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英語

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自分のスケジュールですぐに学習を始めてください。

柔軟性のある期限

スケジュールに従って期限をリセットします。

中級レベル

約39時間で修了

推奨:12 hours/week...

英語

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シラバス - 本コースの学習内容

1
8時間で修了

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件のビデオ (合計109分), 8 readings, 9 quizzes
10件のビデオ
Real line, decimals and significant figures15 分
The Theorem of Pythagoras and properties of the square root of 211 分
Algebraic expressions, surds and approximations10 分
Equations and inequalities17 分
Sign diagrams, solution sets and intervals (Part 1)10 分
Sign diagrams, solution sets and intervals (Part 2)10 分
Coordinate systems8 分
Distance and absolute value5 分
Lines and circles in the plane14 分
8件の学習用教材
Notes: Real line, decimals and significant figures20 分
Notes: The Theorem of Pythagoras and properties of the square root of 220 分
Notes: Algebraic expressions, surds and approximations20 分
Notes: Equations and inequalities20 分
Notes: Sign diagrams, solution sets and intervals20 分
Notes: Coordinate systems20 分
Notes: Distance and absolute value20 分
Notes: Lines and circles in the plane20 分
9の練習問題
Real line, decimals and significant figures20 分
The Theorem of Pythagoras and properties of the square root of 220 分
Algebraic expressions, surds and approximations20 分
Equations and inequalities20 分
Sign diagrams, solution sets and intervals20 分
Coordinate systems20 分
Distance and absolute value20 分
Lines and circles in the plane20 分
Module 1 quiz
2
11時間で修了

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件のビデオ (合計142分), 12 readings, 13 quizzes
13件のビデオ
Parabolas and quadratics11 分
The quadratic formula10 分
Functions as rules, with domain, range and graph11 分
Polynomial and power functions13 分
Composite functions7 分
Inverse functions12 分
The exponential function13 分
The logarithmic function8 分
Exponential growth and decay13 分
Sine, cosine and tangent9 分
The unit circle and trigonometry16 分
Inverse circular functions11 分
12件の学習用教材
Notes: Parabolas and quadratics20 分
Notes: The quadratic formula20 分
Notes: Functions as rules, with domain, range and graph20 分
Notes: Polynomial and power functions20 分
Notes: Composite functions20 分
Notes: Inverse functions20 分
Notes: The exponential function20 分
Notes: The logarithmic function15 分
Notes: Exponential growth and decay20 分
Notes: Sine, cosine and tangent20 分
Notes: The unit circle and trigonometry20 分
Notes: Inverse circular functions20 分
13の練習問題
Parabolas and quadratics20 分
The quadratic formula20 分
Functions as rules, with domain, range and graph20 分
Polynomial and power functions20 分
Composite functions20 分
Inverse functions20 分
The exponential function20 分
The logarithmic function20 分
Exponential growth and decay20 分
Sine, cosine and tangent20 分
The unit circle and trigonometry20 分
Inverse circular functions20 分
Module 2 quiz
3
10時間で修了

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件のビデオ (合計132分), 10 readings, 11 quizzes
12件のビデオ
Slopes and average rates of change10 分
Displacement, velocity and acceleration11 分
Tangent lines and secants10 分
Different kinds of limits12 分
Limit laws15 分
Limits and continuity9 分
The derivative as a limit10 分
Finding derivatives from first principles14 分
Leibniz notation14 分
Differentials and applications (Part 1)13 分
Differentials and applications (Part 2)7 分
10件の学習用教材
Notes: Slopes and average rates of change20 分
Notes: Displacement, velocity and acceleration20 分
Notes: Tangent lines and secants20 分
Notes: Different kinds of limits20 分
Notes: Limit laws20 分
Notes: Limits and continuity20 分
Notes: The derivative as a limit20 分
Notes: Finding derivatives from first principles20 分
Notes: Leibniz notation20 分
Notes: Differentials and applications20 分
11の練習問題
Slopes and average rates of change20 分
Displacement, velocity and acceleration20 分
Tangent lines and secants20 分
Different kinds of limits20 分
Limit laws20 分
Limits and continuity20 分
The derivative as a limit20 分
Finding derivatives from first principles20 分
Leibniz notation20 分
Differentials and applications20 分
Module 3 quiz
4
12時間で修了

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件のビデオ (合計155分), 13 readings, 14 quizzes
14件のビデオ
Increasing and decreasing functions11 分
Sign diagrams12 分
Maxima and minima12 分
Concavity and inflections10 分
Curve sketching16 分
The Chain Rule9 分
Applications of the Chain Rule14 分
The Product Rule8 分
Applications of the Product Rule9 分
The Quotient Rule8 分
Application of the Quotient Rule10 分
Optimisation12 分
The Second Derivative Test16 分
13件の学習用教材
Notes: Increasing and decreasing funtions20 分
Notes: Sign diagrams20 分
Notes: Maxima and minima20 分
Notes: Concavity and inflections20 分
Notes: Curve sketching20 分
Notes: The Chain Rule20 分
Notes: Applications of the Chain Rule20 分
Notes: The Product Rule20 分
Notes: Applications of the Product Rule20 分
Notes: The Quotient Rule20 分
Notes: Application of the Quotient Rule20 分
Notes: Optimisation20 分
Notes: The Second Derivative Test20 分
14の練習問題
Increasing and decreasing functions20 分
Sign diagrams20 分
Maxima and minima20 分
Concavity and inflections20 分
Curve sketching20 分
The Chain Rule20 分
Applications of the Chain Rule20 分
The Product Rule20 分
Applications of the Product Rule20 分
The Quotient Rule20 分
Application of the Quotient Rule20 分
Optimisation20 分
The Second Derivative Test20 分
Module 4 quiz
5
10時間で修了

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件のビデオ (合計162分), 10 readings, 9 quizzes
14件のビデオ
Inferring displacement from velocity15 分
Areas bounded by curves17 分
Riemann sums and definite integrals17 分
The Fundamental Theorem of Calculus and indefinite integrals16 分
Connection between areas and derivatives (Part 1)9 分
Connection between areas and derivatives (Part 2)10 分
Integration by substitution (Part 1)11 分
Integration by substitution (Part 2)8 分
Odd and even functions (Part 1)10 分
Odd and even functions (Part 2)9 分
The logistic function (Part 1)12 分
The logistic function (Part 2)6 分
The escape velocity of a rocket15 分
10件の学習用教材
Notes: Inferring displacement from velocity20 分
Notes: Areas bounded by curves20 分
Notes: Riemann sums and definite integrals20 分
Notes: The Fundamental Theorem of Calculus and indefinite integrals20 分
Notes: Connection between areas and derivatives20 分
Notes: Integration by substitution20 分
Notes: Odd and even functions20 分
Notes: The logistic function20 分
Notes: The escape velocity of a rocket20 分
Formula Sheet10 分
9の練習問題
Inferring displacement from velocity20 分
Areas bounded by curves20 分
Riemann sums and definite integrals20 分
The Fundamental Theorem of Calculus and indefinite integrals20 分
Connection between areas and derivatives20 分
Integration by substitution20 分
Odd and even functions20 分
The logistic function20 分
Module 5 quiz
4.9
20件のレビューChevron Right

人気のレビュー

by 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.

by 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.

講師

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David Easdown

Associate Professor
Department of Mathematics and Statistics

シドニー大学(The University of Sydney)について

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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