Skip navigation Download free eBooks and textbooks

Choose a category

Elementary Algebra and Calculus

The Whys and Hows

Elementary Algebra and Calculus
4.7 (27 reviews) Read reviews
ISBN: 978-87-403-0151-9
1 edition
Pages : 261
Price: Free

Download for FREE in 4 easy steps...

We are terribly sorry, but in order to download our books or watch our videos, you will need a browser that allows JavaScript.
After entering your email address, a confirmation email will be sent to your inbox. Please approve this email to receive our weekly eBook update. We will not share your personal information with any third party.

This is a Premium eBook - get it free for 30 days

You can also read this in Premium


The book is based on lecture notes Larissa created while teaching large classes of STEM students at a University of widening access and embodies a systematic and efficient teaching method.

300+ Business books exclusively in our Premium eReader

  • No adverts
  • Advanced features
  • Personal library
More about Premium

Buy this eBook

Buy now

Subscribe to all 800+ eBooks

Start free trial 30 day FREE trial

About the book

  1. Reviews
  2. Description
  3. Content
  4. About the Author
  5. Embed


Sorin Neagu-Ventzel ★★★★★

Very well written. Thanks!


The book is based on lecture notes Larissa created while teaching large classes of STEM students at a University of widening access and embodies a systematic and efficient teaching method that marries modern evidence-based pedagogical findings with ideas that can be traced back to such educational and mathematical giants as Socrates and Euler. The courses, which incorporated Larissa's modules, had been accredited by several UK professional bodies, often after ascertaining that there was no correlation between quality of student degrees and quality of their qualifications on entry.


Part I Introduction

Part II Concept Maps

Part III Lectures

Lecture 1 ALGEBRA: Addition, Subtraction, Multiplication and Division of Rational Numbers

Lecture 2 Applications of Elementary ALGEBRA: Solving Simple Equations

Lecture 3 ALGEBRA: Exponentiation, Roots and Logarithms of Real Numbers


Lecture 5 Real FUNCTIONS of One Real Variable: Graphs, Polynomials

Lecture 6 Real FUNCTIONS of One Real Variable: Exponential Functions, Logarithmic Functions, Inverse Functions

Lecture 7 Real FUNCTIONS of One Real Variable: Trigonometric Functions, Inverse Trigonometric Functions, Hyperbolic Functions

Lecture 8 Real FUNCTIONS of One Real Variable: Sketching and Using Graphs, Simple Transformations

Lecture 9 Real FUNCTIONS of One Real Variable: Sketching Graphs by Simple Transformations (ctd.)

Lecture 10 ALGEBRA: Addition of Complex Numbers, the Argand Diagram, Forms of Complex Numbers

Lecture 11 ALGEBRA: Multiplication and Division of Complex Numbers

Lecture 12 ALGEBRA: Fractional Powers, Logs and Loci of Complex Numbers

Lecture 13 CALCULUS: Sequences, Limits and Series

Lecture 14 DIFFERENTIAL CALCULUS: Limits, Continuity and Differentiation of Real Functions of One Real Variable

Lecture 15 DIFFERENTIAL CALCULUS: Differentiation (ctd.)

Lecture 16 DIFFERENTIAL CALCUUS: Sketching Graphs Using Analysis

Lecture 17 Application of DIFFERENTIAL CALCULUS to Approximation of Functions: the Taylor and Maclaurin Series

Lecture 18 INTEGRAL CALCULUS: Integration of Real Functions of One Real Variable (Definite Integrals)

Lecture 19 INTEGRAL CALCULUS: Integration of Real Functions of One Real Variable (Indefinite Integrals)

Lecture 20 INTEGRAL CALCULUS: Advanced Integration Methods

Lecture 21 INTEGRAL CALCULUS: Applications of Integration

Lecture 22 Ordinary Differential Equations

Part IV Summaries

Part V Glossary

Part VI Study Skills for Maths

Part VII Teaching Methodology (FAQs)

About the Author

Larissa Fradkin is Emerita Professor,London South Bank University, UK and Associated Professor, Brunel University,UK. She graduated from the Physics Department of St Petersburg University,Russia in 1973 and received her PhD in Applied Mathematics from Victoria University of Wellington, NZ in 1978. She was employed as a Research Scientist at the NZ Department of Scientific and Industrial Research from 1978 till 1984, as a Research Associate at the Department of Applied Mathematics and Theoretical Physics of Cambridge University, UK from 1985 till 1992 and as a member of academic staff at London South Bank University from 1993 till 2009. She is now a Managing Director of Sound Mathematics Ltd., working on mathematical modelling of ultrasonic inspection of nuclear reactors, mainly in collaboration with CEA (the French Atomic Commission). Larissa is a Fellow of IMA (UK Institute for Mathematics and Its Applications), IOP (UK Institute of Physics) and IET (UK Institute of Engineering and Technology).


Choose color
Implementation code. Copy into your own page
Embed Frame - Terms of Use

The embed frame is free to use for private persons, universities and schools. It is not allowed to be used by any company for commercial purposes unless it is for media coverage. You may not modify, build upon, or block any portion or functionality of the embed frame, including but not limited to links back to the website.

The Embed frame may not be used as part of a commercial business offering. The embed frame is intended for private people who want to share eBooks on their website or blog, professors or teaching professionals who want to make an eBook available directly on their page, and media, journalists or bloggers who wants to discuss a given eBook

If you are in doubt about whether you can implement the embed frame, you are welcome to contact Thomas Buus Madsen on and seek permission.

This website uses cookies to improve user experience. By using our website you consent to all cookies in accordance with EU regulation.