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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Part 1 of the syllabusपाठ्यक्रम भाग 1Unit-wise coaching with notes and doubt classes.
Unit 1: Metric SpacesUnit 2: Completeness, Compactness and ConnectednessUnit 3: Analytic Functions
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Part 2 of the syllabusपाठ्यक्रम भाग 2Unit-wise coaching with notes and doubt classes.
Unit 4: Complex IntegrationUnit 5: Series and Residues
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Unit tests & assignmentsयूनिट टेस्टRegular tests in the university / board pattern.
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Semester 6 exam (university / board)विश्वविद्यालय / बोर्ड परीक्षाPrevious papers and full revision before the exam.
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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.
Syllabus · पाठ्यक्रम
1 subject · 5 chapters · 28 topics
01Unit 1: Metric Spaces
6 topics+
- 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 topics+
- 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 topics+
- 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 topics+
- 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 topics+
- Taylor and Laurent series
- Zeros and singularities
- Classification of singularities
- Residues and Cauchy's residue theorem
- Evaluation of real definite integrals
About this course
You will be able to
- Identify open, closed, bounded and dense sets in metric spaces
- Test completeness, compactness and connectedness and apply the contraction principle
- Test analyticity using the Cauchy-Riemann equations and find harmonic conjugates
- Evaluate contour integrals using Cauchy's theorem and integral formula
- Expand functions in Taylor and Laurent series and classify singularities
- Evaluate integrals using the residue theorem
Who it is for
- B.Sc Mathematics students of Semester 6 (UP State Universities, NEP 2020)
- Students preparing for end-semester theory papers of Mathematics
What you need
- 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 →
Questions
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.
