 70,260

1

## 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 個視頻 （總計 109 分鐘）, 8 個閱讀材料, 9 個測驗
10 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
8 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
9 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
2

## 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 個視頻 （總計 142 分鐘）, 12 個閱讀材料, 13 個測驗
13 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
12 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
13 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
3

## 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 個視頻 （總計 132 分鐘）, 10 個閱讀材料, 11 個測驗
12 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
10 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
11 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
4

## 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 個視頻 （總計 155 分鐘）, 13 個閱讀材料, 14 個測驗
14 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
13 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
14 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
5

## 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 個視頻 （總計 162 分鐘）, 10 個閱讀材料, 9 個測驗
14 個視頻
Inferring displacement from velocity15分鐘
Areas bounded by curves17分鐘
Riemann sums and definite integrals17分鐘
The Fundamental Theorem of Calculus and indefinite integrals16分鐘
Connection between areas and derivatives (Part 1)9分鐘
Connection between areas and derivatives (Part 2)10分鐘
Integration by substitution (Part 1)11分鐘
Integration by substitution (Part 2)8分鐘
Odd and even functions (Part 1)10分鐘
Odd and even functions (Part 2)9分鐘
The logistic function (Part 1)12分鐘
The logistic function (Part 2)6分鐘
The escape velocity of a rocket15分鐘
10 個閱讀材料
Notes: Inferring displacement from velocity20分鐘
Notes: Areas bounded by curves20分鐘
Notes: Riemann sums and definite integrals20分鐘
Notes: The Fundamental Theorem of Calculus and indefinite integrals20分鐘
Notes: Connection between areas and derivatives20分鐘
Notes: Integration by substitution20分鐘
Notes: Odd and even functions20分鐘
Notes: The logistic function20分鐘
Notes: The escape velocity of a rocket20分鐘
Formula Sheet10分鐘
9 個練習
Inferring displacement from velocity20分鐘
Areas bounded by curves20分鐘
Riemann sums and definite integrals20分鐘
The Fundamental Theorem of Calculus and indefinite integrals20分鐘
Connection between areas and derivatives20分鐘
Integration by substitution20分鐘
Odd and even functions20分鐘
The logistic function20分鐘
Module 5 quiz
4.9
20 個審閱

### 熱門審閱

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.

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.

## 關於 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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