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Geometry and Calculus for Computing · LearnSpace
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Geometry and Calculus for Computing

Курс от University of London, Goldsmiths, University of London
Начальный≈ 15.5 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

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.

Навыки, которые вы освоите

CalculusGeometryTrigonometryDerivativesGraphingGraphic DesignMathematics and Mathematical ModelingComputer GraphicsFunctional RequirementMathematical Theory & AnalysisComputer ScienceGraph TheoryApplied MathematicsMathematical ModelingPlot (Graphics)Mechanics

Программа курса

4 модулей · 65 учебных материалов

01Angles, triangles and trigonometry19 материалов

Lesson 1.0 Introduction

Course structure and navigationЧтениеHow to learn effectively on this courseЧтениеIntroduction to the courseВидеоCourse SyllabusЧтение

Lesson 1.1 Introduction to Angles, triangles and trigonometry

Учитесь у экспертов

Omar Karakchi

Lecture

Geometry and Calculus for Computing
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≈ 15.5 ч

4 модулей

Язык: Английский

Часть программы вашего университета
Introduction to triangles and trigonometryВидео
The circleВидео
From the circle to the sine and cosine graphsВидео
Introducing the tangentВидео
Applying trigonometry to solve triangle problemsDIALOGUE
Introduction to triangles and trigonometryЗадание

Lesson 1.2 Generic Triangles

Applications of sine and cosine rules – examplesВидеоSine and cosine rulesЗадание

Lesson 1.3 Trigonometric Functions

Unit circumference and definition of trigonometric functions for every angleВидеоPlotting tanВидеоUnit circumference and definition of trigonometric functions for every angleЗаданиеTrigonometric functions, plots and propertiesВидеоTrigonometric functions, plots and propertiesЗадание

Lesson 1.4 Summary and Assessments

Check your understanding: End of module 1ЗаданиеSummaryЧтение
02Graph sketching and kinematics 15 материалов

Lesson 2.1 Introduction to graph sketching and kinematics

Definition of a function and Cartesian coordinatesВидеоThe inverse of a functionВидеоPlotting linear functions on a Cartesian planeВидеоDefinition of a function and Cartesian coordinatesЗадание

Lesson 2.2 Higher-order polynomials

Plotting quadratic functions on the Cartesian planeВидеоHigher-order functions and limitsВидеоTransformations of functionsВидеоUsing DesmosВидеоTesting DesmosЧтениеHigher-order polynomialsЗадание

Lesson 2.3 Kinematics

Introduction to kinematics and the laws of motionВидеоKinematics – worked examples ВидеоKinematicsЗадание

Lesson 2.4 Topic summary

Check your understanding: End of module 2ЗаданиеSummaryЧтение
03Exponential and logarithmic functions11 материалов

Lesson 3.1 Exponential function, definition, plot and properties

Exponential function, definition, plot and properties – propertiesВидеоExponential function, definition, plot and properties – graphsВидеоExponential function, definition, plot and properties – identityВидеоExponential functionsЗадание

Lesson 3.2 Logarithmic function, definition, plot and properties

Logarithmic function, definition, plot and properties – algebraВидеоLogarithmic function, definition, plot and properties – graphsВидеоLogarithmic function, definition, plot and properties – equationsВидеоSolving equations involving exp and logВидеоLogarithmic functionsЗадание

Lesson 3.3 Summary and Assessments

Check your understanding: End of module 3ЗаданиеTopic 7 – looking backВидео
04Limits and differentiation20 материалов

Lesson 4.1 Definition of a limit for a convergent sequence

Continuous and discontinuous functionsВидеоBinomial expansionВидеоContinual expansion and binomial differentiationЗадание

Lesson 4.2 Definition of limits of a function, continuous and discontinuous functions

Introducing differentiationВидеоWorked examplesВидеоFurther differentiation IЗаданиеExamples of differentiating polynomialsВидеоWorked examples of differentiationВидеоDifferentials of key functionsВидеоDifferentiating polynomialsЗаданиеMastering limits and first principles of differentiationDIALOGUE

Lesson 4.3 Product, quotient and chain rules

The product ruleВидеоThe quotient ruleВидеоThe chain ruleВидеоFurther differentiation II – product, quotient and chain ruleЗадание

Lesson 4.4 Topic summary

Check your understanding: End of module 4ЗаданиеTopic 8 – looking backВидео

Course Wrap-up

Geometry and Calculus for Computing: Course SummaryЧтениеThe Clockwork Chamber: A Mechanical Escape MysteryDIALOGUECourse summaryВидео