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Course11510509760 lectures

Mathematical methods in Physics -I

Prof. Samudra Roy · IIT Kharagpur

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lecture 1 : Set, Group, Field, Ring Video
  2. Lecture 2 : Vector Space Video
  3. Lecture 3 : Span, Linear combination of vectors Video
  4. Lecture 4 : Linearly dependent and independent vector, Basis Video
  5. Lecture 5 : Dual Space Video

Week 2

  1. Lecture 6 : Inner Product Video
  2. Lecture 7 : Schwarz Inequality Video
  3. Lecture 8 : Inner product space, Gram- Schmidt Ortho-normalization Video
  4. Lecture 9 : Projection operator Video
  5. Lecture 10 : Transformation of Basis Video

Week 3

  1. Lecture 11 : Transformation of Basis (Continue) Video
  2. Lecture 12 : Unitary transformation, Similarity Transformation Video
  3. Lecture 13 : Eigen Value, Eigen Vectors Video
  4. Lecture 14 : Normal Matrix Video
  5. Lecture 15 : Diagonalization of a Matrix Video

Week 4

  1. Lecture 16: Hermitian Matrix Video
  2. Lecture 17 : Rank of a Matrix Video
  3. Lecture 18 : Cayley - Hamilton Theorem, Function space Video
  4. Lecture 19: Metric Space, Linearly dependent -independent functions Video
  5. Lecture 20 : Linearly dependent -independent functions (Cont), Inner Product of functions Video

Week 5

  1. Lecture 21: Orthogonal functions Video
  2. Lecture 22: Delta Function, Completeness Video
  3. Lecture 23: Fourier Video
  4. Lecture 24: Fourier Series (Contd.) Video
  5. Lecture 25: Parseval Theorem, Fourier Transform Video

Week 6

  1. Lecture 26: Parseval Relation, Convolution Theorem Video
  2. Lecture 27: Polynomial space, Legendre Polynomial Video
  3. Lecture 28: Monomial Basis, Factorial Basis, Legendre Basis Video
  4. Lecture 29: Complex Numbers Video
  5. Lecture 30: Geometrical interpretation of complex numbers Video

Week 7

  1. Lecture 31 : de Moivre's Theorem Video
  2. Lecture 32 : Roots of a complex number Video
  3. Lecture 33 : Set of complex no, Stereographic projection Video
  4. Lecture 34 : Complex Function, Concept of Limit Video
  5. Lecture 35 : Derivative of Complex Function, Cauchy-Riemann Equation Video

Week 8

  1. Lecture 36 : Analytic Function Video
  2. Lecture 37 : Harmonic Conjugate Video
  3. Lecture 38 : Polar form of Cauchy-Riemann Equation Video
  4. Lecture 39 : Multi-valued function and Branches Video
  5. Lecture 40 : Complex Line Integration, Contour , Regions Video

Week 9

  1. Lecture 41: Complex Line Integration(Cont.) Video
  2. Lecture 42: Cauchy-Goursat Theorem Video
  3. Lecture 43 : Application of Cauchy-Goursat Theorem Video
  4. Lecture 44: Cauchy's Integral Formula Video
  5. Lecture 45: Cauchy's Integral Formula (Contd.) Video

Week 10

  1. Lecture 46:Series and Sequence Video
  2. Lecture 47:Series and Sequence (Contd.) Video
  3. Lecture 48:Circle and radius of convergence Video
  4. Lecture 49: Taylor Series Video
  5. Lecture 50 Classification of singularity Video

Week 11

  1. Lecture 51: Laurent Series, Singularity Video
  2. Lecture 52: Laurent series expansion Video
  3. Lecture 53: Laurent series expansion (Cont), Concept of Residue Video
  4. Lecture 54: Classification of Residue Video
  5. Lecture 55: Calculation of Residue for quotient from Video

Week 12

  1. Lecture 56 : Cauchy's Residue Theorem Video
  2. Lecture 57 : Cauchy's Residue Theorem (Cont) Video
  3. Lecture 58 : Real Integration using Cauchy's Residue Theorem Video
  4. Lecture 59 : Real Integration using Cauchy's Residue Theorem (Cont) Video
  5. Lecture 60 : Real Integration using Cauchy's Residue Theorem (Cont) Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Physics
Teacher
Prof. Samudra Roy
Level
Undergraduate
Language
English
Subjects
Physics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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