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.

## About this Course

### Learner Career Outcomes

## 13%

## Skills you will gain

### Learner Career Outcomes

## 13%

## Offered by

### The University of Sydney

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.

## Syllabus - What you will learn from this course

**9 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.

**9 hours to complete**

**13 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.

**13 hours to complete**

**12 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.

**12 hours to complete**

**14 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.

**14 hours to complete**

## Reviews

### TOP REVIEWS FROM INTRODUCTION TO CALCULUS

I have completed quite a few courses on Coursera. This is by far the best instructor. I really hope David is going to do teach another Coursera course soon - I will sign up regardless of the content!

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.

Best instructor. Made calculus very approachable connecting topics, illustrating applications, and his enthusiasm (which is contagious). Wish he'd do follow-up courses for more advanced mathematics.

This is an amazing course. I loved the way the instructor used classic examples to explain calculus by helping us approach problems from the perspectives of Newton, Leibniz, and the ancient greeks!

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