Systems of linear equations, Solution by Gauss elimination, row echelon form and rank of a matrix, fundamental theorem for linear systems homogeneous and non-homogeneous, without proof , Eigenvalues and eigenvectors.
Diagonalization of matrices, orthogonal transformation, quadratic forms and their canonical forms. Concept of limit and continuity of functions of two variables, partial derivatives, chain rule, total derivative, Relative maxima and minima, Absolute maxima and minima on closed and bounded set. Double integrals Cartesian , reversing the order of integration, Change of coordinates Cartesian to polar , finding areas and volume using double integrals, mass and centre of gravity of inhomogeneous laminas using double integral.
Triple integrals, volume calculated as triple integral, triple integral in cylindrical and spherical coordinates computations involving spheres, cylinders. Convergence of sequences and series, the convergence of geometric series and p-series without proof , a test of convergence comparison, ratio and root tests without proof ; Alternating series and Leibnitz test, absolute and conditional convergence.
Latest Updates. Header 1. These notes will help you to revise and consolidate all the concepts from the basic level to the higher level. All the chapters are given as textbook reading notes, revision notes and MCQs based on various question papers. Module 1 - Syllabus Linear Algebra Systems of linear equations, Solution by Gauss elimination, row echelon form and rank of a matrix, fundamental theorem for linear systems homogeneous and non-homogeneous, without proof , Eigenvalues and eigenvectors.
Module 2 - Syllabus Multivariable Calculus-Differentiation Concept of limit and continuity of functions of two variables, partial derivatives, chain rule, total derivative, Relative maxima and minima, Absolute maxima and minima on closed and bounded set. Chapter 3 Aug 7, Matrix multiplication as composition How to think about matrix multiplication visually as successively applying two different linear transformations. Chapter 4 Aug 8, Three-dimensional linear transformations How to think of 3x3 matrices as transforming 3d space Chapter 5 Aug 9, The determinant The determinant has a very natural visual intuition, even though it's formula can make it seem more complicated than it really is.
Chapter 6 Aug 10, Inverse matrices, column space and null space How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix? Chapter 7 Aug 15, Nonsquare matrices as transformations between dimensions How do you think about a non-square matrix as a transformation? Chapter 8 Aug 16, Dot products and duality What is the dot product? What does it represent?
Why does it have the formula that it does? All this is explained visually. Chapter 9 Aug 24, Cross products The cross product is a way to multiple to vectors in 3d. This video shows how to visualize what it means. Chapter 10 Sep 1, Cross products in the light of linear transformations The formula for the cross product can feel like a mystery, or some kind of crazy coincidence.
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