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Engineering Mathematics

A series of free Engineering Mathematics Videos.

Chain rule: partial derivative
Chain rule: identity involving partial derivatives
Chain rule & partial derivatives
Partial derivatives and PDEs tutorial
Partial derivatives and error estimation

Taylor polynomials: functions of two variables
Leibniz' rule: Integration via differentiation
Evaluating challenging integrals via differentiation: Leibniz rule

How to find critical points of functions
Critical points + 2nd derivative test: Multivariable calculus
How to find and classify critical points of functions

Lagrange multipliers: Extreme values of a function subject to a constraint
Lagrange multiplier example: Minimizing a function subject to a constraint
Multivariable Calculus: Directional derivative of $f(x,y)$
Lagrange multipliers example

Divergence of a vector field: Vector Calculus
Curl of a vector field (ex. no.1): Vector Calculus
Curl of a vector field (ex. no.2): Vector calculus

Path integral (scalar line integral) from vector calculus
Line integral example in 3D-space
Line integral from vector calculus over a closed curve
Line integral from vector calculus over a closed curve
Line integral example from Vector Calculus

Double integral tutorial
Double integrals in polar co-ordinates
Double integrals and area
Double integrals: Volume between two surfaces
Double integrals: Volume of a tetrahedron
Double integrals: reversing the order of integration
Reversing order in double integrals

Homogeneous first order ordinary differential equation
Solution to a 2nd order, linear homogeneous ODE with repeated roots
2nd order ODE with constant coefficients: simple method of solution
2nd order ODE with constant coefficients: non-standard method of solution

Intro to Laplace transform
Laplace transform + differential equations
First shifting theorem of Laplace transforms
Laplace Transform: First Shifting Theorem
Second shifting theorem of Laplace transforms
Laplace Transform: Second Shifting Theorem
Laplace Transform of tf(t)

Intro to Fourier series and how to calculate them
How to compute a Fourier series: an example
Fourier series + differential equations

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