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Introduction to Calculus · LearnSpace
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Introduction to Calculus

Курс от The University of Sydney
Средний≈ 59.4 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce. The course emphasises the key ideas and historical motivation for calculus, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics. Students taking Introduction to Calculus will: • gain familiarity with key ideas of precalculus, including the manipulation of equations and elementary functions (first two weeks), • develop fluency with the preliminary methodology of tangents and limits, and the definition of a derivative (third week), • develop and practice methods of differential calculus with applications (fourth week), • develop and practice methods of the integral calculus (fifth week).

Навыки, которые вы освоите

CalculusAlgebraIntegral CalculusTrigonometryDerivativesGeometryGraphing

Программа курса

5 модулей · 172 учебных материалов

01Precalculus (Setting the scene)27 материалов

Introduction to the course

Welcome and introduction to PrecalculusВидео

Numbers and their representations

Real line, decimals and significant figuresВидеоNotes: Real line, decimals and significant figuresЧтение

Учитесь у экспертов

David Easdown

Associate Professor

Introduction to Calculus
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Обучение на Coursera

≈ 59.4 ч

5 модулей

Язык: Английский

Субтитры: Арабский, Французский, Бенгальский, Узбекский, Украинский, Китайский (Китай), Греческий, Итальянский, Бразильский португальский, Вьетнамский, Нидерландский, Корейский, Немецкий, Пушту, Урду, Русский, Тайский, Индонезийский, Шведский, Турецкий, Азербайджанский, Испанский, Дари, Хинди, Японский, Казахский, Венгерский, Польский

Часть программы вашего университета
Real line, decimals and significant figures Задание
The Theorem of Pythagoras and properties of the square root of 2Видео
Notes: The Theorem of Pythagoras and properties of the square root of 2Чтение
The Theorem of Pythagoras and properties of the square root of 2 Задание
Algebraic expressions, surds and approximationsВидео
Notes: Algebraic expressions, surds and approximationsЧтение
Algebraic expressions, surds and approximations Задание

Equations, inequalities and solutions sets

Equations and inequalitiesВидеоNotes: Equations and inequalitiesЧтениеEquations and inequalities ЗаданиеSign diagrams, solution sets and intervals (Part 1)ВидеоSign diagrams, solution sets and intervals (Part 2)ВидеоNotes: Sign diagrams, solution sets and intervalsЧтениеSign diagrams, solution sets and intervalsЗадание

The Cartesian plane and distance

Coordinate systemsВидеоNotes: Coordinate systemsЧтениеCoordinate systems ЗаданиеDistance and absolute valueВидеоNotes: Distance and absolute valueЧтениеDistance and absolute value ЗаданиеLines and circles in the planeВидеоNotes: Lines and circles in the planeЧтениеLines and circles in the plane Задание

Assessment

Module 1 quizЗадание
02Functions (Useful and important repertoire)38 материалов

Introduction

Introduction to Module 2Видео

Parabolas, quadratics and the quadratic formula

Parabolas and quadraticsВидеоNotes: Parabolas and quadraticsЧтениеParabolas and quadraticsЗаданиеThe quadratic formulaВидеоNotes: The quadratic formulaЧтениеThe quadratic formulaЗадание

Functions, composition and inversion

Functions as rules, with domain, range and graphВидеоNotes: Functions as rules, with domain, range and graphЧтениеFunctions as rules, with domain, range and graphЗаданиеPolynomial and power functionsВидеоNotes: Polynomial and power functionsЧтениеPolynomial and power functionsЗадание

Exponential and logarithmic functions

The exponential functionВидеоNotes: The exponential functionЧтениеThe exponential functionЗаданиеThe logarithmic functionВидеоNotes: The logarithmic functionЧтениеThe logarithmic functionЗадание

Circular functions and trigonometry

Sine, cosine and tangentВидеоNotes: Sine, cosine and tangentЧтениеSine, cosine and tangentЗаданиеThe unit circle and trigonometryВидеоNotes: The unit circle and trigonometryЧтениеThe unit circle and trigonometryЗадание

Assessment

Module 2 quizЗадание
03Introducing the differential calculus33 материалов

Introduction

Introduction to Module 3Видео

Rates of change and tangent lines

Slopes and average rates of changeВидеоNotes: Slopes and average rates of changeЧтениеSlopes and average rates of changeЗаданиеDisplacement, velocity and accelerationВидеоNotes: Displacement, velocity and accelerationЧтениеDisplacement, velocity and accelerationЗаданиеTangent lines and secantsВидеоNotes: Tangent lines and secantsЧтениеTangent lines and secantsЗадание

