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 1 — subject classesसेमेस्टर 1 — विषयवार कक्षाएँEvery theory subject of the term, unit by unit, with notes, numericals and doubt classes.
Differential Calculus and Integral Calculus
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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-I
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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 1 mock testमॉक टेस्टA full mock test of all subjects before the exam, with analysis.
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Semester 1 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
2 subjects · 10 chapters · 50 topics
Differential Calculus and Integral Calculus6 chapters · 6 Months
Subject page →+
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
Mathematics Practical-I4 chapters · 6 Months
Subject page →+
01Introduction to Mathematical Software
5 टॉपिक+
- Installing Maxima / wxMaxima
- Syntax, ; and $ terminators
- Variables, functions and lists
- Constants %pi, %e and %i
- Help and documentation
02Limits, Derivatives and Series
5 टॉपिक+
- limit() including one-sided limits
- diff() and successive derivatives
- Verifying Leibnitz theorem
- taylor() expansions
- Maxima and minima of functions
03Plotting and Curve Tracing
5 टॉपिक+
- plot2d for Cartesian curves
- Parametric curves
- Polar curves: cardioid, lemniscate, rose
- Asymptotes and tangents on plots
- Saving plots
04Integration and Special Functions
5 टॉपिक+
- integrate() for indefinite and definite integrals
- Improper integrals
- Numerical integration with quad_qags
- beta() and gamma() functions
- Double integrals, area and volume
About this course
आप यह कर पाएँगे
- Complete Differential Calculus and Integral Calculus syllabus with regular tests
- Complete Mathematics Practical-I syllabus with regular tests
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.
Which syllabus does this lab course 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.
