[PDF] [PDF] Lecture 1 (Review of High School Math: Functions and Models

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[PDF] Lecture 1 (Review of High School Math: Functions and Models

Mathematical models: What kind of functions are there? A mathematical model is a mathematical description (function or equation) of a real-world phenomenon

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Lecture 1 (Review of High School Math: Functions and Models)

Introduction: Numbers and their properties

Addition:

(1) (Associative law) If a, b, and c are any numbers, then (2) (Existence of an additive identity) If a is any number, then (3) (Existence of additive inverses) For every number a, there is a number a such that (4) (Commutative law) If a and b are any numbers, then

Multiplication:

(5) (Associative law) If a, b, and c are any numbers, then (6) (Existence of an multiplicative identity) If a is any number, then (7) (Existence of multiplicative inverses) For every number ܽ is a number ܽ (Note: division by 0 is always undefined!) (8) (Commutative law) If a and b are any numbers, then (9) (Distributive law) If a, b, and c are any numbers, then

Definition: The numbers a satisfying ܽ

numbers a satisfying ܽ For any number a, we define the absolute value |a| of a as follows:

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