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 for logarithmic & hyperbolic functions**

**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**

**Polar form of a complex number**

**Modulus and argument of a complex number**

**Functions of complex variables**

**Vectors**

**Differentiation**

**Differentiation of functions using product rule**

**Differentiation of parametric functions**

**Logarithmic differentiation of functions**

**Differentiation of implicit functions**

Qu**otient rule of differentiation**

**Differentiation application**

**Integration**

**Integration of trigonometric functions**

**Sequences**

**Examples of arithmetic sequences**

**Examples of geometric 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)**

**Separation of variables in ODE**

**Solve first order ODE using ‘transformations of variables’**

**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**

**Expand & evaluate determinants **

**Check the consistency of equations using 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**

**Shifted data problem | Laplace transform**

**Heaviside unit step function | Laplace transform**

**Laplace transform of a unit step function**

**Second shift theorem | inverse Laplace transform**

**Matrix analysis**

**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**

**Symmetric, skew-symmetric and orthogonal matrices – how to find out these?**

**Gauss-Jordan method to find out the inverse of a matrix**

**Vector analysis**

**Scalar triple product of vectors**

**Differentiation of a vector field**

**Divergence of a vector function**

**The line integral of a scalar field**

**Difference equations and Z-transform**

**Recursive description of a sequence**

**Solve a homogeneous difference equation**

**Solve second-order difference equations**

**Multiple Integrations**

**Determine the exact differential in two variables**

**Determine the exact differential in three variables**

**How to integrate exact differentials?**

**Partial differential equations**

**Solve PDE with direct integration**