The University of Sydney

Introduction to Calculus

David Easdown

Instructor: David Easdown

Top Instructor

252,206 already enrolled

Included with Coursera Plus

Gain insight into a topic and learn the fundamentals.
4.8

(3,718 reviews)

Intermediate level
Some related experience required
Flexible schedule
Approx. 58 hours
Learn at your own pace
97%
Most learners liked this course
Gain insight into a topic and learn the fundamentals.
4.8

(3,718 reviews)

Intermediate level
Some related experience required
Flexible schedule
Approx. 58 hours
Learn at your own pace
97%
Most learners liked this course

Skills you'll gain

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

56 assignments

Taught in English

See how employees at top companies are mastering in-demand skills

Placeholder
Placeholder

Earn a career certificate

Add this credential to your LinkedIn profile, resume, or CV

Share it on social media and in your performance review

Placeholder

There are 5 modules in this course

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.

What's included

10 videos8 readings9 assignments

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.

What's included

13 videos12 readings13 assignments

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.

What's included

12 videos10 readings11 assignments

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.

What's included

14 videos13 readings14 assignments

This fifth and final module introduces integral calculus, looking at the slopes of tangent lines and areas under curves. This leads to the Fundamental Theorem of Calculus. We explore the use of areas under velocity curves to estimate displacement, using averages of lower and upper rectangular approximations. We then look at limits of approximations, to discover the formula for the area of a circle and the area under a parabola. We then develop methods for capturing precisely areas under curves, using Riemann sums and the definite integral. The module then introduces indefinite integrals and the method of integration by substitution. Finally, we discuss properties of odd and even functions, related to rotational and reflectional symmetry, and the logistic function, which modifies exponential growth.

What's included

14 videos10 readings9 assignments

Instructor

Instructor ratings
4.9 (1,399 ratings)
David Easdown

Top Instructor

The University of Sydney
3 Courses255,393 learners

Offered by

Recommended if you're interested in Math and Logic

Why people choose Coursera for their career

Felipe M.
Learner since 2018
"To be able to take courses at my own pace and rhythm has been an amazing experience. I can learn whenever it fits my schedule and mood."
Jennifer J.
Learner since 2020
"I directly applied the concepts and skills I learned from my courses to an exciting new project at work."
Larry W.
Learner since 2021
"When I need courses on topics that my university doesn't offer, Coursera is one of the best places to go."
Chaitanya A.
"Learning isn't just about being better at your job: it's so much more than that. Coursera allows me to learn without limits."

Learner reviews

4.8

3,718 reviews

  • 5 stars

    87.16%

  • 4 stars

    10.23%

  • 3 stars

    1.18%

  • 2 stars

    0.59%

  • 1 star

    0.83%

Showing 3 of 3718

SV
5

Reviewed on Aug 29, 2020

AF
5

Reviewed on Apr 8, 2022

AR
5

Reviewed on Apr 2, 2020

Placeholder

Open new doors with Coursera Plus

Unlimited access to 10,000+ world-class courses, hands-on projects, and job-ready certificate programs - all included in your subscription

Advance your career with an online degree

Earn a degree from world-class universities - 100% online

Join over 3,400 global companies that choose Coursera for Business

Upskill your employees to excel in the digital economy

Frequently asked questions