+
- Contour integrals
- Cauchy-Goursat theorem
- Cauchy's integral formula
- Morera's and Liouville's theorems
- Fundamental theorem of algebra
05Unit 5: Series and Residues
5 टॉपिक+
- Taylor and Laurent series
- Zeros and singularities
- Classification of singularities
- Residues and Cauchy's residue theorem
- Evaluation of real definite integrals
Numerical Analysis and Operations Research5 chapters · 6 Months
Subject page →+
01Unit 1: Finite Differences and Interpolation
5 टॉपिक+
- Forward, backward and central differences
- Shift operator E
- Newton forward and backward interpolation
- Lagrange interpolation
- Divided differences
02Unit 2: Numerical Solution of Equations
6 टॉपिक+
- Bisection method
- Regula falsi
- Newton-Raphson method
- Iteration method and convergence
- Gauss elimination
- Gauss-Seidel iteration
03Unit 3: Numerical Integration and ODEs
5 टॉपिक+
- Trapezoidal rule
- Simpson's 1/3 and 3/8 rules
- Errors in quadrature
- Euler's method
- Runge-Kutta methods
04Unit 4: Linear Programming
5 टॉपिक+
- Formulation of LPP
- Graphical method
- Simplex method
- Big-M method
- Duality
05Unit 5: Transportation and Assignment Problems
5 टॉपिक+
- North-west corner rule
- Least cost and Vogel's approximation methods
- MODI method and optimality
- Degeneracy
- Hungarian method for assignment
Mathematics Practical-VI4 chapters · 6 Months
Subject page →+
01Programming Basics for Numerical Methods
4 टॉपिक+
- Variables, loops and functions
- Tolerance and stopping criteria
- Tabulating and plotting results
- Error measurement
02Roots of Equations and Linear Systems
4 टॉपिक+
- Bisection program
- Newton-Raphson program
- Gauss elimination with pivoting
- Gauss-Seidel iteration
03Interpolation and Numerical Integration
4 टॉपिक+
- Newton forward interpolation
- Lagrange interpolation
- Trapezoidal rule
- Simpson's 1/3 and 3/8 rules
04Optimisation Problems
4 टॉपिक+
- Graphical solution of LPP with plots
- Simplex solution with a solver (linprog)
- Transportation problem
- Assignment problem (linear_sum_assignment)
About this course
आप यह कर पाएँगे
- Complete Metric Spaces and Complex Analysis syllabus with regular tests
- Complete Numerical Analysis and Operations Research syllabus with regular tests
- Complete Mathematics Practical-VI syllabus with regular tests
यह किसके लिए है
- B.Sc Mathematics students of Semester 6 (UP State Universities, NEP 2020)
- Students preparing for end-semester theory papers of Mathematics
आपको क्या चाहिए
- Real analysis and calculus of earlier semesters
Online tests & result
Practice and unit tests online; marks and result show in your student login and at the centre.
Student login →
सवाल
Which syllabus does this subject follow?
It follows the B.Sc Mathematics Semester 6 syllabus of the UP State Universities (NEP 2020 common minimum syllabus). Where your own university's syllabus differs, the centre follows your university syllabus.
How are students assessed at the centre?
Through unit-wise multiple-choice tests, a final test paper and doubt-clearing sessions that follow the university examination pattern.
Will this help in the semester examination?
Yes. Units are taught in the university order with solved numericals and exam-pattern questions.
Which syllabus does this lab course follow?
It follows the B.Sc Mathematics Semester 6 syllabus of the UP State Universities (NEP 2020 common minimum syllabus). Where your own university's syllabus differs, the centre follows your university syllabus.
