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.

Offered By

## Introduction to Calculus

## About this Course

### Learner Career Outcomes

## 50%

### Learner Career Outcomes

## 50%

#### 100% online

#### Flexible deadlines

#### Intermediate Level

#### Approx. 48 hours to complete

#### English

### Offered by

#### 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.

## Syllabus - What you will learn from this course

**8 hours to complete**

## 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.

**8 hours to complete**

**10 videos**

**8 readings**

**9 practice exercises**

**11 hours to complete**

## 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.

**11 hours to complete**

**13 videos**

**12 readings**

**13 practice exercises**

**10 hours to complete**

## 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.

**10 hours to complete**

**12 videos**

**10 readings**

**11 practice exercises**

**12 hours to complete**

## 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.

**12 hours to complete**

**14 videos**

**13 readings**

**14 practice exercises**

### Top reviews from Introduction to Calculus

This professor explained all topics covered in a year long calculus class in the span of five weeks. I highly recommend taking this course either to learn calculus or for a review.

its a very interesting course and i really want to learn this so thanks coursera community and specially the speaker for providing such a wonderful and handy knowledge and notes.

## Frequently Asked Questions

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?

More questions? Visit the Learner Help Center.