This is an overview of the posts/articles published so far in “Engineering mathematics blog”, ‘engineeringmathgeek.com‘.

I have also provided here the names of these posts together with the topics. If you click on any of these links, it will open a new window together with that topic.

### Overview

## Collection of formulas

List of formulas uploaded so far:

- Formulas in integration
- Formulas in differentiation
- Formulas in trigonometry
- Formulas in series
- Formulas for logarithmic & hyperbolic functions
- Formulas in Laplace transform
- Formulas for the solution of second-order ordinary differential equations (ODEs)

## Basic engineering mathematics

Topics in basic engineering mathematics covered so far are partial fractions and vectors.

###### Partial fractions

- Partial fractions of lower degree numerators
- Partial fractions of higher degree numerators
- Partial fractions of repeated roots
- Partial fractions of irreducible quadratic factors
- Partial fractions of equal degree expressions

###### Complex numbers

- Addition and subtraction of complex numbers
- Multiplication and division of complex numbers
- Conjugates of complex numbers
- Polar form of a complex number
- Modulus and argument of a complex number

###### Vectors

- Direction cosines of vectors
- Angle between two vectors
- Scalar and vector products
- Few basic facts about vectors

###### Differentiation

- Differentiation of functions using product rule
- Differentiation of parametric functions
- Logarithmic differentiation of functions
- Differentiation of implicit functions
- Chain rule of differentiation
- Quotient rule of differentiation

###### Differentiation application

###### Integration

###### Sequences

###### Series

L’Hopital’s rule to evaluate the limit of a function

## Advanced engineering mathematics

Topics in advanced engineering mathematics covered so far are first order ordinary differential equations, determinants and vector analysis.

###### First-order ordinary differential equations (ODE)

- First order linear ODE
- Separation of variables in ODE
- First order homogeneous ODE
- Solve first order ODE using ‘transformations of variables’
- Solve Bernoulli’s equations

###### Second-order ordinary differential equations (ODE)

- Second-order homogeneous ODE with real and different roots
- Second-order homogeneous ODE with real and equal roots
- Second-order homogeneous ODE with complex roots
- What is a particular integral in second-order ODE
- Exponential functions as particular integrals
- Trigonometric functions as particular integrals

###### Determinants

###### Partial differentiation

- First-order partial derivatives of functions with two variables
- Second-order partial derivatives of functions with two variables
- First-order partial derivatives of functions with three variables
- How to use partial differentiation to identify the nature of stationary points
- Partial derivatives of inverse functions
- Change of variables in first-order partial differentiation

###### Laplace transform

- First shift theorem in Laplace transform
- Laplace transform of functions multiplied by variables
- Laplace transform of functions divided by a variable
- Cover up rule in inverse Laplace transform
- How to use partial fractions in inverse Laplace transform
- Laplace transform in first order ODE
- How to use Laplace transform to solve a second-order homogeneous ODE
- How to use Laplace transform to solve a second-order ODE

###### Matrix analysis

- What is a singular matrix?
- Inverse of a matrix
- Rank of a square matrix
- Rank of a rectangular matrix
- Nature of solutions of a system of equations using matrices
- Determine the eigenvalues of a given matrix
- Determine the corresponding eigenvectors
- Faddeev’s method to determine the characteristic polynomial of a matrix
- Eigenvectors of repeated eigenvalues
- Gaussian elimination method in 3 × 3 matrices
- Gaussian elimination method in 4 × 4 matrices
- Row transformation method to solve a system of equations
- Inverse matrix method to solve a system of equations
- Complex eigenvalues and eigenvectors of a matrix
- Triangular decomposition method in 3 × 3 matrices
- Cayley-Hamilton theorem

###### Vector analysis

- Scalar triple product of vectors
- Vector triple product
- Coplanar vectors
- Differentiation of a vector field
- Integration of vector fields
- Gradient of a scalar field
- Unit tangent vector
- Unit normal vector
- Directional derivatives
- Curl of a vector function
- Divergence of a vector function

###### Difference equations and Z-transform

- Recursive description of a sequence
- Solve a homogeneous difference equation
- Solve second-order difference equations

###### Multiple Integrations

- Determine the differential dz
- Determine the exact differential in two variables
- Determine the exact differential in three variables

###### Partial differential equations

Solve PDE with direct integration