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Vector calculus is one of the most useful branches of mathematics for game development. The [course_title] is designed to provide an introduction to functions of several real variables. Topics discussed are partial derivatives; directional derivatives; gradients; extremal problems and  Lagrange’s multiplier method; multiple integrals, line and surface integrals; vector-valued functions; divergence, curl and flux of vector fields; the theorems of Green and Stokes; the divergence theorem; and applications. 

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: Open Culture

Course Curriculum

Module: 01
How to compute a Fourier series: an example 00:08:00
What are Fourier series? 00:45:00
Tutorial on Fourier series 00:33:00
Fourier series + differential equations 00:18:00
Applications of Double integrals. Chris Tisdell UNSW 00:44:00
Path integrals – How to integrate over curves. Chris Tisdell UNSW 00:47:00
What is a vector field?? Chris Tisdell UNSW 00:43:00
What is the divergence? Chris Tisdell UNSW 00:46:00
What is the Curl? Chris Tisdell UNSW 00:48:00
What is a line integral? Chris Tisdell UNSW 00:48:00
Applications of Line Integrals. Chris Tisdell UNSW 00:46:00
Module: 02
Fundamental theorem of line integrals. Chris Tisdell UNSW 00:40:00
What is Green’s theorem? Chris Tisdell UNSW 00:48:00
Green’s Theorem. Chris Tisdell UNSW 00:39:00
Parametrised surfaces. Chris Tisdell UNSW 00:33:00
What is a surface integral? (part 1) Chris Tisdell UNSW 00:48:00
More on surface integrals. Chris Tisdell UNSW 00:31:00
Surface integrals + vector fields. Chris Tisdell UNSW. 00:25:00
Divergence theorem of Gauss 00:12:00
How to solve PDEs via separation of variables + Fourier series. Chris Tisdell UNSW 00:42:00
Vector Revision 00:43:00
Intro to curves and vector functions 00:49:00
Limits of vector functions 00:44:00
Module: 03
Calculus of vector functions – 1 variable 00:20:00
Calculus of vector functions tutorial 00:44:00
Vector functions tutorial 00:29:00
Intro to functions of two variables 00:34:00
Limits of functions of two variables 00:49:00
Partial derivatives 00:46:00
Partial derivatives and PDEs tutorial 00:09:00
2 variable functions: graphs + limits tutorial 00:41:00
Multivariable chain rule and differentiability 00:49:00
Chain rule: partial derivative of $\arctan (y/x)$ w.r.t. $x$ 00:05:00
Chain rule & partial derivatives 00:09:00
Module: 04
Chain rule: identity involving partial derivatives 00:08:00
Multivariable chain rule tutorial 00:34:00
Leibniz’ rule: Integration via differentiation under integral sign 00:05:00
Evaluating challenging integrals via differentiation: Leibniz rule 00:08:00
Gradient and directional derivative 01:00:00
Gradient & directional derivative tutorial 00:45:00
Gradient & directional derivative tutorial 00:45:00
Directional derivative of f(x,y) 00:07:00
Tangent plane approximation and error estimation 00:28:00
Tutorial on gradient and tangent plane 00:23:00
Partial derivatives and error estimation 00:12:00
Multivariable Taylor Polynomials 00:54:00
Taylor polynomials: functions of two variables 00:11:00
Module: 05
Limits, chain rule, arc length. Multivariable calculus. 00:35:00
Critical points of functions 00:34:00
How to find critical points of functions 00:14:00
How to find critical points of functions 00:14:00
Second derivative test: two variables 00:27:00
Critical points + 2nd derivative test: Multivariable calculus 00:07:00
How to find and classify critical points of functions 00:12:00
Lagrange multipliers 00:45:00
Lagrange multipliers: 2 constraints 00:14:00
Lagrange multipliers: Extreme values of a function subject to a constraint 00:07:00
Module: 06
Lagrange multipliers example 00:11:00
Lagrange multiplier example: Minimizing a function subject to a constraint 00:08:00
2nd derivative test, max / min and Lagrange multipliers tutorial 00:42:00
Intro to Jacobian + differentiability 00:42:00
Jacobian chain rule and inverse function theorem 00:27:00
Intro to double integrals 00:29:00
Double integrals over general regions 00:50:00
Double integrals: Volume between two surfaces 00:05:00
Double integrals: Volume of a tetrahedron 00:05:00
Double integral tutorial 00:11:00
Double integrals and area 00:10:00
Module: 07
Double integrals in polar co-ordinates 00:16:00
Reversing order in double integrals 00:12:00
Double integrals: reversing the order of integration 00:08:00
Applications of double integrals. 00:45:00
Double integrals and polar co-ordinates 00:36:00
Tutorial on double integrals 00:27:00
Centroid + double integral tutorial 00:25:00
Center of mass, double integrals and polar co-ordinates tutorial 00:33:00
Triple integral tutorial 00:39:00
Triple integrals in Cylindrical and Spherical Coordinates 00:40:00
Triple integrals & Center of Mass 00:28:00
Module: 08
Change of variables in double integrals tutorial 00:33:00
Path integral (scalar line integral) from vector calculus 00:06:00
Line integral example in 3D-space 00:06:00
Line integral from vector calculus over a closed curve 00:08:00
Line integral example from Vector Calculus 00:07:00
Divergence of a vector field: Vector Calculus 00:06:00
Curl of a vector field (ex. no.1): Vector Calculus 00:05:00
Curl of a vector field (ex. no.2): Vector calculus 00:08:00
Divergence theorem of Gauss 00:12:00
Intro to Fourier series and how to calculate them 00:14:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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