Limits

Different kinds of limitsВидеоNotes: Different kinds of limitsЧтениеDifferent kinds of limitsЗаданиеLimit lawsВидеоNotes: Limit lawsЧтениеLimit lawsЗаданиеLimits and continuityВидео

The derivative

The derivative as a limitВидеоNotes: The derivative as a limitЧтениеThe derivative as a limitЗаданиеFinding derivatives from first principlesВидеоNotes: Finding derivatives from first principlesЧтениеFinding derivatives from first principlesЗадание

Leibniz notation and differentials

Leibniz notationВидеоNotes: Leibniz notationЧтениеLeibniz notationЗаданиеDifferentials and applications (Part 1)ВидеоDifferentials and applications (Part 2)ВидеоNotes: Differentials and applicationsЧтение

Assessment

Module 3 quizЗадание
04Properties and applications of the derivative41 материалов

Introduction

Introduction to Module 4Видео

First derivatives and turning points

Increasing and decreasing functionsВидеоNotes: Increasing and decreasing functionsЧтениеIncreasing and decreasing functionsЗаданиеSign diagramsВидеоNotes: Sign diagramsЧтениеSign diagramsЗаданиеMaxima and minimaВидеоNotes: Maxima and minimaЧтениеMaxima and minimaЗадание

Second derivatives and curve sketching

Concavity and inflectionsВидеоNotes: Concavity and inflectionsЧтениеConcavity and inflectionsЗаданиеCurve sketchingВидеоNotes: Curve sketchingЧтениеCurve sketchingЗадание

The Chain Rule

The Chain RuleВидеоNotes: The Chain RuleЧтениеThe Chain RuleЗаданиеApplications of the Chain RuleВидеоNotes: Applications of the Chain RuleЧтениеApplications of the Chain RuleЗадание

The Product Rule

The Product RuleВидеоNotes: The Product RuleЧтениеThe Product RuleЗаданиеApplications of the Product RuleВидеоNotes: Applications of the Product RuleЧтениеApplications of the Product RuleЗадание

The Quotient Rule

The Quotient RuleВидеоNotes: The Quotient RuleЧтениеThe Quotient RuleЗаданиеApplication of the Quotient RuleВидеоNotes: Application of the Quotient RuleЧтениеApplication of the Quotient RuleЗадание

Optimisation

OptimisationВидеоNotes: OptimisationЧтениеOptimisationЗаданиеThe Second Derivative TestВидеоNotes: The Second Derivative TestЧтениеThe Second Derivative TestЗадание

Assessment

Module 4 quizЗадание
05Introducing the integral calculus33 материалов

Introduction

Introduction to Module 5Видео

Velocity and displacement

Inferring displacement from velocityВидеоNotes: Inferring displacement from velocityЧтениеInferring displacement from velocityЗадание

Areas under curves, Riemann sums and definite integrals

Areas bounded by curvesВидеоNotes: Areas bounded by curvesЧтениеAreas bounded by curvesЗаданиеRiemann sums and definite integralsВидеоNotes: Riemann sums and definite integralsЧтениеRiemann sums and definite integralsЗадание

The Fundamental Theorem of Calculus and indefinite integrals

The Fundamental Theorem of Calculus and indefinite integralsВидеоNotes: The Fundamental Theorem of Calculus and indefinite integralsЧтениеThe Fundamental Theorem of Calculus and indefinite integralsЗаданиеConnection between areas and derivatives (Part 1)ВидеоConnection between areas and derivatives (Part 2)ВидеоNotes: Connection between areas and derivativesЧтение

Integration by substitution

Integration by substitution (Part 1)ВидеоIntegration by substitution (Part 2)ВидеоNotes: Integration by substitutionЧтениеIntegration by substitutionЗадание

Symmetry and the logistic function

Odd and even functions (Part 1)ВидеоOdd and even functions (Part 2)ВидеоNotes: Odd and even functionsЧтениеOdd and even functionsЗаданиеThe logistic function (Part 1)ВидеоThe logistic function (Part 2)Видео

Conclusion

The escape velocity of a rocketВидеоNotes: The escape velocity of a rocketЧтениеFormula SheetЧтение

Assessment

Module 5 quizЗадание
Composite functionsВидео
Notes: Composite functionsЧтение
Composite functionsЗадание
Inverse functionsВидео
Notes: Inverse functionsЧтение
Inverse functionsЗадание
Exponential growth and decayВидео
Notes: Exponential growth and decayЧтение
Exponential growth and decayЗадание
Inverse circular functionsВидео
Notes: Inverse circular functionsЧтение
Inverse circular functionsЗадание
Notes: Limits and continuityЧтение
Limits and continuityЗадание
Differentials and applicationsЗадание
Connection between areas and derivativesЗадание
Notes: The logistic functionЧтение
The logistic functionЗадание