Learn · Advanced Engineering Mathematics
Lecture 43 of 63week-09
Lecture 43: Partial differentiation of vector function
Prof. H S Mahato · IIT Kharagpur
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All the lectures
- Lecture 1: Introduction on functions of a single variable
- Lecture 2: Basic definitions
- Lecture 3: Mean value Theorems
- Lecture 4: Extremum of function of single variable
- Lecture 5: Examples
- Lecture 6: Introduction on functions of two variable
- Lecture 7: Basic definitions
- Lecture 8: Partial differentiation
- Lecture 9: Extremum of function of two variable
- Lecture 10: Examples
- Lecture 11: Convergence and divergence test
- Lecture 12: Beta function, Gamma function
- Lecture 13: Differentiation under integral sign
- Lecture 14: Line integral, integration in R^2 (Double integral)
- Lecture 15: Examples
- Lecture 16: Double integral
- Lecture 17: Integration in R3
- Lecture 18: Triple integral
- Lecture 19: Examples
- Lecture 20: Introduction to Differential equation
- Lecture 21: Exact form
- Lecture 22: Second order differential equation
- Lecture 23: Iterative method (bisection and fixed point)
- Lecture 24: Newton-Raphson, Jacobi and Gauss-Seidel method
- Lecture 25: Finite difference method
- Lecture 26: Newton’s forward and backward interpolation
- Lecture 27: Numerical integration
- Lecture 28: Vector space and Subspace
- Lecture 29: Basis and dimension
- Lecture 30: Rank of a matrix
- Lecture 31: Gauss-Elimination Method
- Lecture 32: Linear Transformation
- Lecture 33: Examples
- Lecture 34: Matrix Representation
- Lec 35: Eigenvalues and Eigenvectors
- Lecture 36: Cayley-Hamilton Theorem
- Lecture 37: Diagonalisation of a Matrix
- Lecture 38: Examples and applications
- Lecture 39: Types of matrices
- Lecture 40: Equivalent Matrices and Elementary Matrices
- Lecture 41: Introduction to the vector function
- Lecture 42: Differentiation and integration of the vector function
- Lecture 43: Partial differentiation of vector function
- Lecture 44: Directional derivative of a vector function
- Lecture 45: Examples on directional derivative, tangent plane and normal
- Lecture 46: Divergence and curl of a vector function
- Lecture 47: Application to mechanics of vector calculus
- Lecture 48: Serret-Frenet formula and more applications to mechanics
- Lecture 49: Examples on finding unit vectors, curvature and torsion
- Lecture 50: Application of vector calculus to the particle dynamics
- Lecture 51: Line integral of vector function
- Lecture 52: Surface integral of vector function
- Lecture 53: Volume integral of vector function and Gauss Divergence Theorem
- Lecture 54: Green's theorem and Stoke's theorem
- Lecture 55: Verification and application of Divergencen theorem, Green's theorem and Stoke's theorem
- Lecture 56: Basic properties of a complex valued function
- Lecture 57: Analytic Complex valued function
- Lecture 58: Complex Integration and theorems
- Lecture 59: Application of Cauchy's integral formula
- Lecture 60: Regular and Singular point of a complex valued function
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- Live Session 11-02-2025