WorldMathBook English

Tom Pedersen. Company: WorldMathBook
cvr. 44731703 Denmark.
ISBN 978-87-975307-0-2

WorldMathBook, Summary

English

For high school and beyond

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A textbook well suited for study as well as for self study.

All subjects for high School are included – and more.

Thistextbook is meant to be:

• Your math companion for upper secondary school, high school, and the first semester(s) of study.
• Textbook for high school or similar as well as the first semester(s) of study.
• Textbook which should be supplemented by the accompanying exercise book “WorldMathBook, Exercises” as well as a formula collection.

The book is independent of which formula collection is used.You can use the book without a formula collection, but it will be harder.

The book is also independent of using a calculator or a calculator program.You can use the book without a calculator, but it will be much harder.

The demands for a calculator/calculator program are:

Part 1. All calculators/programs.

Part 2. Calculators/programs with functions, - almost all kinds have that.

Part 3. Advanced calculators/programs able to differentiate and integrate and for plotting curves in diagrams.

Part 4. The setup of vectors is not beneficial using calculators/programs, but if so, an advanced calculator/program is necessary.

Part 5. Advanced calculators/programs for regression.

 

We start with the four basic arithmetic operations, and finish in the first or second semester of the study for bachelor or candidate.

The language is clear, understanding is in focus, and technical terms are explained.

 

Overall Content:

This textbook (as well as the exercise book) is divided into five parts:

1. Basics
2. The coordinate system in the plane (2D) and functions
3. Differentiation and integration
4. Vectors
5. Statistics (including Probability)

Also, at the end we present “Numbers and Complex numbers”, and some “Rarely used proofs and calculations”.

Finally, we present a detailed Subject index.

 

Content in details:

Part 1. Basics

Number system

The four basic arithmetic operations: Sum, Difference, Product, Division

Fractions (Quotients)

Percent and Percentage point

Calculation with letters (algebra)

Parenthesis, Square rules, Squareroot

Exponentiation

Equations, Second degree equations, Higher degree equations, Two equations with two unknowns

Functions and proportionality

Intervals and inequalities

Imaginary numbers, briefly

Part 2. The coordinate system in the plane(2D) and functions

The coordinate system and distance, The straight line, The parabola, Polynomials

Functions and the four basic arithmetic operations, Composite functions, Inverse functions

The right triangles

The circle

Sine, Cosine and Tangent

Radian, Angle, Arc length, Survey

The sine function and the sine oscillation

The not right-angled triangles (arbitrary triangles)

Proof of the sine-relation and the cosine-relations

Exponential functions

Logarithm functions:log 10-logarithm, natural logarithm: ln (log e)

Other functions

Hyperbola, Third degree polynomial function, Fourth degreepolynomial function, Fractional polynomial function, A special thirddegree polynomial function, Partly defined functions

Part 3. Differentiation and Integration

Introduction

Differential calculus, Proofs of differential calculus 1

The horizontal line, The straight line, The parabola, The square rootfunction, Polynomials, The natural exponential function, The naturallogarithm function

Notations

Differentiation and the four basic arithmetic operations

Sum, Difference, Product, Division

Differentiation of composite functions

Proofs of differential calculus 2

The e^kx function, The exponential function, The sine function, Thecosine function, The tangent function

Survey

Differentiable, non-differentiable

Integral calculus

Survey and Notations

Integration and the four basic arithmetic operations

Sum, Difference, Product

Integration by substitution

Integration by parts

The specific integral

Areas, Volumes, Guldin’s rules, Curve length

Differential equations

Typical differential equations, The logistic differential equation

Slope fields

Functions of two variables

Ways of expression, 3D figures

The gradient

Part 4. Vectors

2D vectors in the plane

Basics, Special vectors, Computations, Angle, Projection,Determinant, Area and angle, The parametric equation for a straightline, Distance point-line

Polar coordinates in 2D

Vector functions (parametric curves) in 2D

The vector function for a straight line, The vector function for acircle.

Differentiation of vector functions: the line, the circle, Doublepoints

3D vectors in the space

Distance point-point, Cross product, Angle between vectors, Area,Equation of a plane, Distance point-plane, The straight line in thespace, Distance between skewed lines, Distance point-line, Distancebetween two parallel planes, Angle between two planes, Anglebetween line and plane

The sphere

Part 5. Statistics

Data (Observations), Non-grouped data, Grouped data

The normal distribution, variance and standard deviation

Goodness of fit (Chi to the power of two - testing)

Regression, Linear - , Power - , Exponential -

Probability and combination, Introduction, Theory, Examples

Binomial distribution, random sample, and confidence interval

Notations and technical terms

 

Brief on set theory

Natural numbers, whole, rational, irrational, real, imaginarynumbers

Complex numbers, rectangular, polar, exponential

Rarely used proofs and calculations:

• Proof of Pythagoras theorem
• Proof of factorization of a second degree polynomium
• Division of polynomials
• Showing the formulas for permutation and combination
• Proof of product and division of complex numbers in the polar and
• the exponential form