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RIMT University
Engineering Mathematics-I
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School of Engineering & Technology
Computer Science Engineering
B.Tech Computer Science & Engineeirng
Semester I
BMAT-1111
Statement & Proof of Cayley – Hamilton Theorem
Statement & Proof of Cayley – Hamilton Theorem
Statement & Proof of Cayley – Hamilton Theorem
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◄ Eigen Values and Eigen Vectors of a matrix with suitable example
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We have learnt about Elementary Transformations, rank of a matrix and how to find rank using Row reduced Echelon form
We studied the conversion of the matrix to the normal form and finding the rank of the matrix
Inverse of a matrix and finding inverse using Gauss Jordan Method
We discussed how to check the consistency of system of simultaneous equations and to find the values of unknowns
We discussed the system of a homogeneous linear equations and its solutions
We discussed Linear transformations and Orthogonal transformations
Eigen Values and Eigen Vectors of a matrix with suitable example
Diagonal Matrices, Similar Matrices
Introduction, Differential Equation, Kinds of Differential Equation, Order and Degree of Differential Equation, Formation of ODE, Solution of ODE, Exact Differential Equation, Theorem on Exactness
Examples of Exact Differential Equations, Equation Reducible to Exact Equations, Integrating Factor by Inspection Method, Rules for Find Integrating Factors, Clairaut’s Equation
Equation Solvable for p,y,x, Leibnitz's Linear Differential Equation, Bernoulli's Equation
Leibnitz Linear Form
Introduction, Types of Differential Equations, Complete Solution of Homogeneous DE, Rules for Finding the Complementary Function, Complete Solution of Non-Homogeneous DE, Rules for Finding the Particular Integral
Method of Variation of Parameters, Operator Method, Cauchy’ s Homogeneous Linear Equation, Legendre’s Linear Equation, Simultaneous Linear Equation with constant coefficients
Complex Numbers, De-Moivre’s Theorem, Roots of complex numbers, Express n power of cos and sin in terms of cosine or sine of multiples of angle
Expansion of Cos nq and Sin nq, Expansion of tan nq, Expansion of tan (q1 + q2 + q3 + …+ qn ), Exponential Function of a Complex Variable, Circular Functions of a Complex Variable
Diagonal Matrices, Similar Matrices ►
BMAT-1111
General
We have learnt about Elementary Transformations, rank of a matrix and how to find rank using Row reduced Echelon form.
We studied the conversion of the matrix to the normal form and finding the rank of the matrix
Inverse of a matrix and finding inverse using Gauss Jordan Method
We discussed how to check the consistency of system of simultaneous equations and to find the values of unknowns
We discussed the system of a homogeneous linear equations and its solutions
We discussed Linear transformations and Orthogonal transformations
Eigen Values and Eigen Vectors of a matrix with suitable example
Statement & Proof of Cayley – Hamilton Theorem
Diagonal Matrices, Similar Matrices
Introduction, Differential Equation, Kinds of Differential Equation, Order and Degree of Differential Equation, Formation of ODE, Solution of ODE, Exact Differential Equation, Theorem on Exactness
Examples of Exact Differential Equations, Equation Reducible to Exact Equations, Integrating Factor by Inspection Method, Rules for Find Integrating Factors, Clairaut’s Equation
Equation Solvable for p,y,x, Leibnitz's Linear Differential Equation, Bernoulli's Equation
Leibnitz linear form
Introduction, Types of Differential Equations, Complete Solution of Homogeneous DE, Rules for Finding the Complementary Function, Complete Solution of Non-Homogeneous DE, Rules for Finding the Particular Integral
Method of Variation of Parameters, Operator Method, Cauchy’ s Homogeneous Linear Equation, Legendre’s Linear Equation, Simultaneous Linear Equation with constant coefficients
Complex Numbers, De-Moivre’s Theorem, Roots of complex numbers, Express n power of cos and sin in terms of cosine or sine of multiples of angle
Expansion of Cos nq and Sin nq, Expansion of tan nq, Expansion of tan (q1 + q2 + q3 + …+ qn ), Exponential Function of a Complex Variable, Circular Functions of a Complex Variable
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