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Course11110516763 lectures

Advanced Engineering Mathematics

Prof. H S Mahato · IIT Kharagpur

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Lecture 1: Introduction on functions of a single variable Video
  2. Lecture 2: Basic definitions Video
  3. Lecture 3: Mean value Theorems Video
  4. Lecture 4: Extremum of function of single variable Video
  5. Lecture 5: Examples Video

week-02

  1. Lecture 6: Introduction on functions of two variable Video
  2. Lecture 7: Basic definitions Video
  3. Lecture 8: Partial differentiation Video
  4. Lecture 9: Extremum of function of two variable Video
  5. Lecture 10: Examples Video

week-03

  1. Lecture 11: Convergence and divergence test Video
  2. Lecture 12: Beta function, Gamma function Video
  3. Lecture 13: Differentiation under integral sign Video
  4. Lecture 14: Line integral, integration in R^2 (Double integral) Video
  5. Lecture 15: Examples Video

week-04

  1. Lecture 16: Double integral Video
  2. Lecture 17: Integration in R3 Video
  3. Lecture 18: Triple integral Video
  4. Lecture 19: Examples Video
  5. Lecture 20: Introduction to Differential equation Video
  6. Lecture 21: Exact form Video
  7. Lecture 22: Second order differential equation Video

week-05

  1. Lecture 23: Iterative method (bisection and fixed point) Video
  2. Lecture 24: Newton-Raphson, Jacobi and Gauss-Seidel method Video
  3. Lecture 25: Finite difference method Video
  4. Lecture 26: Newton’s forward and backward interpolation Video
  5. Lecture 27: Numerical integration Video

week-06

  1. Lecture 28: Vector space and Subspace Video
  2. Lecture 29: Basis and dimension Video
  3. Lecture 30: Rank of a matrix Video
  4. Lecture 31: Gauss-Elimination Method Video
  5. Lecture 32: Linear Transformation Video

week-07

  1. Lecture 33: Examples Video
  2. Lecture 34: Matrix Representation Video
  3. Lec 35: Eigenvalues and Eigenvectors Video
  4. Lecture 36: Cayley-Hamilton Theorem Video

week-08

  1. Lecture 37: Diagonalisation of a Matrix Video
  2. Lecture 38: Examples and applications Video
  3. Lecture 39: Types of matrices Video
  4. Lecture 40: Equivalent Matrices and Elementary Matrices Video

week-09

  1. Lecture 41: Introduction to the vector function Video
  2. Lecture 42: Differentiation and integration of the vector function Video
  3. Lecture 43: Partial differentiation of vector function Video
  4. Lecture 44: Directional derivative of a vector function Video
  5. Lecture 45: Examples on directional derivative, tangent plane and normal Video

week-10

  1. Lecture 46: Divergence and curl of a vector function Video
  2. Lecture 47: Application to mechanics of vector calculus Video
  3. Lecture 48: Serret-Frenet formula and more applications to mechanics Video
  4. Lecture 49: Examples on finding unit vectors, curvature and torsion Video
  5. Lecture 50: Application of vector calculus to the particle dynamics Video

week-11

  1. Lecture 51: Line integral of vector function Video
  2. Lecture 52: Surface integral of vector function Video
  3. Lecture 53: Volume integral of vector function and Gauss Divergence Theorem Video
  4. Lecture 54: Green's theorem and Stoke's theorem Video
  5. Lecture 55: Verification and application of Divergencen theorem, Green's theorem and Stoke's theorem Video

week-12

  1. Lecture 56: Basic properties of a complex valued function Video
  2. Lecture 57: Analytic Complex valued function Video
  3. Lecture 58: Complex Integration and theorems Video
  4. Lecture 59: Application of Cauchy's integral formula Video
  5. Lecture 60: Regular and Singular point of a complex valued function Video

Live Session

  1. Live Session 15-02-2024 Video
  2. Live Session 19-04-2024 Video
  3. Live Session 11-02-2025 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Mathematics
Teacher
Prof. H S Mahato
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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