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About the Book
This book is an introduction to calculus, mainly concerned with real-valued functions of a single variable. It is based on several 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 theorem 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 the approach of providing intuitive explanations and examples followed by formal proofs that build on an intuitive understanding.
About the Author
Martin McBride is a software developer, specialising in computer graphics, sound, and mathematical programming. He has been writing code since the 1980s in a wide variety of languages from assembler through to C++, Java and Python. He writes for PythonInformer.com and is the author of Functional Programming in Python. He is interested in generative art and works on the generativepy open source project.