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.
Introduction to Calculus
Universidad de SidneyAcerca de este Curso
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Resultados profesionales del estudiante
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consiguió un beneficio tangible en su carrera profesional gracias a este curso
Certificado para compartir
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Comienza de inmediato y aprende a tu propio ritmo.
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Nivel intermedio
Aprox. 59 horas para completar
Inglés (English)
Subtítulos: Francés (French), Portugués (de Brasil), Ruso (Russian), Inglés (English), Español (Spanish)
Resultados profesionales del estudiante
50%
consiguió un beneficio tangible en su carrera profesional gracias a este curso
Certificado para compartir
Obtén un certificado al finalizar
100 % en línea
Comienza de inmediato y aprende a tu propio ritmo.
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Nivel intermedio
Aprox. 59 horas para completar
Inglés (English)
Subtítulos: Francés (French), Portugués (de Brasil), Ruso (Russian), Inglés (English), Español (Spanish)
ofrecido por
Universidad de Sidney
Our excellence in research and teaching makes the University of Sydney one of the top universities in Australia and highly ranked among the best universities in the world. In 2020, we were ranked second in the Times Higher Education (THE) University Impact Rankings, and first in Australia in the QS Graduate Employability Rankings.
Programa - Qué aprenderás en este curso
9 horas para completar
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.
9 horas para completar
10 videos (Total 109 minutos), 8 lecturas, 9 cuestionarios
10 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
8 lecturas
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
9 ejercicios de práctica
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 inequalities30m
Sign diagrams, solution sets and intervals30m
Coordinate systems30m
Distance and absolute value30m
Lines and circles in the plane30m
Module 1 quiz1h
13 horas para completar
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 horas para completar
13 videos (Total 142 minutos), 12 lecturas, 13 cuestionarios
13 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
12 lecturas
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
13 ejercicios de práctica
Parabolas and quadratics30m
The quadratic formula30m
Functions as rules, with domain, range and graph30m
Polynomial and power functions30m
Composite functions30m
Inverse functions30m
The exponential function30m
The logarithmic function30m
Exponential growth and decay30m
Sine, cosine and tangent30m
The unit circle and trigonometry30m
Inverse circular functions30m
Module 2 quiz1h
12 horas para completar
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 horas para completar
12 videos (Total 132 minutos), 10 lecturas, 11 cuestionarios
12 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
10 lecturas
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
11 ejercicios de práctica
Slopes and average rates of change30m
Displacement, velocity and acceleration30m
Tangent lines and secants30m
Different kinds of limits30m
Limit laws30m
Limits and continuity30m
The derivative as a limit30m
Finding derivatives from first principles30m
Leibniz notation30m
Differentials and applications30m
Module 3 quiz1h
14 horas para completar
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 horas para completar
14 videos (Total 155 minutos), 13 lecturas, 14 cuestionarios
14 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
13 lecturas
Notes: Increasing and decreasing functions20m
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
14 ejercicios de práctica
Increasing and decreasing functions30m
Sign diagrams20m
Maxima and minima30m
Concavity and inflections30m
Curve sketching30m
The Chain Rule30m
Applications of the Chain Rule30m
The Product Rule30m
Applications of the Product Rule30m
The Quotient Rule30m
Application of the Quotient Rule30m
Optimisation30m
The Second Derivative Test30m
Module 4 quiz1h
Reseñas
Principales reseñas sobre INTRODUCTION TO CALCULUS
por SV29 de ago. de 2020
Exceptional course. Fantastic explaining by Professor Easdown, I wish more teachers were as clear as he is, and as kind and thoughtful towards their students. Many, many thanks in case you see this.
por KP15 de may. de 2020
This course was great and very well explained; it has given me a solid understanding of calculus as well as the tools needed to differentiate, find integrals, etc. I highly recommend this course.
por DL5 de jul. de 2020
Best math instructor ever! Very engaged in the topics covered, so much so that he inspires it within his students, even those of us who do not share his love for the subject. Highly recommended!
por JR20 de jul. de 2020
The course is amazing, the teacher is incredible that makes the course be cooler and easier to do it. I enjoyed a lot the experience and certainly will help me to develop my professional career.
Preguntas Frecuentes
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- es posible que el curso no ofrezca la opción de participar como oyente. En cambio, puedes intentar con una Prueba gratis o postularte para recibir ayuda económica.
- Es posible que el curso ofrezca la opción 'Curso completo, sin certificado'. Esta opción te permite ver todos los materiales del curso, enviar las evaluaciones requeridas y obtener una calificación final. También significa que no podrás comprar una experiencia de Certificado.
¿Qué recibiré si compro el Certificado?
Cuando compras un Certificado, obtienes acceso a todos los materiales del curso, incluidas las tareas calificadas. Una vez que completes el curso, se añadirá tu Certificado electrónico a la página Logros. Desde allí, puedes imprimir tu Certificado o añadirlo a tu perfil de LinkedIn. Si solo quieres leer y visualizar el contenido del curso, puedes participar del curso como oyente sin costo.
Is financial aid available?
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