Elementary Algebra and Calculus
The Whys and Hows
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About the book
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Sorin NeaguVentzel ★★★★★
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 evidencebased 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)