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: Limits, Continuity and DifferentiabilityUnit 2: Mean Value Theorems and ExpansionsUnit 3: Partial Differentiation and Curve Tracing
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Part 2 of the syllabusपाठ्यक्रम भाग 2Unit-wise coaching with notes and doubt classes.
Unit 4: Definite Integrals and Reduction FormulaeUnit 5: Beta and Gamma FunctionsUnit 6: Multiple Integrals and Applications
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Unit tests & assignmentsयूनिट टेस्टRegular tests in the university / board pattern.
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Semester 1 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.
सिलेबस · पाठ्यक्रम
1 subject · 6 chapters · 30 topics
01Unit 1: Limits, Continuity and Differentiability
5 टॉपिक+
- Epsilon-delta definition of limit
- Continuity and types of discontinuity
- Differentiability
- Successive differentiation
- Leibnitz theorem
02Unit 2: Mean Value Theorems and Expansions
5 टॉपिक+
- Rolle's theorem
- Lagrange's and Cauchy's mean value theorems
- Taylor's and Maclaurin's theorems with remainders
- Expansion of functions
- Indeterminate forms and L'Hospital's rule
03Unit 3: Partial Differentiation and Curve Tracing
6 टॉपिक+
- Partial derivatives
- Euler's theorem on homogeneous functions
- Asymptotes
- Curvature
- Singular points
- Tracing of Cartesian and polar curves
04Unit 4: Definite Integrals and Reduction Formulae
4 टॉपिक+
- Riemann integral and properties
- Fundamental theorem of calculus
- Reduction formulae for sin^n x and cos^n x
- Wallis' formula
05Unit 5: Beta and Gamma Functions
5 टॉपिक+
- Definitions and convergence
- Properties of Gamma function
- Relation B(m, n) = Gamma(m) Gamma(n)/Gamma(m + n)
- Duplication formula
- Evaluation of integrals
06Unit 6: Multiple Integrals and Applications
5 टॉपिक+
- Double and triple integrals
- Change of order of integration
- Change of variables and Jacobian
- Dirichlet's integral
- Area, volume, rectification and volumes of revolution
About this course
आप यह कर पाएँगे
- Test limits, continuity and differentiability of real functions
- Apply Leibnitz, Rolle, Lagrange and Taylor theorems and evaluate indeterminate forms
- Use partial differentiation and Euler's theorem; find asymptotes and trace curves
- Evaluate definite integrals with reduction formulae and Wallis' formula
- Use Beta and Gamma functions to evaluate integrals
- Evaluate double and triple integrals and find areas and volumes
यह किसके लिए है
- B.Sc Mathematics students of Semester 1 (UP State Universities, NEP 2020)
- First-year students starting the B.Sc Mathematics major
आपको क्या चाहिए
- Class 12 Mathematics (calculus)
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 1 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.
