About this Course
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Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Intermediate Level

Intermediate Level

Hours to complete

Approx. 10 hours to complete

Suggested: 7 hours/week...
Available languages

English

Subtitles: English
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Intermediate Level

Intermediate Level

Hours to complete

Approx. 10 hours to complete

Suggested: 7 hours/week...
Available languages

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
Hours to complete
8 hours to complete

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 videos (Total 109 min), 8 readings, 9 quizzes
Video10 videos
Real line, decimals and significant figures15m
The Theorem of Pythagoras and properties of the square root of 211m
Algebraic expressions, surds and approximations10m
Equations and inequalities17m
Sign diagrams, solution sets and intervals (Part 1)10m
Sign diagrams, solution sets and intervals (Part 2)10m
Coordinate systems8m
Distance and absolute value5m
Lines and circles in the plane14m
Reading8 readings
Notes: Real line, decimals and significant figures20m
Notes: The Theorem of Pythagoras and properties of the square root of 220m
Notes: Algebraic expressions, surds and approximations20m
Notes: Equations and inequalities20m
Notes: Sign diagrams, solution sets and intervals20m
Notes: Coordinate systems20m
Notes: Distance and absolute value20m
Notes: Lines and circles in the plane20m
Quiz9 practice exercises
Real line, decimals and significant figures20m
The Theorem of Pythagoras and properties of the square root of 220m
Algebraic expressions, surds and approximations20m
Equations and inequalities20m
Sign diagrams, solution sets and intervals20m
Coordinate systems20m
Distance and absolute value20m
Lines and circles in the plane20m
Module 1 quizm
Week
2
Hours to complete
11 hours to complete

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 videos (Total 142 min), 12 readings, 13 quizzes
Video13 videos
Parabolas and quadratics11m
The quadratic formula10m
Functions as rules, with domain, range and graph11m
Polynomial and power functions13m
Composite functions7m
Inverse functions12m
The exponential function13m
The logarithmic function8m
Exponential growth and decay13m
Sine, cosine and tangent9m
The unit circle and trigonometry16m
Inverse circular functions11m
Reading12 readings
Notes: Parabolas and quadratics20m
Notes: The quadratic formula20m
Notes: Functions as rules, with domain, range and graph20m
Notes: Polynomial and power functions20m
Notes: Composite functions20m
Notes: Inverse functions20m
Notes: The exponential function20m
Notes: The logarithmic function15m
Notes: Exponential growth and decay20m
Notes: Sine, cosine and tangent20m
Notes: The unit circle and trigonometry20m
Notes: Inverse circular functions20m
Quiz13 practice exercises
Parabolas and quadratics20m
The quadratic formula20m
Functions as rules, with domain, range and graph20m
Polynomial and power functions20m
Composite functions20m
Inverse functions20m
The exponential function20m
The logarithmic function20m
Exponential growth and decay20m
Sine, cosine and tangent20m
The unit circle and trigonometry20m
Inverse circular functions20m
Module 2 quizm
Week
3
Hours to complete
10 hours to complete

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 videos (Total 132 min), 10 readings, 11 quizzes
Video12 videos
Slopes and average rates of change10m
Displacement, velocity and acceleration11m
Tangent lines and secants10m
Different kinds of limits12m
Limit laws15m
Limits and continuity9m
The derivative as a limit10m
Finding derivatives from first principles14m
Leibniz notation14m
Differentials and applications (Part 1)13m
Differentials and applications (Part 2)7m
Reading10 readings
Notes: Slopes and average rates of change20m
Notes: Displacement, velocity and acceleration20m
Notes: Tangent lines and secants20m
Notes: Different kinds of limits20m
Notes: Limit laws20m
Notes: Limits and continuity20m
Notes: The derivative as a limit20m
Notes: Finding derivatives from first principles20m
Notes: Leibniz notation20m
Notes: Differentials and applications20m
Quiz11 practice exercises
Slopes and average rates of change20m
Displacement, velocity and acceleration20m
Tangent lines and secants20m
Different kinds of limits20m
Limit laws20m
Limits and continuity20m
The derivative as a limit20m
Finding derivatives from first principles20m
Leibniz notation20m
Differentials and applications20m
Module 3 quizm
Week
4
Hours to complete
12 hours to complete

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 videos (Total 155 min), 13 readings, 14 quizzes
Video14 videos
Increasing and decreasing functions11m
Sign diagrams12m
Maxima and minima12m
Concavity and inflections10m
Curve sketching16m
The Chain Rule9m
Applications of the Chain Rule14m
The Product Rule8m
Applications of the Product Rule9m
The Quotient Rule8m
Application of the Quotient Rule10m
Optimisation12m
The Second Derivative Test16m
Reading13 readings
Notes: Increasing and decreasing funtions20m
Notes: Sign diagrams20m
Notes: Maxima and minima20m
Notes: Concavity and inflections20m
Notes: Curve sketching20m
Notes: The Chain Rule20m
Notes: Applications of the Chain Rule20m
Notes: The Product Rule20m
Notes: Applications of the Product Rule20m
Notes: The Quotient Rule20m
Notes: Application of the Quotient Rule20m
Notes: Optimisation20m
Notes: The Second Derivative Test20m
Quiz14 practice exercises
Increasing and decreasing functions20m
Sign diagrams20m
Maxima and minima20m
Concavity and inflections20m
Curve sketching20m
The Chain Rule20m
Applications of the Chain Rule20m
The Product Rule20m
Applications of the Product Rule20m
The Quotient Rule20m
Application of the Quotient Rule20m
Optimisation20m
The Second Derivative Test20m
Module 4 quizm

Instructor

Avatar

David Easdown

Associate Professor
Department of Mathematics and Statistics

About 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....

Frequently Asked Questions

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  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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