NDSS Academy

Mathematics Practical-III (B.Sc Mathematics)

Computer exercises on group theory, transforms and special functions.

6 महीनेअवधि 4Chapters17टॉपिक
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सिलेबस · पाठ्यक्रम

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01Group Theory on Computer 5 टॉपिक
  1. Cayley tables of Z_n and U(n)
  2. Checking group axioms
  3. Orders of elements
  4. Cyclic subgroups and cosets
  5. Permutation groups
02Laplace Transforms 4 टॉपिक
  1. laplace() and ilt() commands
  2. Shifting theorems checked on computer
  3. Solving IVPs with Laplace transforms
  4. Convolution
03Fourier Series and Transforms 4 टॉपिक
  1. Computing Fourier coefficients
  2. Plotting partial sums
  3. Gibbs phenomenon
  4. Half-range series
04Special Functions 4 टॉपिक
  1. Legendre polynomials (legendre_p)
  2. Verifying orthogonality
  3. Bessel functions (bessel_j) and their plots
  4. Checking recurrence relations

परिचय

आप यह कर पाएँगे

  • Build Cayley tables and test group properties of Z_n and U(n) on computer
  • Find orders of elements, cyclic subgroups and cosets using software
  • Compute Laplace and inverse Laplace transforms and solve initial value problems
  • Compute Fourier coefficients and plot partial sums of Fourier series
  • Evaluate and plot Legendre polynomials and Bessel functions

यह किसके लिए है

  • B.Sc Mathematics students of Semester 3 (UP State Universities, NEP 2020)
  • Students preparing for the B.Sc Mathematics practical examination and viva

आपको क्या चाहिए

  • Theory of Algebra and Mathematical Methods
  • Free mathematical software (Maxima / wxMaxima, SageMath or Python) installed

सवाल

Which syllabus does this lab course follow?

It follows the B.Sc Mathematics Semester 3 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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