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

#### 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

##### Differentiation application

##### Integration

#### 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

##### Determinants

##### Laplace transform

##### Matrix analysis

- What is a singular matrix?
- 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