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Mathematics Practical-IV (B.Sc Mathematics)

Numerical and symbolic solution of differential equations and mechanics problems using software.

6 MonthsDuration 4Chapters16Topics
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Syllabus · पाठ्यक्रम

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01Higher Order ODEs (Symbolic) 4 topics
  1. ode2() for second-order equations
  2. ic2() and bc2()
  3. Verifying solutions by substitution
  4. Variation of parameters
02Numerical Solution of ODEs 4 topics
  1. Euler's method
  2. Modified Euler method
  3. Fourth-order Runge-Kutta (rk)
  4. Error compared with exact solution
03Partial Differential Equations 4 topics
  1. Heat equation by separation of variables
  2. Wave equation solutions
  3. Surface plots with plot3d
  4. Animating solutions
04Mechanics Problems 4 topics
  1. Projectile trajectories and range
  2. Simple harmonic motion
  3. Resultant of forces
  4. Central orbits and catenary plots

About

You will be able to

  • Solve higher-order ODEs symbolically and apply initial and boundary conditions
  • Program Euler and Runge-Kutta methods and compare with exact solutions
  • Plot solutions of heat and wave equations obtained by separation of variables
  • Simulate and plot projectile, SHM and central orbit problems

Who it is for

  • B.Sc Mathematics students of Semester 4 (UP State Universities, NEP 2020)
  • Students preparing for the B.Sc Mathematics practical examination and viva

What you need

  • Theory of Differential Equations and Mechanics
  • Free mathematical software (Maxima / wxMaxima, SageMath or Python) installed

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.

How are students assessed at the centre?

The trainer watches each experiment and marks it on a rubric (set-up, observations, calculation and viva); viva-style questions revise the theory behind the experiments.

Will this help in the semester examination?

Yes. The experiments match the university practical examination, including the record file and viva.

Download the syllabus (PDF)

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