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A Simplified Home School and High School Algebra and Basic Mathematics Course | home
A Simplified High School Mathematics Tutorial Course for Education and Careers | Find Out For Yourself | Advantages | Description | What Skills Will You Learn? | Critical Skills Learned | For Mothers | What Will You Learn? | Increase Your Confidence With a Knowledge of Math! | What Topics Will You Learn | Program Contents | How Program Works | Sample Lesson #1 | Sample Lesson #2 | Sample Lesson #3 | Save $$ | Free | Order | Free Lesson 1 Order Form | Lesson 2 Order Form | Contact Us |
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The outline of subjects presented in the MATH 2000' program which presents the background behind the underlying ideas taught in college and graduate school math, engineering, science and business courses.
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Program Contents
TABLE OF CONTENTSThis table of contents shows the topics presented in this math course. Preface xiii
CHAPTER 1
Introduction to Applied Mathematics
#####################Prologue To Chapter 1 1 INTRODUCTION 1 Why is it Important to Learn Mathematics? 1 Mathematics is a Tool That Helps Us Understand What is Already Here 6 What is the Suggested Method for Learning Mathematics? 9 A Notable Amount of Mathematics Was Developed Because of a Need to Understand Wave Motion 12 Isaac Newton 14 The Bernoulli Family 16 Jean Le Rond d'Alembert 18 CHAPTER 1 - Introduction To Applied Mathematics 21 )))))))))))))))))))))))))))))))) 1.0 Why Do We Study Waves? 21 1.1 What Caused People to Become Interested in the Study of Waves? 23 1.2 The Formation of Waves 26 A LOOK INTO THE FORMATION OF WATER WAVES 28 1.3 The theory of Oscillation 30 Max Planck 32 A. H. Compton 33 Louis deBroglie 34 1.4 Why Does a Wave Travel Away From the Point of Disturbance? 35 1.5 Frequency, Wavelength and Period 1.6 The Relationship between Velocity, Frequency and Wavelength - FREQUENCY DEPENDS ON VELOCITY 42 Chapter Review 45 Glossary of Terms 46 Written Assignments 52 Problems 53
CHAPTER 2
Theory of Waves
###################################Prologue to Chapter 2 55 INTRODUCTION 55 How Does a Stretched String Produce a Musical Tone? 55 CHAPTER 2 - Theory of Waves 60 ))))))))))))))))))))))))))))))) 2.0 The Boundary Value Problem 60 2.1 Stationary Waves 63 How to Determine the Frequencies at Which a String Will Vibrate - ANALYSIS OF THE FIRST NATURAL WAVELENGTH 68 ANALYSIS OF THE SECOND NATURAL WAVELENGTH 70 ANALYSIS OF THE THIRD NATURAL WAVELENGTH 70 2.2 Representing a Wave by a Corresponding Mathematical Relation - A SINE-CURVE IS A REPRESENTATION OF A CIRCULAR MOTION 75 2.3 The Definition of a Sine-Curve 77 2.4 A Point On The Circumference Of A Circle And The Vertex Of A Triangle Contacting That Point Are Isomorphic 85 Chapter Review 86 Glossary Of Terms 89 Written Assignments 91 Problems 93
CHAPTER 3
The Trigonometric Functions
#########################Prologue to CHAPTER 3 97 CHAPTER 3 - The Trigonometric Functions 101 ))))))))))))))))))))))))))))))))))))) 3.0 Definitions of the Trigonometric Functions 101 THE PYTHAGOREAN THEOREM 106 3.1 Why are the Trigonometric Functions Important? 108 What Is The Purpose Of Solving A Triangle? 109 3.2 The Law of Sines - A Formula For Solving Triangles That Are Not Right Triangles 112 3.3 Application of Trigonometry to the Solution of Practical Problems 117 THE VECTOR 117 3.4 Application of the Method of Resolution of a Vector to Solving Practical Problems 123 Using Trigonometry for Solving Problems Involving Electric Fields 126 3.5 The Area of an Obtuse Triangle 131 3.6 The Law of Cosines 134 Chapter Review 137 Glossary of Terms 138 Written Assignments 141 Problems 142
