IT103: Algebra

Course: IT103 ALGEBRA
Credits: 3 (3-0-6)
Class Scheduling: MON/TH 9:00-10:30
Venue: PC301
Instructor: Dr. Robert Batzinger
Mid-Term Exam: 10 Oct 2024 9:00-11:00
Final Exam: 6 Dec 2024 9:00-12:00

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• What is your experience with Math?
• What is your goal?

Mathematics is a language to express numerical relationships between entities and the solution spaces related to a given set of parameters.

• Persian mathematician (780-850 AD)
• introduced Hindu-Arabic numerals
• invented algebra as a process (algorithm)
• European mathematics adopted his concepts of algebra during the medieval era

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• Contents

\[\eqalign{- Slides &\quad - Exercises &\quad - Quizzes \\ - Review & \quad - Handouts \\}\]

Universal gas law:

\[\eqalign{PV& =& nrT\\ Where& \\ P & : & pressure\\ V & : & volume \\ n & : & number\ of\ atoms\\ r & : & gas\ constant \\ T & : & temperature\ (in\ K)\\ }\]

If an empty tank is quickly filled with a powerful compressor, what happens to the temperature of the gas inside?

• A bat and a ball together cost $1.10.
• The bat costs $1 more that the ball.

How much does the ball cost?

• Assume water lilies double in surface area every day.
• A pond becomes full after 45 days.

How long does it take for the pond to become half full?

An Egyptian farmer has 19 camels. In his will, he state 1/2 of the camels were to go to his eldest son, 1/4 of the camels to his middle son, and 1/5 of the camels to his youngest son. The will also stipulated that no camels were to be killed or cut up in the process.

What was the solution? How many camels did each son recieve as per the terms of the will?

• 1.1 Real Numbers: Algebra Essentials
• 1.2 Exponents and Scientific Notation
• 1.3 Radicals and Rational Exponents
• 1.4 Polynomials
• 1.5 Factoring Polynomials
• 1.6 Rational Expressions
• 1.7 The basic rules of algebra

• 2.1 The Rectangular Coordinate Systems and Graphs
• 2.2 Linear Equations in One Variable
• 2.3 Models and Applications
• 2.4 Complex Numbers
• 2.5 Quadratic Equations
• 2.6 Other Types of Equations
• 2.7 Linear Inequalities and Absolute Value

• 3.1 Functions and Function Notation
• 3.2 Domain and Range
• 3.3 Rates of Change and Behavior of Graphs
• 3.4 Composition of Functions
• 3.5 Transformation of Functions
• 3.6 Absolute Value Functions
• 3.7 Inverse Functions

• 4.1 Linear Functions
• 4.2 Modeling with Linear Functions
• 4.3 Fitting Linear Models to Data

• 5.1 Quadratic Functions
• 5.2 Power Functions and Polynomial Functions
• 5.3 Graphs of Polynomial Functions
• 5.4 Dividing Polynomials
• 5.5 Zeros of Polynomial Functions
• 5.6 Rational Functions
• 5.7 Inverses and Radical Functions
• 5.8 Modeling Using Variation

• 6.1 Exponential Functions
• 6.2 Graphs of Exponential Functions
• 6.3 Logarithmic Functions
• 6.4 Graphs of Logarithmic Functions
• 6.5 Logarithmic Properties
• 6.6 Exponential and Logarithmic Equations
• 6.7 Exponential and Logarithmic Models
• 6.8 Fitting Exponential Models to Data

• 8.1 The Ellipse
• 8.2 The Hyperbola
• 8.3 The Parabola
• 8.4 Rotation of Axes
• 8.5 Conic Sections in Polar Coordinates

• 9.1 Sequences and Their Notations
• 9.2 Arithmetic Sequences
• 9.3 Geometric Sequences
• 9.4 Series and Their Notations
• 9.5 Counting Principles
• 9.6 Binomial Theorem
• 9.7 Probability