课程信息
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中级

中级

完成时间(小时)

完成时间大约为10 小时

建议:7 hours/week...
可选语言

英语(English)

字幕:英语(English)
100% 在线

100% 在线

立即开始,按照自己的计划学习。
可灵活调整截止日期

可灵活调整截止日期

根据您的日程表重置截止日期。
中级

中级

完成时间(小时)

完成时间大约为10 小时

建议:7 hours/week...
可选语言

英语(English)

字幕:英语(English)

教学大纲 - 您将从这门课程中学到什么

1
完成时间(小时)
完成时间为 8 小时

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 个视频 (总计 109 分钟), 8 个阅读材料, 9 个测验
Video10 个视频
Real line, decimals and significant figures15分钟
The Theorem of Pythagoras and properties of the square root of 211分钟
Algebraic expressions, surds and approximations10分钟
Equations and inequalities17分钟
Sign diagrams, solution sets and intervals (Part 1)10分钟
Sign diagrams, solution sets and intervals (Part 2)10分钟
Coordinate systems8分钟
Distance and absolute value5分钟
Lines and circles in the plane14分钟
Reading8 个阅读材料
Notes: Real line, decimals and significant figures20分钟
Notes: The Theorem of Pythagoras and properties of the square root of 220分钟
Notes: Algebraic expressions, surds and approximations20分钟
Notes: Equations and inequalities20分钟
Notes: Sign diagrams, solution sets and intervals20分钟
Notes: Coordinate systems20分钟
Notes: Distance and absolute value20分钟
Notes: Lines and circles in the plane20分钟
Quiz9 个练习
Real line, decimals and significant figures20分钟
The Theorem of Pythagoras and properties of the square root of 220分钟
Algebraic expressions, surds and approximations20分钟
Equations and inequalities20分钟
Sign diagrams, solution sets and intervals20分钟
Coordinate systems20分钟
Distance and absolute value20分钟
Lines and circles in the plane20分钟
Module 1 quiz分钟
2
完成时间(小时)
完成时间为 11 小时

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 个视频 (总计 142 分钟), 12 个阅读材料, 13 个测验
Video13 个视频
Parabolas and quadratics11分钟
The quadratic formula10分钟
Functions as rules, with domain, range and graph11分钟
Polynomial and power functions13分钟
Composite functions7分钟
Inverse functions12分钟
The exponential function13分钟
The logarithmic function8分钟
Exponential growth and decay13分钟
Sine, cosine and tangent9分钟
The unit circle and trigonometry16分钟
Inverse circular functions11分钟
Reading12 个阅读材料
Notes: Parabolas and quadratics20分钟
Notes: The quadratic formula20分钟
Notes: Functions as rules, with domain, range and graph20分钟
Notes: Polynomial and power functions20分钟
Notes: Composite functions20分钟
Notes: Inverse functions20分钟
Notes: The exponential function20分钟
Notes: The logarithmic function15分钟
Notes: Exponential growth and decay20分钟
Notes: Sine, cosine and tangent20分钟
Notes: The unit circle and trigonometry20分钟
Notes: Inverse circular functions20分钟
Quiz13 个练习
Parabolas and quadratics20分钟
The quadratic formula20分钟
Functions as rules, with domain, range and graph20分钟
Polynomial and power functions20分钟
Composite functions20分钟
Inverse functions20分钟
The exponential function20分钟
The logarithmic function20分钟
Exponential growth and decay20分钟
Sine, cosine and tangent20分钟
The unit circle and trigonometry20分钟
Inverse circular functions20分钟
Module 2 quiz分钟
3
完成时间(小时)
完成时间为 10 小时

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 个视频 (总计 132 分钟), 10 个阅读材料, 11 个测验
Video12 个视频
Slopes and average rates of change10分钟
Displacement, velocity and acceleration11分钟
Tangent lines and secants10分钟
Different kinds of limits12分钟
Limit laws15分钟
Limits and continuity9分钟
The derivative as a limit10分钟
Finding derivatives from first principles14分钟
Leibniz notation14分钟
Differentials and applications (Part 1)13分钟
Differentials and applications (Part 2)7分钟
Reading10 个阅读材料
Notes: Slopes and average rates of change20分钟
Notes: Displacement, velocity and acceleration20分钟
Notes: Tangent lines and secants20分钟
Notes: Different kinds of limits20分钟
Notes: Limit laws20分钟
Notes: Limits and continuity20分钟
Notes: The derivative as a limit20分钟
Notes: Finding derivatives from first principles20分钟
Notes: Leibniz notation20分钟
Notes: Differentials and applications20分钟
Quiz11 个练习
Slopes and average rates of change20分钟
Displacement, velocity and acceleration20分钟
Tangent lines and secants20分钟
Different kinds of limits20分钟
Limit laws20分钟
Limits and continuity20分钟
The derivative as a limit20分钟
Finding derivatives from first principles20分钟
Leibniz notation20分钟
Differentials and applications20分钟
Module 3 quiz分钟
4
完成时间(小时)
完成时间为 12 小时

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 个视频 (总计 155 分钟), 13 个阅读材料, 14 个测验
Video14 个视频
Increasing and decreasing functions11分钟
Sign diagrams12分钟
Maxima and minima12分钟
Concavity and inflections10分钟
Curve sketching16分钟
The Chain Rule9分钟
Applications of the Chain Rule14分钟
The Product Rule8分钟
Applications of the Product Rule9分钟
The Quotient Rule8分钟
Application of the Quotient Rule10分钟
Optimisation12分钟
The Second Derivative Test16分钟
Reading13 个阅读材料
Notes: Increasing and decreasing funtions20分钟
Notes: Sign diagrams20分钟
Notes: Maxima and minima20分钟
Notes: Concavity and inflections20分钟
Notes: Curve sketching20分钟
Notes: The Chain Rule20分钟
Notes: Applications of the Chain Rule20分钟
Notes: The Product Rule20分钟
Notes: Applications of the Product Rule20分钟
Notes: The Quotient Rule20分钟
Notes: Application of the Quotient Rule20分钟
Notes: Optimisation20分钟
Notes: The Second Derivative Test20分钟
Quiz14 个练习
Increasing and decreasing functions20分钟
Sign diagrams20分钟
Maxima and minima20分钟
Concavity and inflections20分钟
Curve sketching20分钟
The Chain Rule20分钟
Applications of the Chain Rule20分钟
The Product Rule20分钟
Applications of the Product Rule20分钟
The Quotient Rule20分钟
Application of the Quotient Rule20分钟
Optimisation20分钟
The Second Derivative Test20分钟
Module 4 quiz分钟

讲师

Avatar

David Easdown

Associate Professor
Department of Mathematics and Statistics

关于 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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