# Elementary Algebra and Calculus

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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).