Calculus: Single Variable

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include:

• the introduction and use of Taylor series and approximations from the beginning;
• a novel synthesis of discrete and continuous forms of Calculus;
• an emphasis on the conceptual over the computational; and
• a clear, dynamic, unified approach.

THE COURSE CERTIFICATE OPTION

By signing up and paying a nominal fee (financial aid can be provided), you'll be eligible to earn a Course Certificate in this course, including a higher level of identity verification to your Coursera coursework. For each assignment, your identity is confirmed through your photo and unique typing pattern. If you earn a Course Certificate, you will also be given a personal URL through which your course records can be shared with employers and educational institutions.

THE COLLEGE CREDIT RECOMMENDATION OPTION

Note: The following only applies to sessions starting on September 8th, 2014, and prior. This Calculus course has been evaluated and recommended by the American Council on Education’s College Credit Recommendation Service (ACE CREDIT) for college credit so you can get a head start on your college education. More than 2,000 higher education institutions consider ACE credit recommendations for transfer to degree programs. If you add this option to sessions starting on or prior to September 8th, 2014, towards the end of the course, you will take an online proctored exam which will be combined with your coursework to determine your eligibility for college credit recommendation.

The course is divided into five "chapters":

CHAPTER 1: Functions
After a brief review of the basics, we will dive into Taylor series as a way of working with and approximating complicated functions. The chapter will use a series-based approach to understanding limits and asymptotics.

CHAPTER 2: Differentiation
Though you already know how to differentiate some functions, you may not know what differentiation means. This chapter will emphasize conceptual understanding and applications of derivatives.

CHAPTER 3: Integration
We will use the indefinite integral (an anti-derivative) as a motivation to look at differential equations in applications ranging from population models to linguistics to coupled oscillators. Techniques of integration up to and including computer-assisted methods will lead to Riemann sums and the definite integral.

CHAPTER 4: Applications
We will get busy in this chapter with applications of the definite integral to problems in geometry, physics, economics, biology, probability, and more. You will learn how to solve a wide array of problems using a consistent conceptual approach.

CHAPTER 5: Discretization
Having covered Calculus for functions with a single real input and a single real output, we turn to functions with a discrete input and a real output: sequences. We will re-develop all of Calculus (limits, derivatives, integrals, differential equations) in this new context, and return to the beginning of the course with a deeper consideration of Taylor series.