NDSS Academy

Algebra and Mathematical Methods (B.Sc Mathematics)

Groups, subgroups and homomorphisms, Laplace and Fourier transforms and special functions.

6 MonthsDuration 5Chapters28Topics
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Syllabus · पाठ्यक्रम

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01Unit 1: Groups 6 topics
  1. Binary operations
  2. Definition and examples of groups
  3. Abelian groups and order of an element
  4. Subgroups
  5. Cyclic groups
  6. Cosets and Lagrange's theorem
02Unit 2: Normal Subgroups and Homomorphisms 6 topics
  1. Normal subgroups
  2. Quotient groups
  3. Homomorphism and kernel
  4. Isomorphism theorems
  5. Permutation groups
  6. Cayley's theorem
03Unit 3: Laplace Transforms 6 topics
  1. Definition and existence
  2. Linearity and shifting theorems
  3. Transforms of derivatives and integrals
  4. Inverse Laplace transform
  5. Convolution theorem
  6. Solving linear ODEs
04Unit 4: Fourier Series and Transforms 5 topics
  1. Fourier series and Dirichlet conditions
  2. Even and odd functions
  3. Half-range series
  4. Fourier transform
  5. Fourier sine and cosine transforms
05Unit 5: Special Functions 5 topics
  1. Legendre equation and polynomials
  2. Rodrigues' formula and generating function
  3. Orthogonality of Legendre polynomials
  4. Bessel equation and Bessel functions
  5. Recurrence relations

About

You will be able to

  • Verify group axioms, find orders of elements and identify subgroups and cyclic groups
  • Apply Lagrange's theorem, normal subgroups, quotient groups and homomorphisms
  • Find Laplace transforms and inverse transforms and solve ODEs with them
  • Expand functions in Fourier series and find Fourier transforms
  • Use Legendre polynomials and Bessel functions with their properties

Who it is for

  • B.Sc Mathematics students of Semester 3 (UP State Universities, NEP 2020)
  • Students preparing for end-semester theory papers of Mathematics

What you need

  • Mathematics of Semesters 1 and 2

Questions

Which syllabus does this subject 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?

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.

Download the syllabus (PDF)

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