IIT Madras Maths 2 Lectures: Mathematics for Data Science II
BSMA1003111 lectures11 weeks
Weeks
- Week 110 lecturesVectors · Matrices · Systems of linear equations · Determinants | part 1 · Determinants | part 2 · Tutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5
- Week 26 lecturesDeterminants | part 3 · Cramer's rule · Solutions to a system of linear equations with an invertible coefficient matrix · The echelon form · Row reduction · The gaussian elimination method
- Week 35 lecturesIntroduction to vector spaces · Some properties of vector spaces · Linear dependence · Linear independence - part 1 · Linear independence - part 2
- Week 47 lecturesWhat is a basis for a vector space? · Finding bases for vector spaces · What is the rank/dimension for a vector space · Rank and dimension using gaussian elimination · Tutorial 6 · Tutorial 7 · Tutorial 8
- Week 513 lecturesThe null space of a matrix : finding nullity and a basis - part 1 · The null space of a matrix : finding nullity and a basis - part 2 · What is a linear mapping - part 1 · What is a linear mapping - part 2 · What is a linear transformation · Tutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5 · Tutorial 6 · Tutorial 7 · Tutorial 8
- Week 611 lecturesLinear transformations, ordered bases & matrices · Image & kernel of linear transformations · Examples of finding bases for the kernel & image of a linear transformation · Tutorial 1 · Tutorial 2 · Tutorial 4 · Tutorial 5 · Tutorial 6 · Tutorial 7 · Tutorial 8 · Tutorial 9
- Week 711 lecturesEquivalence & similarity of matrices · Affine subspaces & affine mappings · Lengths & angles · Inner products & norms on a vector space · Tutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5 · Tutorial 6 · Tutorial 7
- Week 811 lecturesOrthogonality & linear independence · What is an orthonormal basis? · Projections using inner products · The gram-schmidt process · Orthogonal transformations & rotations · Tutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5 · Tutorial 6
- Week 919 lecturesMultivariable functions : visualization · Partial derivatives · Directional derivatives · Limits for scalar-valued multivariable functions · Continuity for multivariable functions · Directional derivatives in terms of the gradient · Tutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5 · Tutorial 6 · Tutorial 7 · Refresher week - tutorial 1 · Refresher week - tutorial 2 · Refresher week - tutorial 3 · Refresher week - tutorial 4 · Refresher week - tutorial 5 · Refresher week - tutorial 6
- Week 104 lecturesThe direction of steepest ascent/descent · Tangents for scalar-valued multivariable functions · Finding the tangent hyper(plane) · Critical points for multivariable functions
- Week 1110 lecturesHigher order partial derivatives and the hessian matrix · The hessian matrix & local extrema for f(x,y) · The hessian matrix & local extrema for f(x,y,z) · Differentiability for multivariable functions · Review of maths - 2 · Tutorial 1 · Tutorial 2 · Tutorial 3 · Tutorial 4 · Tutorial 5