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

###### 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

###### 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

###### Sequences

Examples of arithmetic 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

###### 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

###### 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