oferecido por

The University of Sydney

Informações sobre o curso

The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce. The course emphasises the key ideas and historical motivation for calculus, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics.
Students taking Introduction to Calculus will:
• gain familiarity with key ideas of precalculus, including the manipulation of equations and elementary functions (first two weeks),
• develop fluency with the preliminary methodology of tangents and limits, and the definition of a derivative (third week),
• develop and practice methods of differential calculus with applications (fourth week),
• develop and practice methods of the integral calculus (fifth week).

Comece imediatamente e aprenda em seu próprio cronograma.

Redefinir os prazos de acordo com sua programação.

Sugerido: 7 hours/week...

Legendas: Inglês

Comece imediatamente e aprenda em seu próprio cronograma.

Redefinir os prazos de acordo com sua programação.

Sugerido: 7 hours/week...

Legendas: Inglês

Semana

1This 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 videos (Total 109 min), 8 leituras, 9 testes

Real line, decimals and significant figures15min

The Theorem of Pythagoras and properties of the square root of 211min

Algebraic expressions, surds and approximations10min

Equations and inequalities17min

Sign diagrams, solution sets and intervals (Part 1)10min

Sign diagrams, solution sets and intervals (Part 2)10min

Coordinate systems8min

Distance and absolute value5min

Lines and circles in the plane14min

Notes: Real line, decimals and significant figures20min

Notes: The Theorem of Pythagoras and properties of the square root of 220min

Notes: Algebraic expressions, surds and approximations20min

Notes: Equations and inequalities20min

Notes: Sign diagrams, solution sets and intervals20min

Notes: Coordinate systems20min

Notes: Distance and absolute value20min

Notes: Lines and circles in the plane20min

Real line, decimals and significant figures20min

The Theorem of Pythagoras and properties of the square root of 220min

Algebraic expressions, surds and approximations20min

Equations and inequalities20min

Sign diagrams, solution sets and intervals20min

Coordinate systems20min

Distance and absolute value20min

Lines and circles in the plane20min

Module 1 quizmin

Semana

2This 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 videos (Total 142 min), 12 leituras, 13 testes

Parabolas and quadratics11min

The quadratic formula10min

Functions as rules, with domain, range and graph11min

Polynomial and power functions13min

Composite functions7min

Inverse functions12min

The exponential function13min

The logarithmic function8min

Exponential growth and decay13min

Sine, cosine and tangent9min

The unit circle and trigonometry16min

Inverse circular functions11min

Notes: Parabolas and quadratics20min

Notes: The quadratic formula20min

Notes: Functions as rules, with domain, range and graph20min

Notes: Polynomial and power functions20min

Notes: Composite functions20min

Notes: Inverse functions20min

Notes: The exponential function20min

Notes: The logarithmic function15min

Notes: Exponential growth and decay20min

Notes: Sine, cosine and tangent20min

Notes: The unit circle and trigonometry20min

Notes: Inverse circular functions20min

Parabolas and quadratics20min

The quadratic formula20min

Functions as rules, with domain, range and graph20min

Polynomial and power functions20min

Composite functions20min

Inverse functions20min

The exponential function20min

The logarithmic function20min

Exponential growth and decay20min

Sine, cosine and tangent20min

The unit circle and trigonometry20min

Inverse circular functions20min

Module 2 quizmin

Semana

3This 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 videos (Total 132 min), 10 leituras, 11 testes

Slopes and average rates of change10min

Displacement, velocity and acceleration11min

Tangent lines and secants10min

Different kinds of limits12min

Limit laws15min

Limits and continuity9min

The derivative as a limit10min

Finding derivatives from first principles14min

Leibniz notation14min

Differentials and applications (Part 1)13min

Differentials and applications (Part 2)7min

Notes: Slopes and average rates of change20min

Notes: Displacement, velocity and acceleration20min

Notes: Tangent lines and secants20min

Notes: Different kinds of limits20min

Notes: Limit laws20min

Notes: Limits and continuity20min

Notes: The derivative as a limit20min

Notes: Finding derivatives from first principles20min

Notes: Leibniz notation20min

Notes: Differentials and applications20min

Slopes and average rates of change20min

Displacement, velocity and acceleration20min

Tangent lines and secants20min

Different kinds of limits20min

Limit laws20min

Limits and continuity20min

The derivative as a limit20min

Finding derivatives from first principles20min

Leibniz notation20min

Differentials and applications20min

Module 3 quizmin

Semana

4This 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 videos (Total 155 min), 13 leituras, 14 testes

Increasing and decreasing functions11min

Sign diagrams12min

Maxima and minima12min

Concavity and inflections10min

Curve sketching16min

The Chain Rule9min

Applications of the Chain Rule14min

The Product Rule8min

Applications of the Product Rule9min

The Quotient Rule8min

Application of the Quotient Rule10min

Optimisation12min

The Second Derivative Test16min

Notes: Increasing and decreasing funtions20min

Notes: Sign diagrams20min

Notes: Maxima and minima20min

Notes: Concavity and inflections20min

Notes: Curve sketching20min

Notes: The Chain Rule20min

Notes: Applications of the Chain Rule20min

Notes: The Product Rule20min

Notes: Applications of the Product Rule20min

Notes: The Quotient Rule20min

Notes: Application of the Quotient Rule20min

Notes: Optimisation20min

Notes: The Second Derivative Test20min

Increasing and decreasing functions20min

Sign diagrams20min

Maxima and minima20min

Concavity and inflections20min

Curve sketching20min

The Chain Rule20min

Applications of the Chain Rule20min

The Product Rule20min

Applications of the Product Rule20min

The Quotient Rule20min

Application of the Quotient Rule20min

Optimisation20min

The Second Derivative Test20min

Module 4 quizmin

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....

When will I have access to the lectures and assignments?

Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

What will I get if I purchase the Certificate?

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.

What is the refund policy?

Is financial aid available?

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