Assignment Help With Linear Algebra

Linear Algebra And Calculus Topics Which You Must Do!

Linear Algebra :

Rn as a vector space over R, subspaces of Rn, linear independence and linear span, standard basis for Rn and examples of different bases in R2 and R3. Linear transformations from Rn to Rm, null space, range space, statement and illustration of the rank-nullity theorem, matrix of a linear transformation with respect to standard basis, matrices as linear transformations.Hermitian, unitary and normal matrices. Rn as a real inner product space (dot product), orthogonality, length of a vector, examples of orthonormal basis, Pythagoras’ theorem, Cauchy- Schwartz Inequality.

Real valued functions of one variable:

Limit and continuity of real valued functions of one variable, sum and product of continuous functions, sign preserving property for continuous functions, intermediate value theorem, extreme value theorem for continuous functions. Derivability of real valued functions of one variable, Rolle’s theorem, mean value theorem.

Calculus of several variables:

Definition and examples of sequences, open sets, closed sets, compact sets, connected subsets of R1 and R2 Limit and continuity for real valued functions on R2, differentiability of real valued functions on R2, directional derivatives and gradients for these functions. Statement of Taylor’s theorem for functions of two variables, Maxima and Minima of functions of two variables.

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Details about linear algebra

Linear algebra is one of the important branches of the mathematics, which include several things, and moreover, the linear equations are solved by using the matrix operations. This course was evolved from the numbers to the vectors, and finally to the subspaces. You cannot ignore this paper if you are opting for the higher studies. Every sector has some importance of linear algebra.

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The linear algebra concept was initially started in Europe by Rene Descartes in the year 1637. The new geometry called the Cartesian geometry, planes and lines are thus represented in the linear equations to make the calculations easy and flexible to remember. Study of the matrixes and determinants are never going to be an easy option for you, and moreover, the connection between the matrices and equations are surely going to make you crazy.

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Recommended books:

1. T. M. Apostol: Calculus, Volume 1, John Wiley and Sons (Asia) Pvt. Ltd., 2002.

2. R. G. Bartle and D. R. Sherbert: Introduction to real analysis, John Wiley and Sons (Asia) Pte. Ltd. 2000.

3. H. Anton, I Bivens and S. Davis: Calculus, John Wiley and Sons (Asia) Pvt. Ltd., 2002.

4. C. P. Simon and L. Blume: Mathematics for Economists, W W Norton and Company, 1994.

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