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中级

完成时间大约为39 小时

建议:11 hours/week...

英语(English)

字幕:英语(English)

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

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中级

完成时间大约为39 小时

建议:11 hours/week...

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....
10 个视频 (总计 109 分钟), 8 个阅读材料, 9 个测验
10 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
8 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
9 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
2
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....
13 个视频 (总计 142 分钟), 12 个阅读材料, 13 个测验
13 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
12 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
13 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
3
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....
12 个视频 (总计 132 分钟), 10 个阅读材料, 11 个测验
12 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
10 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
11 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
4
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....
14 个视频 (总计 155 分钟), 13 个阅读材料, 14 个测验
14 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
13 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
14 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
5
完成时间为 10 小时

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 个视频 (总计 162 分钟), 10 个阅读材料, 9 个测验
14 个视频
Inferring displacement from velocity15分钟
Areas bounded by curves17分钟
Riemann sums and definite integrals17分钟
The Fundamental Theorem of Calculus and indefinite integrals16分钟
Connection between areas and derivatives (Part 1)9分钟
Connection between areas and derivatives (Part 2)10分钟
Integration by substitution (Part 1)11分钟
Integration by substitution (Part 2)8分钟
Odd and even functions (Part 1)10分钟
Odd and even functions (Part 2)9分钟
The logistic function (Part 1)12分钟
The logistic function (Part 2)6分钟
The escape velocity of a rocket15分钟
10 个阅读材料
Notes: Inferring displacement from velocity20分钟
Notes: Areas bounded by curves20分钟
Notes: Riemann sums and definite integrals20分钟
Notes: The Fundamental Theorem of Calculus and indefinite integrals20分钟
Notes: Connection between areas and derivatives20分钟
Notes: Integration by substitution20分钟
Notes: Odd and even functions20分钟
Notes: The logistic function20分钟
Notes: The escape velocity of a rocket20分钟
Formula Sheet10分钟
9 个练习
Inferring displacement from velocity20分钟
Areas bounded by curves20分钟
Riemann sums and definite integrals20分钟
The Fundamental Theorem of Calculus and indefinite integrals20分钟
Connection between areas and derivatives20分钟
Integration by substitution20分钟
Odd and even functions20分钟
The logistic function20分钟
Module 5 quiz
4.9
20 个审阅Chevron Right

热门审阅

创建者 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.

创建者 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.

讲师

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David Easdown

Associate Professor
Department of Mathematics and Statistics

关于 悉尼大学

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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