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中級

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完成時間大約為10 小時

建議:7 hours/week...
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英語(English)

字幕:英語(English)
100% 在線

100% 在線

立即開始,按照自己的計劃學習。
可靈活調整截止日期

可靈活調整截止日期

根據您的日程表重置截止日期。
中級

中級

完成時間(小時)

完成時間大約為10 小時

建議:7 hours/week...
可選語言

英語(English)

字幕:英語(English)

教學大綱 - 您將從這門課程中學到什麼

1
完成時間(小時)
完成時間為 8 小時

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....
Reading
10 個視頻 (總計 109 分鐘), 8 個閱讀材料, 9 個測驗
Video10 個視頻
Real line, decimals and significant figures15分鐘
The Theorem of Pythagoras and properties of the square root of 211分鐘
Algebraic expressions, surds and approximations10分鐘
Equations and inequalities17分鐘
Sign diagrams, solution sets and intervals (Part 1)10分鐘
Sign diagrams, solution sets and intervals (Part 2)10分鐘
Coordinate systems8分鐘
Distance and absolute value5分鐘
Lines and circles in the plane14分鐘
Reading8 個閱讀材料
Notes: Real line, decimals and significant figures20分鐘
Notes: The Theorem of Pythagoras and properties of the square root of 220分鐘
Notes: Algebraic expressions, surds and approximations20分鐘
Notes: Equations and inequalities20分鐘
Notes: Sign diagrams, solution sets and intervals20分鐘
Notes: Coordinate systems20分鐘
Notes: Distance and absolute value20分鐘
Notes: Lines and circles in the plane20分鐘
Quiz9 個練習
Real line, decimals and significant figures20分鐘
The Theorem of Pythagoras and properties of the square root of 220分鐘
Algebraic expressions, surds and approximations20分鐘
Equations and inequalities20分鐘
Sign diagrams, solution sets and intervals20分鐘
Coordinate systems20分鐘
Distance and absolute value20分鐘
Lines and circles in the plane20分鐘
Module 1 quiz分鐘
2
完成時間(小時)
完成時間為 11 小時

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....
Reading
13 個視頻 (總計 142 分鐘), 12 個閱讀材料, 13 個測驗
Video13 個視頻
Parabolas and quadratics11分鐘
The quadratic formula10分鐘
Functions as rules, with domain, range and graph11分鐘
Polynomial and power functions13分鐘
Composite functions7分鐘
Inverse functions12分鐘
The exponential function13分鐘
The logarithmic function8分鐘
Exponential growth and decay13分鐘
Sine, cosine and tangent9分鐘
The unit circle and trigonometry16分鐘
Inverse circular functions11分鐘
Reading12 個閱讀材料
Notes: Parabolas and quadratics20分鐘
Notes: The quadratic formula20分鐘
Notes: Functions as rules, with domain, range and graph20分鐘
Notes: Polynomial and power functions20分鐘
Notes: Composite functions20分鐘
Notes: Inverse functions20分鐘
Notes: The exponential function20分鐘
Notes: The logarithmic function15分鐘
Notes: Exponential growth and decay20分鐘
Notes: Sine, cosine and tangent20分鐘
Notes: The unit circle and trigonometry20分鐘
Notes: Inverse circular functions20分鐘
Quiz13 個練習
Parabolas and quadratics20分鐘
The quadratic formula20分鐘
Functions as rules, with domain, range and graph20分鐘
Polynomial and power functions20分鐘
Composite functions20分鐘
Inverse functions20分鐘
The exponential function20分鐘
The logarithmic function20分鐘
Exponential growth and decay20分鐘
Sine, cosine and tangent20分鐘
The unit circle and trigonometry20分鐘
Inverse circular functions20分鐘
Module 2 quiz分鐘
3
完成時間(小時)
完成時間為 10 小時

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....
Reading
12 個視頻 (總計 132 分鐘), 10 個閱讀材料, 11 個測驗
Video12 個視頻
Slopes and average rates of change10分鐘
Displacement, velocity and acceleration11分鐘
Tangent lines and secants10分鐘
Different kinds of limits12分鐘
Limit laws15分鐘
Limits and continuity9分鐘
The derivative as a limit10分鐘
Finding derivatives from first principles14分鐘
Leibniz notation14分鐘
Differentials and applications (Part 1)13分鐘
Differentials and applications (Part 2)7分鐘
Reading10 個閱讀材料
Notes: Slopes and average rates of change20分鐘
Notes: Displacement, velocity and acceleration20分鐘
Notes: Tangent lines and secants20分鐘
Notes: Different kinds of limits20分鐘
Notes: Limit laws20分鐘
Notes: Limits and continuity20分鐘
Notes: The derivative as a limit20分鐘
Notes: Finding derivatives from first principles20分鐘
Notes: Leibniz notation20分鐘
Notes: Differentials and applications20分鐘
Quiz11 個練習
Slopes and average rates of change20分鐘
Displacement, velocity and acceleration20分鐘
Tangent lines and secants20分鐘
Different kinds of limits20分鐘
Limit laws20分鐘
Limits and continuity20分鐘
The derivative as a limit20分鐘
Finding derivatives from first principles20分鐘
Leibniz notation20分鐘
Differentials and applications20分鐘
Module 3 quiz分鐘
4
完成時間(小時)
完成時間為 12 小時

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....
Reading
14 個視頻 (總計 155 分鐘), 13 個閱讀材料, 14 個測驗
Video14 個視頻
Increasing and decreasing functions11分鐘
Sign diagrams12分鐘
Maxima and minima12分鐘
Concavity and inflections10分鐘
Curve sketching16分鐘
The Chain Rule9分鐘
Applications of the Chain Rule14分鐘
The Product Rule8分鐘
Applications of the Product Rule9分鐘
The Quotient Rule8分鐘
Application of the Quotient Rule10分鐘
Optimisation12分鐘
The Second Derivative Test16分鐘
Reading13 個閱讀材料
Notes: Increasing and decreasing funtions20分鐘
Notes: Sign diagrams20分鐘
Notes: Maxima and minima20分鐘
Notes: Concavity and inflections20分鐘
Notes: Curve sketching20分鐘
Notes: The Chain Rule20分鐘
Notes: Applications of the Chain Rule20分鐘
Notes: The Product Rule20分鐘
Notes: Applications of the Product Rule20分鐘
Notes: The Quotient Rule20分鐘
Notes: Application of the Quotient Rule20分鐘
Notes: Optimisation20分鐘
Notes: The Second Derivative Test20分鐘
Quiz14 個練習
Increasing and decreasing functions20分鐘
Sign diagrams20分鐘
Maxima and minima20分鐘
Concavity and inflections20分鐘
Curve sketching20分鐘
The Chain Rule20分鐘
Applications of the Chain Rule20分鐘
The Product Rule20分鐘
Applications of the Product Rule20分鐘
The Quotient Rule20分鐘
Application of the Quotient Rule20分鐘
Optimisation20分鐘
The Second Derivative Test20分鐘
Module 4 quiz分鐘

講師

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David Easdown

Associate Professor
Department of Mathematics and Statistics

關於 The University of Sydney

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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