[فيزيائي 2009]

Elementary Mathematics

by WWL Chen and XT Duong



This set of notes has been compiled over a number of years. Chapters 1, 3-6 and 8 are based on lecture notes used by the second author in the second semester of 1998. Most of the remaining chapters were used for the first time in the second semester of 1999.

The material has been organized in such a way to create a single volume suitable for use in the unit MATH130 at Macquarie University. This unit is currently taught in two parallel strands. The following is the suggested order for the presentation of the material:

A: Chapters 1, 3, 4, 5, 6, 7, 8 and 9.
C: Chapters 2, 10, 11, 12, 13 and 14.
The overall emphasis of this set of notes is on examples, of which there are many. The only way to study mathematics satisfactorily at this level is to study many examples and to attempt many exercises while going back regularly to the discussion in the notes for appropriate references.

The material is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, the documents may not be kept on any information storage and retrieval system without permission from the author, unless such system is not accessible to any individuals other than its owners.



SECTION A --- ALGEBRA



Chapter 1: BASIC ALGEBRA

The Real Number System
Arithmetic
Distributive Laws
Arithmetic of Fractions
Factorization


Chapter 2: INTRODUCTION TO MATRICES

Linear Equations
Arithmetic
Application to Linear Equations


Chapter 3: TRIGONOMETRY

Radian and Arc Length
The Trigonometric Functions
Some Trigonometric Identities


Chapter 4: INDICES AND LOGARITHMS

Indices
The Exponential Functions
The Logarithmic Functions


Chapter 5: POLYNOMIAL EQUATIONS

Linear Equations
Quadratic Equations
Factorization Again
Higher Order Equations


Chapter 6: INEQUALITIES AND ABSOLUTE VALUES

Some Simple Inequalities
Absolute Values


Chapter 7: PROGRESSIONS

Arithmetic Progressions
Geometric Progressions


Chapter 8: ELEMENTARY COUNTING TECHNIQUES

The Fundamental Principle of Counting
Permutation
Combination
The Binomial Theorem
Application to Probability Theory


Chapter 9: COMPLEX NUMBERS

Introduction
The Complex Plane


SECTION B --- CALCULUS



Chapter 10: FUNCTIONS AND LINES

Functions and Graphs
Lines on the Plane


Chapter 11: INTRODUCTION TO DIFFERENTIATION

Tangent to a Curve
Arithmetic of Derivatives
Derivatives of the Trigonometric Functions


Chapter 12: FURTHER TECHNIQUES OF DIFFERENTIATION

The Chain Rule
Implicit Differentiation
Derivatives of the Exponential and Logarithmic Functions
Derivatives of the Inverse Trigonometric Functions


Chapter 13: APPLICATIONS OF DIFFERENTIATION

Second Derivatives
Applications to Problem Solving
Newton's Method


Chapter 14: INTRODUCTION TO INTEGRATION

Antiderivatives
Integration by Substitution
Definite Integrals
Areas


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http://rutherglen.ics.mq.edu.au/wche...lder/lnem.html

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[فيزيائي 2009]

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[فيزيائي 2009]

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9-1-2010