Linear Algebra and Calculus
- Course: Linear Algebra and Calculus
- Course Modules
- Module: SEQUENCES AND SERIES
- Module Units
- Unit: Introduction to Sequences, Bounded and unbounded
- Unit: Limit of a sequence, Convergent, Divergent and Oscillatory sequences
- Unit: Infinite series and geometric series, auxiliary series,Comparison test ,Problems on comparison test
- Unit: D’Alembert’s Ratio Test,Raabe’s Test,Cauchy’s n th root test and related problems
- Unit: Cauchy’s Integral Test,Alternating series-Leibnitz’s test,Absolute and Conditional convergence related problems
- Module Units
- Module: ORDINARY DIFFERENTIAL EQUATIONS
- Module Units
- Unit: Introduction to Differential equations,Exact differential equation.
- Unit: Non Exact DE reducible to exact methods 1,2,3,4,5
- Unit: Solvable for p,x,y, cairauts method
- Unit: Introduction of Non homogeneous Linear Differential equation with variable and constant coefficients , Rules for finding complimentary function & problems
- Unit: Rules for finding particular integrals R.H.S terms of type eax , sin ax,cos ax, xn and problems
- Unit: Rules for finding particular integrals R.H.S terms of type eax V(x) , xn V(x) ,Method of Variation of Parametersand problems.
- Module Units
- Module: THEORY OF MATRICES
- Module Units
- Unit: Introduction to matrices and types of matrices,Rank of matrix by echelon form, normal form
- Unit: Inverse of matrix using Gauss Jordan Method,Solution of System of simultaneous equations by Gauss Elimination method
- Unit: Consistency and In consistency of Simultaneous equations,Solution of Non Homogeneous system of Equations
- Unit: Solution of homogenous system of equations,Problems on homogenous system of equations
- Unit: Solution of homogenous system of equations,Problems on homogenous system of equations
- Module Units
- Module: VECTOR SPACES
- Module Units
- Unit: The n-dimensional Vectors ,Vector space,linear dependence of vectors
- Unit: Basis and dimensions,linear transformations- range and kernel of a linear map
- Unit: rank and nullity ,Problems on rank and nullity
- Unit: inverse of a linear transformation,composition of linear map-,Matrix associated with a linear map
- Module Units
- Module: EIGEN VALUES, EIGEN VECTORS AND INNER PRODUCT SPACES
- Module Units
- Unit: Linear Transformation Independence of vectors,Method of finding eigen values & vectors ,Problems on finding eigen values & vectors
- Unit: Properties of Eigen values and vectors of Matrices without proofs
- Unit: Digitalization of a matrix and calculation of powers of a matrix
- Unit: Digitalization of a matrix and calculation of powers of a matrix
- Unit: Digitalization of a matrix and calculation of powers of a matrix
- Unit: Inner product spaces,Problems on Inner product space,Norm of a vector
- Unit: Schwarz’s Inequality,Normed vector space,Orthogonal and orthonormal sets,Gram Schmidt orthogonalization process.
- Module Units
- Module: SEQUENCES AND SERIES
Course: Linear Algebra and Calculus