Learn · Engineering Mathematics - I
Lecture 42 of 60Week 9 :
Lecture 42 : Vector Spaces –Basis and Dimension
Prof. Jitendra Kumar · IIT Kharagpur
Credits and licence
- From
- Engineering Mathematics - I, IIT Kharagpur (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Lecture 01 : Rolle’s Theorem
- Lecture 02 : Mean Value Theorems
- Lecture 03 : Indeterminate Forms (Part ‐1)
- Lecture 04 : Indeterminate Forms (Part ‐2)
- Lecture 05 : Taylor Polynomial and Taylor Series
- Lecture 06 : Limit of Functions of Two Variables
- Lecture 07 : Evaluation of Limit of Functions of Two Variables
- Lecture 08 : Continuity of Functions of Two Variables
- Lecture 09 : Partial Derivatives of Functions of Two Variables
- Lecture 10 : Partial Derivatives of Higher Order
- Lecture 11 : Derivative & Differentiability
- Lecture 12 : Differentiability of Functions of Two Variables
- Lecture 13 : Differentiability of Functions of Two Variables (Cont.)
- Lecture 14 : Differentiability of Functions of Two Variables (Cont.)
- Lecture 15 : Composite and Homogeneous Functions
- Lecture 16 : Taylor’s Theorem for Functions of Two Variables
- Lecture 17 : Maxima & Minima of Functions of Two Variables
- Lecture 18 : Maxima & Minima of Functions of Two Variables (Cont.)
- Lecture 19 : Maxima & Minima of Functions of Two Variables (Cont.)
- Lecture 20 : Constrained Maxima & Minima
- Lecture 21 : Improper Integrals
- Lecture 22 : Improper Integrals (Cont.)
- Lecture 23 : Improper Integrals (Cont.)
- Lecture 24 : Improper Integrals (Cont.)
- Lecture 25 : Beta & Gamma Function
- Lecture 26 : Beta & Gamma Function (Cont.)
- Lecture 27 : Differentiation Under Integral Sign
- Lecture 28 : Double Integrals
- Lecture 29 : Double Integrals (Cont.)
- Lecture 30 : Double Integrals (Cont.)
- Lecture 31 : Integral Calculus –Double Integrals in Polar Form
- Lecture 32 : Integral Calculus –Double Integrals: Change of Variables
- Lecture 33 : Integral Calculus – Double Integrals: Surface Area
- Lecture 34 : Integral Calculus –Triple Integrals
- Lecture 35 : Integral Calculus – Triple Integrals (Cont.)
- Lecture 36 : System of Linear Equations
- Lecture 37 : System of Linear Equations – Gauss Elimination
- Lecture 38 : System of Linear Equations – Gauss Elimination (Cont.)
- Lecture 39 : Linear Algebra - Vector Spaces
- Lecture 40 : Linear Independence of Vectors
- Lecture 41 : Vector Spaces –Spanning Set
- Lecture 42 : Vector Spaces –Basis and Dimension
- Lecture 43 : Rank of a Matrix
- Lecture 44 : Linear Transformations
- Lecture 45 : Linear Transformations (cont.)
- Lecture 46 : Eigenvalues & Eigenvectors
- Lecture 47 : Eigenvalues & Eigenvectors (Cont.)
- Lecture 48 : Eigenvalues & Eigenvectors (Cont.)
- Lecture 49 : Eigenvalues & Eigenvectors (Cont.)
- Lecture 50 : Eigenvalues & Eigenvectors: Diagonalization
- Lecture 51 : Differential Equations - Introduction
- Lecture 52 : First Order Differential Equations
- Lecture 53 : Exact Differential Equations
- Lecture 54 : Exact Differential Equations (Cont.)
- Lecture 55 : First Order Linear Differential Equations
- Lecture 56 : Higher Order Linear Differential Equations
- Lecture 57 : Solution of Higher Order Homogeneous Linear Equations
- Lecture 58 : Solution of Higher Order Non-Homogeneous Linear Equations
- Lecture 59 : Solution of Higher Order Non-Homogeneous Linear Equations (cont.)
- Lecture 60 : Cauchy-Euler Equations