Engineering Mathematics-II

About the course

In this course, we will learn in detail about Differential Equations. We will study about Linear Differential equations, Ordinary Differential Equations, and Differential Equations of Different Order. We will also study Matrices, Infinite Series, and Complex Numbers which form an integral part of Linear Algebra.

What will you learn?

The complete online syllabus of this course comprises 7 Learning Modules | 182 Topics of Learning | 7.5 Hours of Learning | 37 Assessments

Module

• Ordinary Differential Equation of First Order
• Linear Ordinary Differential Equation of Second and Higher Order
• Application of Ordinary Differential Equation
• Linear Algebra: Determinants and Matrices
• Matrix and System of Equations
• Infinite Series
• Complex Number and Elementary Functions of Complex Variable

Topics of Learning

• Differential Equation
• Ordinary Differential Equation
• Order and Degree of Differential Equation
• Formation of Differential Equation
• Solution of Differential Equation
• Differential Equation with Separable Variables
• Homogenous Differential Equation
• Equation Reducble to Homogenous Form when a/a’ ≠ b/b’
• Solution of Differential Equation when a/a’ = b/b’
• Leibnitz Linear Equation
• Bernoulli’s Equation
• Exact Differential Equation
• Equation Reducible to Exact Differential Equation
• Equation Reducible to Exact Differential Equation by Inspection
• IF of a Homogenous Equation
• IF for a Equation of Type: { f1(xy)ydx – f2(xy)xdy = 0}
• IF for a Equation of Type: { Mdx + Ndy = 0 }
• Equation Solvable for p
• Equation Solvable for y
• Equation Solvable for x
• Clairaut’s Equation
• Linear Differential Equation
• Solution of Linear Differential Equation
• Operator D
• Rules for Finding Complementary Function
• CF if Roots are Real and Different
• CF if Two Roots are real and Equal
• CF if One Pair of Roots are Imaginary and different
• CF if Two Pairs of Imaginary Roots be Equal
• Rules for Finding Particular Integral
• PI when X = eax
• PI when X = Sin (ax+b) or X = Cos(ax+b)
• PI when X = xm
• PI when X = eax V
• When X is any other Function of x
• Method of Variation of Parameters
• Operator Method
• Working Procedure to Solve the Linear Differential Equation
• Cauchy’s Homogenous Linear Equation
• Legendre’s Linear Equation
• Simultaneous Linear Equation with Constant Coefficient
• Simple Harmonic Motion
• RLC Circuit
• Deflection of Beams
• Introduction to Matrices and Determinants
• Minors and Cofactors of Determinant
• Properties of Dterminants
• Types of Matrices
• Matrix Algebra
• Some Special Matrices
• Adjoint of a Matrix
• Elementary Row/Column Transformation
• Rank of a Matrix
• Homogeneous & Non Homogeneous Equations
• Inverse of a Matrix
• Gauss Jordan Method
• Partition Method of Finding the Inverse
• Matrix Method
• Cramer’s Rule(homog.)
• Gauss Elimination Method
• Linear Dependence of Vectors
• Consistency of Linear System of Equations
• Characteristic Equation
• Eigen Values and Eigen Vectors
• Properties of Eigen Values
• Caley-Hamilton Theorem
• Normal Form of a Matrix
• Reduction to Diagonal Form
• Complex Matrices
• Sequence
• Series
• General Properties of Series
• Series of Positive Terms
• Comparision Test: Case 1
• Comparision Test: Case 2
• Comparision Test: Case 3
• Integral Test
• Comparision of Ratios
• D’Alembert’s Ratio Test
• D’Alembert’s Ratio Test: Case 1 (λ <1)
• D’Alembert’s Ratio Test: Case 2 (λ > 1)
• Rabee’s Test
• Logarithmic Test
• Cauchy’s Ratio Test
• Alternating Series
• Absolute and Conditionally Convergent
• Complex Number
• Modulus and Argument of Complex Number
• Arithmetic Properties of Complex Number
• Conjugate Properties of Complex Number
• De-moivres Theorem
• Expansion of Sin(nθ), Cos(nθ) and tan(nθ)
• Addition Formulae
• Expansion of Sinm θ , Cosn θ, or Sinm θ Cosn θ
• Exponential Function of a Complex Variable
• Circular Function of a Complex Variable
• Hyperbolic Function of a Complex Variable
• Inverse Hyperbolic Function of a Complex Variable
• Logarithmic Function of a Complex Variable
• sin(x+iy) and cos(x+iy)
• tan(x+iy)
• sec(x+iy)
• sinh (x+iy)
• tanh (x+iy)
• Log (x + iy)
• (α+iβ)(x+iy)
• C + iS Method

For a quick review, please watch our videos here  Online Video-Tutorials For Engineering Mathematics