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

The University of Sydney## About this Course

### Learner Career Outcomes

## 11%

## 22%

## Skills you will gain

- logic
- Mathematics
- Calculus

### Learner Career Outcomes

## 11%

## 22%

## 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

- 5 stars86.88%
- 4 stars10.77%
- 3 stars1.17%
- 2 stars0.51%
- 1 star0.65%

### TOP REVIEWS FROM INTRODUCTION TO CALCULUS

This is an excellent course that will provide you with the basic reasoning and algorithms, required for Calculus. The course was not too challenging, but was not easy. I highly recommend it!

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.

An amazing course with detailed explanation of fundamental techniques in Calculus. I would highly recommend other students trying this course before taking any advanced studies in Calculus.

Professor Easdown is an excellent instructor. He has an obvious passion for the subject and teaches with great enthusiasm. His explanations are clear and examples are helpful. Thank you!

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