فيزيائي 2009
06-10-2009, 22:10
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
رابط التحميل
تفضل
http://rutherglen.ics.mq.edu.au/wchen/lnemfolder/lnem.html
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
رابط التحميل
تفضل
http://rutherglen.ics.mq.edu.au/wchen/lnemfolder/lnem.html