# Elementary Algebra and Calculus

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### Summary

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.

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## About the book

### Reviews

#### Sorin Neagu-Ventzel ★★★★★

Very well written. Thanks!

### Description

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.

### Content

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 4 FUNCTIONS

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).