Engineering Mathematics-I

Topic outline

• General
  

  General

  • Announcements Forum
• We have learnt about Elementary Transformations, rank of a matrix and how to find rank using Row reduced Echelon form.
  

  We have learnt about Elementary Transformations, rank of a matrix and how to find rank using Row reduced Echelon form.

  • We have learnt about Elementary Transformations, rank of a matrix and how to find rank using Row reduced Echelon form File
• We studied the conversion of the matrix to the normal form and finding the rank of the matrix
  

  We studied the conversion of the matrix to the normal form and finding the rank of the matrix

  • We studied the conversion of the matrix to the normal form and finding the rank of the matrix File
• Inverse of a matrix and finding inverse using Gauss Jordan Method
  

  Inverse of a matrix and finding inverse using Gauss Jordan Method

  • Inverse of a matrix and finding inverse using Gauss Jordan Method File
• We discussed how to check the consistency of system of simultaneous equations and to find the values of unknowns
  

  We discussed how to check the consistency of system of simultaneous equations and to find the values of unknowns

  • We discussed how to check the consistency of system of simultaneous equations and to find the values of unknowns File
• We discussed the system of a homogeneous linear equations and its solutions
  

  We discussed the system of a homogeneous linear equations and its solutions

  • We discussed the system of a homogeneous linear equations and its solutions File
• We discussed Linear transformations and Orthogonal transformations
  

  We discussed Linear transformations and Orthogonal transformations

  • We discussed Linear transformations and Orthogonal transformations File
• Eigen Values and Eigen Vectors of a matrix with suitable example
  

  Eigen Values and Eigen Vectors of a matrix with suitable example

  • Eigen Values and Eigen Vectors of a matrix with suitable example File
• Statement & Proof of Cayley – Hamilton Theorem
  

  Statement & Proof of Cayley – Hamilton Theorem

  • Statement & Proof of Cayley – Hamilton Theorem File
• Diagonal Matrices, Similar Matrices
  

  Diagonal Matrices, Similar Matrices

  • Diagonal Matrices, Similar Matrices File
• 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
  

  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

  • 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 File
• Examples of Exact Differential Equations, Equation Reducible to Exact Equations, Integrating Factor by Inspection Method, Rules for Find Integrating Factors, Clairaut’s Equation
  

  Examples of Exact Differential Equations, Equation Reducible to Exact Equations, Integrating Factor by Inspection Method, Rules for Find Integrating Factors, Clairaut’s Equation

  • Examples of Exact Differential Equations, Equation Reducible to Exact Equations, Integrating Factor by Inspection Method, Rules for Find Integrating Factors, Clairaut’s Equation File
• Equation Solvable for p,y,x, Leibnitz's Linear Differential Equation, Bernoulli's Equation
  

  Equation Solvable for p,y,x, Leibnitz's Linear Differential Equation, Bernoulli's Equation

  • Equation Solvable for p,y,x, Leibnitz's Linear Differential Equation, Bernoulli's Equation File
• Leibnitz linear form
  

  Leibnitz linear form

  • Leibnitz Linear Form File
• 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
  

  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

  • 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 File
• Method of Variation of Parameters, Operator Method, Cauchy’ s Homogeneous Linear Equation, Legendre’s Linear Equation, Simultaneous Linear Equation with constant coefficients
  

  Method of Variation of Parameters, Operator Method, Cauchy’ s Homogeneous Linear Equation, Legendre’s Linear Equation, Simultaneous Linear Equation with constant coefficients

  • Method of Variation of Parameters, Operator Method, Cauchy’ s Homogeneous Linear Equation, Legendre’s Linear Equation, Simultaneous Linear Equation with constant coefficients File
• 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
  

  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

  • 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 File
• 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
  

  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

  • 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 File
• Topic 18
  

  Topic 18
• Topic 19
  

  Topic 19
• Topic 20
  

  Topic 20
• Topic 21
  

  Topic 21
• Topic 22
  

  Topic 22
• Topic 23
  

  Topic 23
• Topic 24
  

  Topic 24
• Topic 25
  

  Topic 25
• Topic 26
  

  Topic 26
• Topic 27
  

  Topic 27
• Topic 28
  

  Topic 28
• Topic 29
  

  Topic 29
• Topic 30
  

  Topic 30