Online Notes and Lectures

Sunday, March 30, 2014

Subject: Probability and Statistics

0 comments Posted by Anonymous at 9:57 PM

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Course Name

PROBABILITY AND STATISTICS

Course Description

Basic principles of statistics; presentation and analysis of data; averages, median, mode; deviations; probability distributions; normal curves and applications; regression analysis and correlation; application to engineering problems.

Prerequisites:

College Algebra

Course Objectives

After completing this course, the student must be able to:

1. Define relevant statistical terms;

2. Discuss competently the following concepts:

2.1. Frequency distribution
2.2. Measures of central tendency
2.3. Probability distribution
2.4. Normal distribution
2.5. Inferential statistics

3. Apply accurately statistical knowledge in solving specific engineering problem situations.

Probability and Statistics Course Outline

Following is the list of topics we will discuss in this course:

Probability and Statistics

LESSON 1: Introduction to Statistics, General uses of Statistics, Fields of Statistics

LESSON 2: DATA COLLECTION, SAMPLING TECHNIQUE, TABULAR REPRESENTATION

LESSON 3: Measures of Central Tendency: Mean, Median, Mode,Shapes of Distributions

LESSON 4: Measures of Variations: RANGE, Deviation, Average Deviation, Variance, Standard Deviation

LESSON 5: Measures of Positions: Quartiles, Inter-quartile Range, Box and Whisker Plot, Percentile and Decile, Standard Scores, Relative Z-Scores

LESSON 6: Correlation and Regression

LESSON 7: Fundamental Principle of Counting, Permutation , Combination, Factorial

LESSON 8: Probability: Subjective Probability, Empirical Probability, Classical Probability, additional rule, conditional probability and the multiplication rule

LESSON 9: Normal Distributions and Standard Distribution, Areas Under the Standard Normal Curve, z-Score, Sampling Distributions, Central Limit Theorem

Suggested References

Sellers, Gene R. and Stephen A. Vardeman. Elementary Statistics, 2nd ed. Saunders College Publishing, 1982. Walpole, Ronald E., et al. Probability and Statistics for Engineers and Scientists, 7th ed. Prentice Hall, Inc., 2002.

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Probability and Statistics Lecture 9

0 comments Posted by Anonymous at 9:20 PM

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Lesson Objectives - the students should be able to:

Define Normal Distributions and Normal Distributions
Learn the properties of Normal Distributions
Understand The Standard Normal Table
Find Areas Under the Standard Normal Curve
Find probabilities in Normal Distributions
Find values in Normal Distributions
Find z-Scores
Find a z-Score Given a Percentile
Transform a z-Score to an x-Score
Find a Specific Data Value
Learn Sampling Distributions
Learn The Central Limit Theorem

LESSON OUTLINE:

Properties of Normal Distributions
Means and Standard Deviations
The Standard Normal Distribution
The Standard Normal Table
Guidelines for Finding Areas
Probability and Normal Distributions
Finding z-Scores
Finding a z-Score Given a Percentile
Transforming a z-Score to an x-Score
Finding a Specific Data Value
Sampling Distributions
Properties of Sampling Distributions
Sampling Distribution of Sample Means
The Central Limit Theorem
The Mean and Standard Error
Probability and Normal Distributions
Probabilities of x and x
Seatwork/Exercies
Homework

Probability and Statistics Lecture 9

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Probability and Statistics Course Outline

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Subject: Analytic Geometry

0 comments Posted by Anonymous at 6:57 PM

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Course Name

ANALYTIC GEOMETRY

Course Description

Equations of lines and conic sections; curve tracing in both rectangular and polar coordinates in two-dimensional space.

Prerequisites:

College Algebra
Plane and Spherical Trigonometry

Course Objectives

After completing this course, the student must be able to:

1. Set up equations given enough properties of lines and conics;

2. Draw the graph of the given equation of the line and the equation of the conic section; and
3. Analyze and trace completely the curve, given their equations in both rectangular and polar coordinates, in two-dimensional space.

Analytic Geometry Course Outline

Following is the list of topics we will discuss in this course:

I. Plane Analytic Geometry

LESSON 1: Introduction to Geometry, Directed Line Segments, The Cartesian Plane, Distance Formula

LESSON 2: Midpoint of a Line, Point-of-Division Formulas

LESSON 3: Slope of a Line in term of Angle inclination, Slope of a line in terms of Coordinate

LESSON 4: Slope of Perpendicular lines, Slope of Parallel Lines, Angle formed between two lines

LESSON 5: Finding the equation of a line using Two-point Form and Intercept Form

LESSON 6: Finding the equation of a line using Slope-Point Form and Slope-Intercept Form

LESSON 7: Finding the other forms of equation of a lines and Finding the Family of Lines

LESSON 8: Changing from General Form to Standard Equation of a line and Finding distance from line to a point

LESSON 9: Standard form of the equation of the circle, Equation of circles with center at origin, General form of the equation of a circle

LESSON 10: Determine Circles by Geometric Conditions

LESSON 11: Conic Sections: Parabola

LESSON 12: Conic Sections: Ellipse

LESSON 13: Conic Sections: Hyperbola

Suggested References

Fuller, Gordon and Dalton Tarwater. Analytic Geometry, 7th ed. AddisonWesley,1993. Protter, Murray H. and Philip E. Protter. Calculus with Analytic Geometry, 4th ed. Quirino and Mijares. Plane and Analytic Geometry, 2nd ed. Riddle, Douglas F. Analytic Geometry, 6th ed. Swokowski, Earl W. and Jeffrey A. Cole. Algebra and Trigonometry with Analytic Geometry, 10th ed. Brooks/Cole Publishing Co., 2001. Analytic Geometry (Made Easy) Felipe L. Commandante, Jr

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Analytic Geometry Lecture 13

0 comments Posted by Anonymous at 1:27 PM

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Lesson Objectives - the students should be able to:

Classify equations of the conic sections into parabola, ellipse, and hyperbola

Graph the hyperbola with vertex at the origin.
Graph the hyperbola with vertex at (h, k)
Solve problems regarding hyperbola, finding the vertices, eccentricity and length of the latus rectum.
Find the equation of the hyperbola with vertex at the origin.
Find the equation of the hyperbola with vertex at (h, k)
Know the some real life applications of hyperbola.

LESSON OUTLINE:

Definition
General Rules of the Hyperbola
Properties of the Hyperbola

HYPERBOLA WITH VERTEX AT THE ORIGIN
Important Relations and Theorems of Hyperbola
Seatwork
Homework
HYPERBOLA WITH VERTEX AT (h,k)
Properties of the Hyperbola WITH VERTEX AT (h,k)
Examples
Formulas of the Hyperbola
Summaries
Seatwork
Homework