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)****Formulas in Fourier series****Formulas in differentiation applications****Formulas in vector analysis****Formulas in integration applications**

## 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 o****f complex numbers****Polar form of a complex number****Modulus and argument of a complex number****Roots of a complex number****Functions of complex variables****Equations of the locus in complex numbers**

**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**- Qu
**otient rule of differentiation**

**Differentiation application**

**Tangent & normal to any curve****Radius of curvature****Centre of curvature****Differentiate inverse trigonometric functions****Maximum and minimum values of functions****Applications of maximum and minimum values of functions****Points of inflexion**

**Integration**

**Integration by substitution****Integration of trigonometric functions****Integration by partial fraction****Integration by parts****Integrate dz/(z^2 – a^2)****Integrate dz/(a^2 – z^2)****Integrate dz/(z^2 + a^2)****Get the value of d z/√(a^2-z^2)****How to integrate dx/(a cos^2x+bsin^2x+c)****How to integrate dx/(a cos x+bsin x+c)****What is the value of ∫√(a^2 – x^2) dx****Integrate d z /√(z^2-a^2)****Integrate d**x /√(x^2+a^2)

**Reduction formulas**

**Reduction formulas for algebraic functions****Integrate Sec^(n) x****Integrate Tan^(n) x****Integrate Sin^(n) x****Integrate Cos^(n) x****Integrate e^(-x) Sin^(n) x****Integrate e^(-x) Cos^(n) x****Integrate Cot^(n) x****Integrate (ln x)^(n)****Integrate Cosh^(n) x dx**

**Integration applications**

**The area under a curve****The area under a parametric curve****Mean value of a function****Root mean square value of a function****The centroid of a plane figure****Centre of gravity of a solid of revolution****Length of a curve****Length of a parametric curve****The volume of a solid of revolution****The surface of revolution of a curve**

**Polar curves**

**The area enclosed by a polar curve****Length of a polar curve****The volume of revolutions in polar curves****The surface of revolutions in polar curves**

**Sequences**

**Series**

**L’Hopital’s rule to evaluate the limit of a function****Limits of series****Sum of a series****Convergence of series****Absolute convergence of a series****Maclaurin series for e^(x)****Maclaurin series for e^(-x)****Maclaurin series for sin x****Maclaurin series for cos x****Maclaurin series for ln (1+x)****Maclaurin series for Cosh x****Maclaurin series for Sinh x****Power series of Sin x****Maclaurin series for Tan x****Derive binomial series from Maclaurin series****Power series of Cos x****Maclaurin series for Sec x****Maclaurin series for Sin^(-1) x****Maclaurin series for Tan^(-1) x****Expand the series e^(x) Sin^(-1) x – Apply Maclaurin series****Further applications of Maclaurin series**

**Determinants**

**Expand & evaluate determinants****Check the consistency of equations using determinants****Determinants to solve equations****Determinants to solve simultaneous equations**

**Multiple integrals**

**Double integrals****Apply double integrals to find the area****Evaluate triple integrals****The volume of solids**

**Curves and curve tracing**

## 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**

**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****Lagrange multipliers for functions of two variables****Errors using 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**

**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****Symmetric, skew-symmetric and orthogonal matrices – how to find out these?****Cayley-Hamilton theorem****Gauss-Jordan method to find out the inverse of a matrix****Transfer quadratic form to canonical form****Diagonalize any matrix**

**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****The line integral of a scalar field****Combinations of curl, grad, div**

**Complex analysis**

**Harmonic function and its conjugate function****Map the points in the complex plane****Singularities and zeros of the complex numbers****Residues of complex functions**

**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****How to integrate exact differentials?**