Complex Numbers
Complex Numbers
About the Book
This book is an introduction calculus, mainly concerned with real-valued functions of a single variable. It is based on a number of articles I have previously published on graphicmaths.com, plus a lot of new material.
The book assumes high school maths (UK KS4), and is suitable as an introduction to calculus at undergraduate level or for anyone with a general interest in mathematics.
It covers:
- Functions and limits, including domains and codomains, concepts of smoothness and continuity, tangents and slope, and squeeze theorem.
- Differentiation, including rates of change, differentiation from first principles, standard derivatives, stationary points, and L'Hopital's rule.
- Integration, including indefinite and definite integrals, standard integrals, Riemann sums, the fundamental theoren of calculus, and improper integrals.
- Differentiation techniques, including the product rule, chain rule, quotient rule, reciprocal rule, inverse function rule, implicit differentiation and logarithmic differentiation.
- Integration techniques, including integration by substitution, integration by parts and the LIATE rule, trig identities, trig substitution, and partial fractions.
The book takes te approach of providing intuitive explanations and examples followed by formal proofs that build on an intuitive understanding.
About the Author
Table of Contents
- 1 - Introduction
- 1.1 - Content summary
- 2 - Functions and limits
- 2.1 - Functions
- 2.2 - Limits
- 2.3 - Big O notation
- 2.4 - Squeeze theorem
- 2.5 - Tangents to a curve
- 2.6 - More about functions
- 2.7 - Summary
- 3 - Differentiation
- 3.1 - Rate of change
- 3.2 - Differentiation
- 3.3 - Derivative notation
- 3.4 - Differentiability
- 3.4.1 - Continuous functions and differentiability
- 3.5 - Standard derivatives
- 3.6 - Rules for differentiating powers
- 3.7 - Odd and even functions
- 3.8 - Differentiating exponential functions
- 3.9 - Differentiating trig functions
- 3.10 - Differentiating hyperbolic functions
- 3.11 - The link between e^x, sinh x and sin x
- 3.12 - Fermat's theorem of stationary points
- 3.13 - L'Hopital's rule
- 3.14 - Summary
- 4 - Integration
- 4.1 - Antiderivatives
- 4.2 - Indefinite integrals
- 4.3 - Standard integrals
- 4.4 - Integrals and the area under a curve
- 4.5 - Definite integrals
- 4.6 - Some useful theorems
- 4.7 - Mean value theorem for integrals
- 4.8 - The Riemann sum
- 4.9 - Fundamental theorem of calculus
- 4.10 - Improper integrals
- 4.11 - Summary
- 5 - Differentiation techniques
- 5.1 - The product rule
- 5.2 - The chain rule
- 5.3 - The quotient rule
- 5.4 - The reciprocal rule
- 5.5 - The inverse function rule
- 5.6 - Implicit differentiation
- 5.7 - Logarithmic differentiation
- 5.8 - The Weierstrass function
- 5.9 - Summary
- 6 - Integration techniques
- 6.1 - Integration by substitution
- 6.2 - Integration by parts
- 6.3 - LIATE rule for integration by parts
- 6.4 - Using trigonometric identities
- 6.5 - Trigonometric substitutions
- 6.6 - Partial fractions
- 6.7 - Summary
The Leanpub 60 Day 100% Happiness Guarantee
Within 60 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.
Now, this is technically risky for us, since you'll have the book or course files either way. But we're so confident in our products and services, and in our authors and readers, that we're happy to offer a full money back guarantee for everything we sell.
You can only find out how good something is by trying it, and because of our 100% money back guarantee there's literally no risk to do so!
So, there's no reason not to click the Add to Cart button, is there?
See full terms...
Earn $8 on a $10 Purchase, and $16 on a $20 Purchase
We pay 80% royalties on purchases of $7.99 or more, and 80% royalties minus a 50 cent flat fee on purchases between $0.99 and $7.98. You earn $8 on a $10 sale, and $16 on a $20 sale. So, if we sell 5000 non-refunded copies of your book for $20, you'll earn $80,000.
(Yes, some authors have already earned much more than that on Leanpub.)
In fact, authors have earnedover $13 millionwriting, publishing and selling on Leanpub.
Learn more about writing on Leanpub
Free Updates. DRM Free.
If you buy a Leanpub book, you get free updates for as long as the author updates the book! Many authors use Leanpub to publish their books in-progress, while they are writing them. All readers get free updates, regardless of when they bought the book or how much they paid (including free).
Most Leanpub books are available in PDF (for computers) and EPUB (for phones, tablets and Kindle). The formats that a book includes are shown at the top right corner of this page.
Finally, Leanpub books don't have any DRM copy-protection nonsense, so you can easily read them on any supported device.
Learn more about Leanpub's ebook formats and where to read them
