PDF-Syllabus for Biotechnology BT Linear Algebra Matrices and determinants Systems of linear

Calculus Limit continuity and differentiability Partial derivatives Maxima and minima Sequences and series Test for convergence Fourier Series Differential Equations Linear and nonlinear first order ODEs higher order ODEs with constant coefficients. Calculus Mean value theorems Theorems of integral calculus Evaluation of definite and improper integrals Partial Derivatives Maxima and minima Multiple integrals Fourier series Vector identities Directional derivatives Line Surface and Volume integ 1 Introduction D3 D2 Determinants D3 D21 Some Properties of Determinants D3 D22 Cramers Rule D5 D23 Homogeneous Systems D6 D3 Singular Matrices Rank D6 D31 Rank De64257ciency D7 D32 Rank of Matrix Sums and Products D7 D33 Singular Systems Partic Calculus Limit continuity and differentiability Partial Derivatives Maxima and minima Sequences and series Test for convergence Fourier series Vector Calculus Gradient Divergence and Curl Line surface and volume integrals Stokes Gauss and Greens the e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations Calculus Mean value theorems Theorems of integral calculus Evaluation of definite and improper integrals Partial Derivatives Maxima and mini ma Multiple integrals Fourier series Vector identities Directional derivatives Line Surface and Volume integ Calculus Mean value theorems Theorems of integral calculus Evaluation of definite and improper integrals Partial Derivatives Maxima and minima Multiple integrals Fourier series Vector identities Directional derivatives Line Surface and Volume integ Calculus Functions of single variable Limit continuity and differentiability Mean value theorems Evaluation of definite and improper integrals Partial derivatives Total derivative Maxima and minima Gradient Divergence and Cu rl Vector identities Di (what is that?). What . is linear algebra? Functions and equations that arise in the "real world" often involve many tens or hundreds or thousands of variables, and one can only deal with such things by being much more organized than one typically is when treating equations and functions of a single variable. Linear algebra is essentially a ". Matrices. Definition: A matrix is a rectangular array of numbers or symbolic elements. In many applications, the rows of a matrix will represent individuals cases (people, items, plants, animals,...) and columns will represent attributes or characteristics. John Hannah (Canterbury, NZ). Sepideh. Stewart (Oklahoma, US) . Mike Thomas (Auckland, NZ). Summary. Goals for a linear algebra course. Experiments and writing tasks. Examples. Student views. What do today’s students need?. All Lectures. David Woodruff. IBM Almaden. Massive data sets. Examples. Internet traffic logs. Financial data. etc.. Algorithms. Want nearly linear time or less . Usually at the cost of a randomized approximation. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Last modified: . 29. th. August 2015. Introduction. A matrix (plural: matrices) is . simply an ‘array’ of numbers. , e.g.. But the power of matrices comes from being able to multiply matrices by vectors and matrices by matrices and ‘invert’ them: we can:. A cofactor matrix . C. of a matrix . A. is the square matrix of the same order as . A. in which each element a. ij. is replaced by its cofactor c. ij. . . Example:. If. The cofactor C of A is. Matrices - Operations. Rotation of coordinates -the rotation matrixStokes Parameters and unpolarizedlight1916 -20041819 -1903Hans Mueller1900 -1965yyxyEEEElinear arbitrary anglepolarization right or left circularpolarizati