CHAPTER 4
SYMBOLIZING THE FORM AND MOTION OF A WAVE MATHEMATICALLY
Prologue to Chapter 4 145 CHAPTER 4 - Symbolizing The Form And Motion Of A Wave Mathematically 151 S))))))))))))))))))))))))))))))) 4.0 Representing A Waveform In Terms Of The Distance It Traverses 151 Representing a Wave By Means Of A Sine Function 151 4.1 Measuring A Sine-Wave In Terms Of Circular Degrees 154 4.2 The Radian System Of Circular Measurement 155 4.3 Circular Motion 159 4.4 Angular Motion 161 4.5 Measuring the Velocity of an Object Moving Around a Circle 163 THE RADIAN SYSTEM OF MEASUREMENT SIMPLIFIES WORKING WITH CIRCULAR MOTION PROBLEMS 164 4.6 The Equation of a Sine-Wave in Terms of Distance 167 DEFINITION OF A FUNCTION 167 4.7 Representing A Wave In Terms Of Time 173 DESCRIBING A WAVE IN TERMS OF TIME 174 4.8 Representing A Wave In Terms Of Distance And Time 180 4.9 Calculating Wave Motion at a Location that is Shifted from the Origin 181 4.10 A Wave Equation Involving the Propagation Constant, k 188 4.11 Interpreting Simple Sine and Cosine Equations 193 4.12 Equations of the Form y = A Sin (x + p) and y = A Cos (x - p) 201 Chapter Review 205 Glossary of Terms 207 Written Assignments 209 Problems 210
CHAPTER 5
UNDERSTANDING TRIGONOMETRIC
IDENTITIES
####################################Prologue to CHAPTER 5 213 CHAPTER 5 - Understanding Trigonometric Identities 217 S))))))))))))))))))))))))))))))) 5.0 TRIGONOMETRIC IDENTITIES 217 5.1 A Trigonometric Identity Derived From The Pythagorean Theorem 218 5.2 Trigonometric Identities That Relate The Sum And Difference Of Two Angles 224 5.3 Some Insights Into The Trigonometric identities That Relate The Sum And Difference Of Two Angles 226 Chapter Review 230 Writing Assignments 231 Problems 232
CHAPTER 6
THE SUPERPOSITION AND PRODUCT OF
WAVES
#########################################Prologue to CHAPTER 6 233 CHAPTER 6 - THE SUPERPOSITION AND PRODUCT OF WAVES 237 S))))))))))))))))))))))))))))))) 6.0 The Principle Of Superposition And The Product Of Waves 237 6.1 Trigonometric Identities Involving The Sum And Difference Of Two Angles 238 6.2 Trigonometric Identities Involving the Product of Sines and Cosines 248 6.3 INTERPRETATION OF TRIGONOMETRIC IDENTITIES INVOLVING THE SUM, DIFFERENCE AND PRODUCT OF SINES AND COSINES 253 THE FUNCTION OF A FUNCTION 253 THE FUNCTIONAL RELATIONSHIP - A Connection Between an Action and the Result of the Action 255 Modulation and Functions 258 Modulation of a Sine-Curve by x2 263 Chapter Review 265 Glossary of Terms 269 Writing Assignments 271 Problems 273
CHAPTER 7
PRELIMINARIES TO UNDERSTANDING THE
WAVE EQUATION
#########################################Prologue To CHAPTER 7 275 CHAPTER 7 - PRELIMINARIES TO UNDERSTANDING THE WAVE EQUATION 279 ON CALCULATING THE PACE OR RATE OF CHANGE OF A FUNCTION 279 7.1 Representing The Rate Of Change Of A Function With A Derivative 279 7.2 Finding The Equation For The Slope Of A Function 285 7.3 Finding Derivatives 287 7.4 The Power Rule For Derivatives 289 SOLVING A PROBLEM USING IMPLICIT DIFFERENTIATION 296 7.5 The Antiderivative (INTEGRAL) 305 7.6 PARTIAL DERIVATIVES 313 7.7 Partial Derivatives Of Higher Order 317 7.8 The Total Differential 321 7.9 The Differential For A Function With Several Variables 326 CHAPTER REVIEW 335 WRITTEN ASSIGNMENTS 337 PROBLEMS 338 |