Lecture Description
This video lecture, part of the series Vector Calculus by Prof. Christopher Tisdell, does not currently have a detailed description and video lecture title. If you have watched this lecture and know what it is about, particularly what Mathematics topics are discussed, please help us by commenting on this video with your suggested description and title. Many thanks from,
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Course Index
- Applications of Double integrals
- Path Integrals: How to Integrate Over Curves
- What is a Vector Field?
- What is the Divergence?
- What is the Curl?
- What is a Line Integral?
- Applications of Line Integrals
- Fundamental Theorem of Line Integrals
- What is Green's Theorem?
- Green's Theorem
- Parametrised Surfaces
- What is a Surface Integral? (Part I)
- More On Surface Integrals
- Surface Integrals and Vector Fields
- Divergence Theorem of Gauss
- How to Solve PDEs via Separation of Variables and Fourier Series
- Vector Revision
- Intro to Curves and Vector Functions
- Limits of Vector Functions
- Calculus of Vector Functions: One Variable
- Calculus of Vector Functions Tutorial
- Vector Functions Tutorial
- Intro to Functions of Two Variables
- Limits of Functions of Two Variables
- Partial Derivatives
- Partial Derivatives and PDEs Tutorial
- Multivariable Functions: Graphs and Limits
- Multivariable Chain Rule and Differentiability
- Chain Rule: Partial Derivative of $\arctan (y/x)$ w.r.t. $x$
- Chain Rule & Partial Derivatives
- Chain Rule: Identity Involving Partial Derivatives
- Multivariable Chain Rule
- Leibniz' Rule: Integration via Differentiation Under Integral Sign
- Evaluating Challenging Integrals via Differentiation: Leibniz Rule
- Gradient and Directional Derivative
- Gradient and Directional Derivative
- Directional dDerivative of $f(x,y)$
- Tangent Plane Approximation and Error Estimation
- Gradient and Tangent Plane
- Partial Derivatives and Error Estimation
- Multivariable Taylor Polynomials
- Taylor Polynomials: Functions of Two Variables
- Multivariable Calculus: Limits, Chain Rule and Arc Length
- Critical Points of Functions
- How to Find Critical Points of Functions
- How to Find Critical Points of Functions
- Second Derivative Test: Two Variables
- Multivariable Calculus: Critical Points and Second Derivative Test
- How to Find and Classify Critical Points of Functions
- Lagrange Multipliers
- Lagrange Multipliers: Two Constraints
- Lagrange Multipliers: Extreme Values of a Function Subject to a Constraint
- Lagrange Multipliers Example
- Lagrange multiplier Example: Minimizing a Function Subject to a Constraint
- Second Derivative Test, Max/Min and Lagrange Multipliers
- Intro to Jacobian Matrix and Differentiability
- Jacobian Chain Rule and Inverse Function Theorem
- Intro to Double Integrals
- Double Integrals Over General Regions
- Double Integrals: Volume Between Two Surfaces
- Double Integrals: Volume of a Tetrahedron
- Double Integral
- Double Integrals and Area
- Double Integrals in Polar Co-ordinates
- Reversing Order in Double Integrals
- Double Integrals: Reversing the Order of Integration
- Applications of Double Integrals
- Double Integrals and Polar Co-ordinates
- Double Integrals
- Centroid and Double Integral
- Center of Mass, Double Integrals and Polar Co-ordinates
- Triple Integral
- Triple integrals in Cylindrical and Spherical Coordinates
- Triple integrals & Center of Mass
- Change of Variables in Double Integrals
- 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 Example From Vector Calculus
- Divergence of a Vector Field
- Curl of a Vector Field (ex. no.1)
- Curl of a Vector Field (ex. no.2)
- Divergence Theorem of Gauss
- Intro to Fourier Series and How to Calculate Them
- How to Compute a Fourier Series: An Example
- What are Fourier Series?
- Fourier Series
- Fourier Series and Differential Equations
Course Description
In this course, Prof. Chris Tisdell gives 88 video lectures on Vector Calculus. This is a series of lectures for "Several Variable Calculus" and "Vector Calculus", which is a 2nd-year mathematics subject taught at UNSW, Sydney. This playlist provides a shapshot of some lectures presented in Session 1, 2009 and Session 1, 2011. These lectures focus on presenting vector calculus in an applied and engineering context, while maintaining mathematical rigour. Thus, this playlist may be useful to students of mathematics, but also to those of engineering, physics and the applied sciences. There is an emphasis on examples and also on proofs. Dr Chris Tisdell is Senior Lecturer in Applied Mathematics.
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