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Learner Reviews & Feedback for Introduction to Advanced Calculus by The University of Sydney

4.6
stars
27 ratings

About the Course

This course "Introduction to Advanced Calculus" is a natural sequel to the course "Introduction to Calculus", also on this platform, though students who are well-prepared, with some prior calculus experience, can jump straight in. Once again, the focus and themes of this course address important foundations for applications of mathematics in science, engineering and commerce, with now a particular focus on series representations of functions and an introduction to the theory of differential equations. The course emphasises 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 Advanced Calculus will: • review key ideas of differential calculus, with further emphasis on pivotal underlying themes and results, such as the Mean Value Theorem and the Intermediate Value Theorem, and add further tools, such as L'Hopital's Rule, Newton's Method and hyperbolic functions (first week) • review key ideas of integral calculus, extending techniques of integration, including tricky substitutions, the method of integration by parts, including a proof that the number pi is irrational, the method of partial fractions, the disc and shell method for finding volumes of revolutions, formulae for arc length and surface area of revolution, application of Riemann sums to estimate work, and an introduction to improper integrals (second week) • introduce sequences and series, tests for convergence, and series representations of functions, including estimates of error terms using Taylor's theorem and a proof that Euler's number e is irrational (third week) • introduce the theory of differential equations, including discussions of separable equations, including the logistic equation and logistic function, equilibrium solutions, first order equations, solved using the integrating factor method, second order equations with constant coefficients and an introduction to solving systems of equations, modelling two interacting populations, which may be in a symbiotic or predator-prey relationship, finishing with a brief discussion of connections with linear algebra and the matrix exponential (fourth week)....

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1 - 11 of 11 Reviews for Introduction to Advanced Calculus

By Katrina S

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Jan 10, 2025

Professor Easdown has an obvious passion for mathematics and it shows. I truly enjoyed every single one of his courses. It is rare to find a professor who can make advanced mathematics so accessible and easy for the student to understand. Each lesson really builds on the next in a logical progression, and the course structure is simple and straightforward. I used these courses to help review my undergraduate mathematics before starting graduate school and found them incredibly helpful.

By Brian B

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Jan 2, 2026

Professor Easdown is without a doubt my favourite instructor on Coursera! His passion is infectious and he has an acute ability to illustrate the beauty of the fundamental connections and results underlying what appears on the surface. The course is challenging and very rewarding once completed.

By Neeraj K

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Dec 22, 2024

A great course that brings you up to speed with calculus while maintaining a balance between rigor and intuition. I've used this course to refresh my calculus knowledge and have learnt a lot of new things in the process

By Andrey M

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Feb 22, 2026

Professor's David Easdown remarkable attitude towards mathematics is very inspiring and positively contagious.

By Robinson M

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Jul 8, 2025

Fantastic course!!! Congratulations to the great professor for the magnifics lectures.

By Sribalapriyan S

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May 8, 2025

very useful course!!

By Rishika V

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May 11, 2025

very nice

By Rohan .

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May 3, 2025

great

By NAVEEN K V (

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Mar 23, 2025

Good

By Moha A

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Aug 31, 2025

Bien

By rverker

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Mar 5, 2025

This MOOC skims over the various topics without going into them in any depth. There are no links, it's completely disjointed. We go from Rolle's theorem to hyperbolic functions, from volumes of revolution to Taylor series... This MOOC is a complete failure. The quizzes are not corrected, which makes it impossible to progress.