This course on Vector Calculus for Engineers teaches Vector Calculus for Engineers fundamentals through 2 interactive modules. If you are , then this course is for you. You can access this course on web and mobile, it’s available in language.
This course on Vector Calculus for Engineers teaches Vector Calculus for Engineers fundamentals through 2 interactive modules. If you are , then this course is for you. You can access this course on web and mobile. This complete course is available in language.
Learn new concepts from professionals in the field.
Acquire a basic understanding of a topic or skill
Gain practical project experience to enhance employability.
Obtain a career certificate that can be shared.
Topics you will learn
Vectors
15 videos
Course Overview
Week One Introduction
Vectors | Lecture 1
Cartesian Coordinates | Lecture 2
Dot Product | Lecture 3
Cross Product | Lecture 4
Analytic Geometry of Lines | Lecture 5
Analytic Geometry of Planes | Lecture 6
Kronecker Delta and Levi-Civita Symbol | Lecture 7
Vector Identities | Lecture 8
Scalar Triple Product | Lecture 9
Vector Triple Product | Lecture 10
Scalar and Vector Fields | Lecture 11
Matrix Addition and Multiplication
Matrix Determinants and Inverses
28 readings
Welcome and Course Information
Certificate or Audit?
How to Write Math in the Discussions using MathJax
Associative Law
Triangle Midpoint Theorem
Newton's equation for the force between two masses
Commutative and Distributive Properties
Dot Product between Standard Unit Vectors
Law of Cosines
Do you know matrices?
Cross Product Between Standard Unit Vectors
Associative Property
Parametric Equation for a Line
Equation for a Plane
Levi-Civita Identities
The Levi-Civita Symbol and the Cross Product
Kronecker-Delta Identities
Levi-Civita and Kronecker-Delta Identities
Optional Parentheses
Scalar Triple Product with any Two Vectors Equal
Swapping the Position of the Operators
Scalar Triple Product of the Unit Vectors
Jacobi Identity
Scalar Quadruple Product
Lagrange's Identity in Three Dimensions
Vector Quadruple Product
Examples of Scalar and Vector Fields
6 quizzes
Week One Assessment
Diagnostic Quiz
Vectors
Analytic Geometry
Vector Algebra
Week One Assessment (audit)
2 plugins
Deep Dive into Quaternions and Vector Calculus
Deep Dive into Levi-Civita and the Kronecker Delta
Differentiation
13 videos
Week Two Introduction
Partial Derivatives | Lecture 12
The Method of Least Squares | Lecture 13
Chain Rule | Lecture 14
Triple Product Rule | Lecture 15
Triple Product Rule: Example | Lecture 16
Gradient | Lecture 17
Divergence | Lecture 18
Curl | Lecture 19
Laplacian | Lecture 20
Vector Derivative Identities | Lecture 21
Vector Derivative Identities (Proof) | Lecture 22
Electromagnetic Waves | Lecture 23
15 readings
Computing Partial Derivatives
Taylor Series Expansions
Least-squares Method
Chain Rule
Triple Product Rule for a Linear Function
Quadruple Product Rule
Computing the Gradient
The Gradient of the Position Vector
Computing the Divergence
Computing the Curl
The Vorticity in Two Dimensions
Computing the Laplacian
Vector Derivative Identities
The Material Acceleration
Wave Equation for the Magnetic Field
5 quizzes
Week Two Assessment
Partial Derivatives
The Del Operator
Vector Calculus Algebra
Week Two Assessment (audit)
Integration and Curvilinear Coordinates
12 videos
Week Three Introduction
Double and Triple Integrals | Lecture 24
Example: Double Integral with Triangle Base | Lecture 25
Polar Coordinates (Gradient) | Lecture 26
Polar Coordinates (Divergence and Curl) Lecture 27
Polar Coordinates (Laplacian) |Lecture 28
Central Force | Lecture 29
Change of Variables (Single Integral) | Lecture 30
Change of Variables (Double Integral) | Lecture 31
Cylindrical Coordinates | Lecture 32
Spherical Coordinates (Part A) | Lecture 33
Spherical Coordinates (Part B) | Lecture 34
24 readings
Computing the Mass of a Cube
Volume of a surface above a parallelogram
Cartesian Unit Vectors
Cartesian Partial Derivatives
Some Common Two-Dimensional Vectors
Computing the Divergence and Curl in Polar Coordinates
Pipe Flow
Angular Momentum
Velocity Dot Acceleration
Mass of a Disk
Gaussian Integral
Del in Cylindrical Coordinates
Divergence of a Unit Vector
Divergence and Curl of the Unit Vectors
Center-of-Mass of a Uniform Solid Cone
Spherical and Cartesian Unit Vectors
Change-of-variables Formula for Spherical Coordinates
Integrating a Function that only Depends on Distance from the Origin
Mass of a Sphere when the Density is a Linear Function
Derivatives of the Unit Vectors
Laplacian of a Vector Field in Spherical Coordinates
Laplacian of 1/r
Laplacian of a Vector Field with Inverse Square Law
5 quizzes
Week Three Assessment
Multidimensional Integration
Polar Coordinates
Cylindrical and Spherical Coordinates
Week Three Assessment (audit)
Line and Surface Integrals
9 videos
Week Four Introduction
Line Integral of a Scalar Field | Lecture 35
Arc Length | Lecture 36
Line Integral of a Vector Field | Lecture 37
Work-Energy Theorem | Lecture 38
Surface Integral of a Scalar Field | Lecture 39
Surface Area of a Sphere | Lecture 40
Surface Integral of a Vector Field | Lecture 41
Flux Integrals | Lecture 42
11 readings
Circumference of a Circle
Computing the Mass of a Wire
Approximating the Perimeter of an Ellipse
Line Integral around a Square
Line Integral around a Circle
Mass Falling Under Gravity
Surface Area of a Cylinder
Surface Area of a Cone
Surface Area of a Paraboloid
Surface Integral over a Cylinder
Mass Flux Through a Pipe
4 quizzes
Week Four Assessment
Line Integrals
Surface Integrals
Week Four Assessment (audit)
Fundamental Theorems
13 videos
Week Five Introduction
Gradient Theorem | Lecture 43
Conservative Vector Fields | Lecture 44
Conservation of Energy | Lecture 45
Divergence Theorem | Lecture 46
Divergence Theorem: Example I | Lecture 47
Divergence Theorem: Example II | Lecture 48
Continuity Equation | Lecture 49
Green's Theorem | Lecture 50
Stokes' Theorem | Lecture 51
Meaning of the Divergence and the Curl | Lecture 52
Maxwell's Equations | Lecture 53
Concluding Remarks
21 readings
Gradient Theorem
Conservative Vector Fields
Escape Velocity
Divergence Theorem for a Sphere
Test the Divergence Theorem for a Cube
Divergence Theorem for a Cube
Test the Divergence Theorem for a Sphere
Flux Integral of the Position Vector
Source Flow
Continuity Equation
Electrodynamics Continuity Equation
Test Green's Theorem for a Square
Test Green's Theorem for a Circle
Stokes' Theorem in Two Dimensions
Test Stokes' Theorem
Point Vortex
The Navier-Stokes Equation
Electric Field of a Point Charge
Magnetic Field of a Wire
Please Rate this Course
Acknowledgements
5 quizzes
Week Five Assessment
Gradient Theorem
Divergence Theorem
Stokes' Theorem
Week Five Assessment (audit)
Course Offerings
Certificate you will get
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Pre Requsites
Curious Mind to learn new concepts
Strong internet connection
After this Course
Course is for
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FAQ's
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