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.

# Introduction to Calculus

**242,975** already enrolled

(3,617 reviews)

## Skills you'll gain

## Details to know

Add to your LinkedIn profile

56 quizzes

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

## Earn a career certificate

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

Share it on social media and in your performance review

## 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 quizzes

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 quizzes

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 quizzes

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 quizzes

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 quizzes

### Instructor

### Offered by

### Recommended if you're interested in Math and Logic

University of Pennsylvania

The University of Sydney

Universitat Autònoma de Barcelona

Johns Hopkins University

## Why people choose Coursera for their career

## Learner reviews

Showing 3 of 3617

3,617 reviews

- 5 stars
87.05%

- 4 stars
10.32%

- 3 stars
1.21%

- 2 stars
0.57%

- 1 star
0.82%

## Open new doors with Coursera Plus

Unlimited access to 7,000+ 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

Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:

The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.

The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.

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.

You will be eligible for a full refund until two weeks after your payment date, or (for courses that have just launched) until two weeks after the first session of the course begins, whichever is later. You cannot receive a refund once you’ve earned a Course Certificate, even if you complete the course within the two-week refund period. See our full refund policy.