About this Course
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지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

탄력적인 마감일

일정에 따라 마감일을 재설정합니다.

중급 단계

완료하는 데 약 39시간 필요

권장: 11 hours/week...

영어

자막: 영어

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

탄력적인 마감일

일정에 따라 마감일을 재설정합니다.

중급 단계

완료하는 데 약 39시간 필요

권장: 11 hours/week...

영어

자막: 영어

강의 계획 - 이 강좌에서 배울 내용

1
완료하는 데 8시간 필요

Precalculus (Setting the scene)

This module begins by looking at the different kinds of numbers that fall on the real number line, decimal expansions and approximations, then continues with an exploration of manipulation of equations and inequalities, of sign diagrams and the use of the Cartesian plane....
10 videos (Total 109 min), 8 readings, 9 quizzes
10개의 동영상
Real line, decimals and significant figures15m
The Theorem of Pythagoras and properties of the square root of 211m
Algebraic expressions, surds and approximations10m
Equations and inequalities17m
Sign diagrams, solution sets and intervals (Part 1)10m
Sign diagrams, solution sets and intervals (Part 2)10m
Coordinate systems8m
Distance and absolute value5m
Lines and circles in the plane14m
8개의 읽기 자료
Notes: Real line, decimals and significant figures20m
Notes: The Theorem of Pythagoras and properties of the square root of 220m
Notes: Algebraic expressions, surds and approximations20m
Notes: Equations and inequalities20m
Notes: Sign diagrams, solution sets and intervals20m
Notes: Coordinate systems20m
Notes: Distance and absolute value20m
Notes: Lines and circles in the plane20m
9개 연습문제
Real line, decimals and significant figures20m
The Theorem of Pythagoras and properties of the square root of 220m
Algebraic expressions, surds and approximations20m
Equations and inequalities20m
Sign diagrams, solution sets and intervals20m
Coordinate systems20m
Distance and absolute value20m
Lines and circles in the plane20m
Module 1 quiz
2
완료하는 데 11시간 필요

Functions (Useful and important repertoire)

This module introduces the notion of a function which captures precisely ways in which different quantities or measurements are linked together. The module covers quadratic, cubic and general power and polynomial functions; exponential and logarithmic functions; and trigonometric functions related to the mathematics of periodic behaviour. We create new functions using composition and inversion and look at how to move backwards and forwards between quantities algebraically, as well as visually, with transformations in the xy-plane....
13 videos (Total 142 min), 12 readings, 13 quizzes
13개의 동영상
Parabolas and quadratics11m
The quadratic formula10m
Functions as rules, with domain, range and graph11m
Polynomial and power functions13m
Composite functions7m
Inverse functions12m
The exponential function13m
The logarithmic function8m
Exponential growth and decay13m
Sine, cosine and tangent9m
The unit circle and trigonometry16m
Inverse circular functions11m
12개의 읽기 자료
Notes: Parabolas and quadratics20m
Notes: The quadratic formula20m
Notes: Functions as rules, with domain, range and graph20m
Notes: Polynomial and power functions20m
Notes: Composite functions20m
Notes: Inverse functions20m
Notes: The exponential function20m
Notes: The logarithmic function15m
Notes: Exponential growth and decay20m
Notes: Sine, cosine and tangent20m
Notes: The unit circle and trigonometry20m
Notes: Inverse circular functions20m
13개 연습문제
Parabolas and quadratics20m
The quadratic formula20m
Functions as rules, with domain, range and graph20m
Polynomial and power functions20m
Composite functions20m
Inverse functions20m
The exponential function20m
The logarithmic function20m
Exponential growth and decay20m
Sine, cosine and tangent20m
The unit circle and trigonometry20m
Inverse circular functions20m
Module 2 quiz
3
완료하는 데 10시간 필요

Introducing the differential calculus

This module introduces techniques of differential calculus. We look at average rates of change which become instantaneous, as time intervals become vanishingly small, leading to the notion of a derivative. We then explore techniques involving differentials that exploit tangent lines. The module introduces Leibniz notation and shows how to use it to get information easily about the derivative of a function and how to apply it....
12 videos (Total 132 min), 10 readings, 11 quizzes
12개의 동영상
Slopes and average rates of change10m
Displacement, velocity and acceleration11m
Tangent lines and secants10m
Different kinds of limits12m
Limit laws15m
Limits and continuity9m
The derivative as a limit10m
Finding derivatives from first principles14m
Leibniz notation14m
Differentials and applications (Part 1)13m
Differentials and applications (Part 2)7m
10개의 읽기 자료
Notes: Slopes and average rates of change20m
Notes: Displacement, velocity and acceleration20m
Notes: Tangent lines and secants20m
Notes: Different kinds of limits20m
Notes: Limit laws20m
Notes: Limits and continuity20m
Notes: The derivative as a limit20m
Notes: Finding derivatives from first principles20m
Notes: Leibniz notation20m
Notes: Differentials and applications20m
11개 연습문제
Slopes and average rates of change20m
Displacement, velocity and acceleration20m
Tangent lines and secants20m
Different kinds of limits20m
Limit laws20m
Limits and continuity20m
The derivative as a limit20m
Finding derivatives from first principles20m
Leibniz notation20m
Differentials and applications20m
Module 3 quiz
4
완료하는 데 12시간 필요

