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 4 — subject classesसेमेस्टर 4 — विषयवार कक्षाएँEvery theory subject of the term, unit by unit, with notes, numericals and doubt classes.
Differential Equations and Mechanics
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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-IV
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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 4 mock testमॉक टेस्टA full mock test of all subjects before the exam, with analysis.
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Semester 4 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.
Syllabus · पाठ्यक्रम
2 subjects · 9 chapters · 43 topics
Differential Equations and Mechanics5 chapters · 6 Months
Subject page →+
01Unit 1: Linear Differential Equations of Higher Order
5 topics+
- Linear equations with constant coefficients
- Complementary function and particular integral
- Cauchy-Euler equation
- Method of variation of parameters
- Simultaneous differential equations
02Unit 2: Partial Differential Equations
6 topics+
- Formation of PDEs
- Lagrange's linear equation
- Charpit's method
- Linear PDEs with constant coefficients
- Classification of second-order PDEs
- Separation of variables: heat and wave equations
03Unit 3: Statics
6 topics+
- Resultant of coplanar forces
- Equilibrium and Lami's theorem
- Moments and couples
- Friction
- Virtual work
- Common catenary
04Unit 4: Dynamics of a Particle
5 topics+
- Velocity and acceleration: tangential and normal components
- Radial and transverse components
- Simple harmonic motion
- Projectiles
- Motion in a resisting medium
05Unit 5: Central Orbits
5 topics+
- Central forces
- Differential equation of a central orbit
- Pedal (p-r) equation
- Apses and apsidal distances
- Kepler's laws of planetary motion
Mathematics Practical-IV4 chapters · 6 Months
Subject page →+
01Higher Order ODEs (Symbolic)
4 topics+
- ode2() for second-order equations
- ic2() and bc2()
- Verifying solutions by substitution
- Variation of parameters
02Numerical Solution of ODEs
4 topics+
- Euler's method
- Modified Euler method
- Fourth-order Runge-Kutta (rk)
- Error compared with exact solution
03Partial Differential Equations
4 topics+
- Heat equation by separation of variables
- Wave equation solutions
- Surface plots with plot3d
- Animating solutions
04Mechanics Problems
4 topics+
- Projectile trajectories and range
- Simple harmonic motion
- Resultant of forces
- Central orbits and catenary plots
About this course
You will be able to
- Complete Differential Equations and Mechanics syllabus with regular tests
- Complete Mathematics Practical-IV syllabus with regular tests
Who it is for
- B.Sc Mathematics students of Semester 4 (UP State Universities, NEP 2020)
- Students preparing for end-semester theory papers of Mathematics
What you need
- Differential equations of Semester 2
- Class 12 physics (vectors, Newton's laws)
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 4 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 4 syllabus of the UP State Universities (NEP 2020 common minimum syllabus). Where your own university's syllabus differs, the centre follows your university syllabus.
