Introduction to Calculus
Time: 19:00 - 21:00
This course is FREE if a) you live in London and your job is at risk of redundancy or b) you are either on Jobseekers' Allowance (JSA) or Employment & Support Allowance(ESA) or c) you receive other state benefits (including Universal Credit). For more information click here
This course will be delivered online. See the ‘What is the course about?’ section in course details for more information.
Course Code: CLAM08
Duration: 11 sessions (over 13 weeks)
What is the course about?
The calculus is an almost miraculous branch of mathematics whose invention about 350 years ago is one of the great achievements of the modern world. It allows us to describe continuous phenomena in a way that’s precise enough to allow us to solve problems about them. A grasp of the basic ideas and techniques of the calculus is essential if you want to make progress in almost any technical field.
The word “continuous” here means, “changing smoothly, not in jumps”. Examples of continuous phenomena are the motions of projectiles and the distribution of heat in a wire stretched over a candle flame. But many other phenomena can be treated as if they were continuous even though they’re not really: the political preferences of a population, the spread of a disease, the interplay of predators and prey in an ecosystem, the prices in a financial market.
The subject comes in two parts. The differential calculus studies rates of change: it arises from the fact that velocity is the rate of change of position, and acceleration is the rate of change of velocity, making this idea central to classical physics. Studying this requires the strange notion of “instantaneous change”, which is not easy to make precise; we do this is by means of “limits”, which allow us to make sense of the idea of a process that “goes to infinity” or “shrinks to an infinitesimal size”.
The other side of the coin is the integral calculus, which studies the cumulative effect of a continuous phenomenon over time (or some other dimension). Geometrically, integration can quickly solve otherwise-difficult problems about the areas and volumes of complex shapes. The two parts are unified in the surprising and powerful Fundamental Theorem of Calculus, which is really, what makes them so indispensable.
This is a live online course. You will need:
- Internet connection. The classes work best with Chrome.
- A computer with microphone and camera.
We will contact you with joining instructions before your course starts.
What will we cover?
This course puts the emphasis on understanding (through clear ideas) and intuition (through visual pictures). We let computers do the heavy calculations, although we don’t shy away from solving problems by hand if it helps us to sharpen and test our understanding.
• Limits of sequences and series
• The real numbers
• Differentiation and integration of polynomials and selected transcendental functions
• General techniques for differentiation and integration
• Higher-order derivatives with applications to optimization
• Taylor series
• Elementary examples of first- and second-order ordinary differential equations.
What will I achieve?
By the end of this course you should be able to...
• Calculate limits of sequences and infinite sums.
• Describe the real numbers in contrast with the rational numbers.
• Differentiate and integrate a wide variety of functions
• Solve some common optimization problems
• Approximate a transcendental function using Taylor series
• Solve some common forms of ordinary differential equation.
What level is the course and do I need any particular skills?
This course is designed to follow on from the City Lit course Precalculus. You don’t have to do that course first, but you should be confident with:
• The idea of a function
• Linear and polynomial functions
• Local and global minima and maxima
• The basic trigonometric functions (sin, cos, tan).
• Exponential functions, logarithms and the special number e.
Functions on this course will always be single-valued functions of a single variable.
How will I be taught, and will there be any work outside the class?
You will be given weekly readings (5-10 pages) to study in advance and you should allow some time (usually a couple of hours) for this. The session are student-led discussions of the material that you can use to clarify your understanding, work through explicit calculations, visualize geometric ideas and so on.
Are there any other costs? Is there anything I need to bring?
No other costs.
When I've finished, what course can I do next?
Precalculus: introduction to algebra, geometry and trigonometry.
Rich is a programmer, writer and educator with a particular interest in creative practice. In his previous career he worked as a software developer in the CIty, first at a dot-com startup and later at a top-tier investment bank where he worked mostly on trading floor systems and got to play with a wide range of languages and technologies. He now teaches coding and maths-related courses full time. Besides his work at City Lit he also teaches at Central Saint Martins, the Architecture Association and the Photographer's Gallery and is the author of two books about mathematics. His technical collaborations with artists have been shown at, among others, the Hayward gallery, the V&A, the ICA and Camden Arts Centre. He has a BSc in Mathematics from the Open University. He also has a BA in English Literature and a PhD in philosophy (both from Cardiff). He continues to teach a little philosophy and literature, especially as they intersect with his other interests, and as a partner in Minimum Labyrinth he has brought these ideas to wider audiences in collaboration with the Museum of London, the Barbican and various private sponsors.
Please note: We reserve the right to change our tutors from those advertised. This happens rarely, but if it does, we are unable to refund fees due to this. Our tutors may have different teaching styles; however we guarantee a consistent quality of teaching in all our courses.