Properties and applications of the derivative

This module continues the development of differential calculus by introducing the first and second derivatives of a function. We use sign diagrams of the first and second derivatives and from this, develop a systematic protocol for curve sketching. The module also introduces rules for finding derivatives of complicated functions built from simpler functions, using the Chain Rule, the Product Rule, and the Quotient Rule, and how to exploit information about the derivative to solve difficult optimisation problems....
14 videos (Total 155 min), 13 readings, 14 quizzes
14개의 동영상
Increasing and decreasing functions11m
Sign diagrams12m
Maxima and minima12m
Concavity and inflections10m
Curve sketching16m
The Chain Rule9m
Applications of the Chain Rule14m
The Product Rule8m
Applications of the Product Rule9m
The Quotient Rule8m
Application of the Quotient Rule10m
Optimisation12m
The Second Derivative Test16m
13개의 읽기 자료
Notes: Increasing and decreasing funtions20m
Notes: Sign diagrams20m
Notes: Maxima and minima20m
Notes: Concavity and inflections20m
Notes: Curve sketching20m
Notes: The Chain Rule20m
Notes: Applications of the Chain Rule20m
Notes: The Product Rule20m
Notes: Applications of the Product Rule20m
Notes: The Quotient Rule20m
Notes: Application of the Quotient Rule20m
Notes: Optimisation20m
Notes: The Second Derivative Test20m
14개 연습문제
Increasing and decreasing functions20m
Sign diagrams20m
Maxima and minima20m
Concavity and inflections20m
Curve sketching20m
The Chain Rule20m
Applications of the Chain Rule20m
The Product Rule20m
Applications of the Product Rule20m
The Quotient Rule20m
Application of the Quotient Rule20m
Optimisation20m
The Second Derivative Test20m
Module 4 quiz
5
완료하는 데 10시간 필요

Introducing the integral calculus

This fifth and final module introduces integral calculus, looking at the slopes of tangent lines and areas under curves. This leads to the Fundamental Theorem of Calculus. We explore the use of areas under velocity curves to estimate displacement, using averages of lower and upper rectangular approximations. We then look at limits of approximations, to discover the formula for the area of a circle and the area under a parabola. We then develop methods for capturing precisely areas under curves, using Riemann sums and the definite integral. The module then introduces indefinite integrals and the method of integration by substitution. Finally, we discuss properties of odd and even functions, related to rotational and reflectional symmetry, and the logistic function, which modifies exponential growth....
14 videos (Total 162 min), 10 readings, 9 quizzes
14개의 동영상
Inferring displacement from velocity15m
Areas bounded by curves17m
Riemann sums and definite integrals17m
The Fundamental Theorem of Calculus and indefinite integrals16m
Connection between areas and derivatives (Part 1)9m
Connection between areas and derivatives (Part 2)10m
Integration by substitution (Part 1)11m
Integration by substitution (Part 2)8m
Odd and even functions (Part 1)10m
Odd and even functions (Part 2)9m
The logistic function (Part 1)12m
The logistic function (Part 2)6m
The escape velocity of a rocket15m
10개의 읽기 자료
Notes: Inferring displacement from velocity20m
Notes: Areas bounded by curves20m
Notes: Riemann sums and definite integrals20m
Notes: The Fundamental Theorem of Calculus and indefinite integrals20m
Notes: Connection between areas and derivatives20m
Notes: Integration by substitution20m
Notes: Odd and even functions20m
Notes: The logistic function20m
Notes: The escape velocity of a rocket20m
Formula Sheet10m
9개 연습문제
Inferring displacement from velocity20m
Areas bounded by curves20m
Riemann sums and definite integrals20m
The Fundamental Theorem of Calculus and indefinite integrals20m
Connection between areas and derivatives20m
Integration by substitution20m
Odd and even functions20m
The logistic function20m
Module 5 quiz
4.9
20개의 리뷰Chevron Right

최상위 리뷰

대학: MAMar 29th 2019

its a very interesting course and i really want to learn this so thanks coursera community and specially the speaker for providing such a wonderful and handy knowledge and notes.

대학: MBApr 26th 2019

its awesome course...\n\nMentor is skilled and explains everything clearly.\n\nBut if anybody has little bit pre-calculus knowledge it will be more helpful.

강사

Avatar

David Easdown

Associate Professor
Department of Mathematics and Statistics

시드니 대학교 정보

The University of Sydney is one of the world’s leading comprehensive research and teaching universities, consistently ranked in the top 1 percent of universities in the world. In 2015, we were ranked 45 in the QS World University Rankings, and 100 percent of our research was rated at above, or well above, world standard in the Excellence in Research for Australia report....

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