Engineering Mathematics

The topics covered are Chain rule, Partial Derivative, Taylor Polynomials, Critical points of functions, Lagrange multipliers, Vector Calculus, Line Integral, Double Integrals, Laplace Transform, Fourier series.

We also have free math calculators and tools to help you understand the steps and check your answers.

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

Vector Calculus

Divergence of a vector field
Curl of a vector field (ex. no.1 & 2)

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 coordinates
Double integrals and area

Double integrals

Volume between two surfaces
Volume of a tetrahedron
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

Math Calculators and Tools

Chain Rule Calculator
This tool will help you to understand the differentiation process of a composite function. Use show steps to see possible differentiation steps.

Partial Derivative Calculator
This tool will help you to understand the possible partial derivative steps.

Double Integral Calculator
This tool allows you to calculate double integrals in f(x, y)

Laplace Transform Calculator
This tool allows you the calculate the Laplace Transform of the given function.

Fourier Series Calculator
This tool allows you to calculate the Fourier series of a function.

Calculus Calculator with step by step solutions
Functions, Operations on Functions,
Polynomial and Rational Functions,
Exponential and Logarithmic Functions,
Sequences and Series,
Evaluating Limits, Derivatives,
Applications of Differentiation,
Integrals, Applications of Integration,
Techniques of Integration,
Parametric Equations and Polar Coordinates

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