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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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