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Geometry and Calculus for Computing

Geometry and Calculus for Computing

本课程是 Essential Mathematics for Computer Science 专项课程的一部分

位教师：Omar Karakchi

包含在中

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4个模块

深入了解一个主题并学习基础知识。

初级等级

推荐体验

2 周完成

在 10 小时一周

灵活的计划

自行安排学习进度

4个模块

深入了解一个主题并学习基础知识。

初级等级

推荐体验

2 周完成

在 10 小时一周

灵活的计划

自行安排学习进度

您将学到什么

Solve geometric and trigonometric problems involving angles, lines, and triangles, applying them to computing contexts.
Sketch and interpret graphs of functions and apply kinematics to describe displacement, velocity, and acceleration.
Work with exponential and logarithmic functions, exploring their rules, graphs, and applications in computational systems.
Understand limits and apply differentiation to calculate gradients, sketch curves, and solve optimisation problems.

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本课程是 Essential Mathematics for Computer Science 专项课程专项课程的一部分

在注册此课程时，您还会同时注册此专项课程。

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该课程共有4个模块

Mathematics provides the foundation for reasoning, problem-solving, and analysis in computer science. Geometry and Calculus for Computing equips you with essential tools to model shapes, describe motion, and analyse change. Across four modules, you’ll build a solid grounding in trigonometry, graph sketching, kinematics, exponential and logarithmic functions, and introductory calculus. You’ll learn to connect abstract mathematical concepts to practical computing applications, from computer graphics and simulations to optimisation and algorithm analysis. By the end of the course, you’ll have the skills to interpret functions, calculate gradients, and apply mathematical reasoning to a wide range of computational problems. This course prepares you for advanced study in computer science and data science by strengthening the mathematical toolkit you need to succeed in both academic and professional contexts.

单元详情

In this module, we will look at angles, triangles and trigonometry. We will study trigonometric ratios on different triangles, we will work with triangles that are not necessarily right-angled and we will use the sine, cosine and tangent rules relating to the lengths and angles of a triangle. We will also look at Pythagoras' theorem and use it in conjunction with trigonometric ratios.

涵盖的内容

9个视频4篇阅读材料5个作业

9个视频总计83分钟

Introduction to the course1分钟
Introduction to triangles and trigonometry16分钟
The circle8分钟
From the circle to the sine and cosine graphs10分钟
Introducing the tangent6分钟
Applications of sine and cosine rules – examples10分钟
Unit circumference and definition of trigonometric functions for every angle10分钟
Plotting tan2分钟
Trigonometric functions, plots and properties20分钟

4篇阅读材料总计50分钟

Course structure and navigation15分钟
How to learn effectively on this course15分钟
Course Syllabus10分钟
Summary10分钟

5个作业总计140分钟

Check your understanding: End of module 120分钟
Introduction to triangles and trigonometry30分钟
Sine and cosine rules30分钟
Unit circumference and definition of trigonometric functions for every angle30分钟
Trigonometric functions, plots and properties30分钟

In this module, we will learn about three concepts: the definition of a function, Cartesian coordinates and the graph of a function. We will use these concepts to describe simple motion (kinematics).

涵盖的内容

9个视频2篇阅读材料4个作业

9个视频总计70分钟

Definition of a function and Cartesian coordinates14分钟
The inverse of a function4分钟
Plotting linear functions on a Cartesian plane7分钟
Plotting quadratic functions on the Cartesian plane9分钟
Higher-order functions and limits17分钟
Transformations of functions3分钟
Using Desmos3分钟
Introduction to kinematics and the laws of motion11分钟
Kinematics – worked examples 3分钟

2篇阅读材料总计40分钟

Testing Desmos30分钟
Summary10分钟

4个作业总计125分钟

Check your understanding: End of module 220分钟
Definition of a function and Cartesian coordinates45分钟
Higher-order polynomials30分钟
Kinematics30分钟

In this topic (weeks 13 and 14), we will look at exponential and logarithmic functions. This week, we will introduce the exponential functional as extension of elevation to a non-integer power, we derive its properties and plot.

涵盖的内容

8个视频3个作业

8个视频总计42分钟

Exponential function, definition, plot and properties – properties9分钟
Exponential function, definition, plot and properties – graphs7分钟
Exponential function, definition, plot and properties – identity3分钟
Logarithmic function, definition, plot and properties – algebra11分钟
Logarithmic function, definition, plot and properties – graphs5分钟
Logarithmic function, definition, plot and properties – equations3分钟
Solving equations involving exp and log2分钟
Topic 7 – looking back2分钟

3个作业总计80分钟

Check your understanding: End of module 320分钟
Exponential functions30分钟
Logarithmic functions30分钟

In this topic (weeks 15 and 16), we will focus on limits and differentiation. This week, we will look at limits of a function and discuss the concept of continuity of a function. We will then introduce a new tool, differentiation and derive the derivative of common functions from first principles.