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Английский

Субтитры: Английский
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Промежуточный уровень

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Прибл. 10 часа на выполнение

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Доступные языки

Английский

Субтитры: Английский

Программа курса: что вы изучите

Неделя
1
Часов на завершение
8 ч. на завершение

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 видео ((всего 109 мин.)), 8 материалов для самостоятельного изучения, 9 тестов
Video10 видео
Real line, decimals and significant figures15мин
The Theorem of Pythagoras and properties of the square root of 211мин
Algebraic expressions, surds and approximations10мин
Equations and inequalities17мин
Sign diagrams, solution sets and intervals (Part 1)10мин
Sign diagrams, solution sets and intervals (Part 2)10мин
Coordinate systems8мин
Distance and absolute value5мин
Lines and circles in the plane14мин
Reading8 материала для самостоятельного изучения
Notes: Real line, decimals and significant figures20мин
Notes: The Theorem of Pythagoras and properties of the square root of 220мин
Notes: Algebraic expressions, surds and approximations20мин
Notes: Equations and inequalities20мин
Notes: Sign diagrams, solution sets and intervals20мин
Notes: Coordinate systems20мин
Notes: Distance and absolute value20мин
Notes: Lines and circles in the plane20мин
Quiz9 практического упражнения
Real line, decimals and significant figures20мин
The Theorem of Pythagoras and properties of the square root of 220мин
Algebraic expressions, surds and approximations20мин
Equations and inequalities20мин
Sign diagrams, solution sets and intervals20мин
Coordinate systems20мин
Distance and absolute value20мин
Lines and circles in the plane20мин
Module 1 quizмин
Неделя
2
Часов на завершение
11 ч. на завершение

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 видео ((всего 142 мин.)), 12 материалов для самостоятельного изучения, 13 тестов
Video13 видео
Parabolas and quadratics11мин
The quadratic formula10мин
Functions as rules, with domain, range and graph11мин
Polynomial and power functions13мин
Composite functions7мин
Inverse functions12мин
The exponential function13мин
The logarithmic function8мин
Exponential growth and decay13мин
Sine, cosine and tangent9мин
The unit circle and trigonometry16мин
Inverse circular functions11мин
Reading12 материала для самостоятельного изучения
Notes: Parabolas and quadratics20мин
Notes: The quadratic formula20мин
Notes: Functions as rules, with domain, range and graph20мин
Notes: Polynomial and power functions20мин
Notes: Composite functions20мин
Notes: Inverse functions20мин
Notes: The exponential function20мин
Notes: The logarithmic function15мин
Notes: Exponential growth and decay20мин
Notes: Sine, cosine and tangent20мин
Notes: The unit circle and trigonometry20мин
Notes: Inverse circular functions20мин
Quiz13 практического упражнения
Parabolas and quadratics20мин
The quadratic formula20мин
Functions as rules, with domain, range and graph20мин
Polynomial and power functions20мин
Composite functions20мин
Inverse functions20мин
The exponential function20мин
The logarithmic function20мин
Exponential growth and decay20мин
Sine, cosine and tangent20мин
The unit circle and trigonometry20мин
Inverse circular functions20мин
Module 2 quizмин
Неделя
3
Часов на завершение
10 ч. на завершение

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 видео ((всего 132 мин.)), 10 материалов для самостоятельного изучения, 11 тестов
Video12 видео
Slopes and average rates of change10мин
Displacement, velocity and acceleration11мин
Tangent lines and secants10мин
Different kinds of limits12мин
Limit laws15мин
Limits and continuity9мин
The derivative as a limit10мин
Finding derivatives from first principles14мин
Leibniz notation14мин
Differentials and applications (Part 1)13мин
Differentials and applications (Part 2)7мин
Reading10 материала для самостоятельного изучения
Notes: Slopes and average rates of change20мин
Notes: Displacement, velocity and acceleration20мин
Notes: Tangent lines and secants20мин
Notes: Different kinds of limits20мин
Notes: Limit laws20мин
Notes: Limits and continuity20мин
Notes: The derivative as a limit20мин
Notes: Finding derivatives from first principles20мин
Notes: Leibniz notation20мин
Notes: Differentials and applications20мин
Quiz11 практического упражнения
Slopes and average rates of change20мин
Displacement, velocity and acceleration20мин
Tangent lines and secants20мин
Different kinds of limits20мин
Limit laws20мин
Limits and continuity20мин
The derivative as a limit20мин
Finding derivatives from first principles20мин
Leibniz notation20мин
Differentials and applications20мин
Module 3 quizмин
Неделя
4
Часов на завершение
12 ч. на завершение

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 видео ((всего 155 мин.)), 13 материалов для самостоятельного изучения, 14 тестов
Video14 видео
Increasing and decreasing functions11мин
Sign diagrams12мин
Maxima and minima12мин
Concavity and inflections10мин
Curve sketching16мин
The Chain Rule9мин
Applications of the Chain Rule14мин
The Product Rule8мин
Applications of the Product Rule9мин
The Quotient Rule8мин
Application of the Quotient Rule10мин
Optimisation12мин
The Second Derivative Test16мин
Reading13 материала для самостоятельного изучения
Notes: Increasing and decreasing funtions20мин
Notes: Sign diagrams20мин
Notes: Maxima and minima20мин
Notes: Concavity and inflections20мин
Notes: Curve sketching20мин
Notes: The Chain Rule20мин
Notes: Applications of the Chain Rule20мин
Notes: The Product Rule20мин
Notes: Applications of the Product Rule20мин
Notes: The Quotient Rule20мин
Notes: Application of the Quotient Rule20мин
Notes: Optimisation20мин
Notes: The Second Derivative Test20мин
Quiz14 практического упражнения
Increasing and decreasing functions20мин
Sign diagrams20мин
Maxima and minima20мин
Concavity and inflections20мин
Curve sketching20мин
The Chain Rule20мин
Applications of the Chain Rule20мин
The Product Rule20мин
Applications of the Product Rule20мин
The Quotient Rule20мин
Application of the Quotient Rule20мин
Optimisation20мин
The Second Derivative Test20мин
Module 4 quizмин

Преподаватель

Avatar

David Easdown

Associate Professor
Department of Mathematics and Statistics

О 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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