Mathematics of Physics Honors I

1. Mathematics of Physics Honors I

2. Learning on your own: Algebra Review: https://www.youtube.com/watch?v=44odivr7_s4 Algebra Review – Manipulating Equations https://www.youtube.com/watch?v=quD1deDkNr0 Trigonometry Review: https://www.youtube.com/watch?v=OvcDcQ_KgbU Motion Graphs and the Position Equations: https://www.youtube.com/watch?v=RZjREjLJJ_I Interpreting Motion Graphs: https://www.youtube.com/watch?v=7GJ_SYM8cyU Red Class Book: Chapter 1.1 – Mathematics and Physics – page 3.

3. Lesson Objective: • Recall the Order of Operations. • Learn to use a calculator – Seriously, you don’t know how. • Algebra – Graphing. • Algebra – Equation manipulation (Solve for x). • Algebra - Proportionality • Trigonometry – Pythagorean Theorem • Trigonometry – learn about sine, cosine, and tangent. • Recall SI Prefixes • Greek Alphabet

4. Order of Operations: • PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. • PEMDAS is a general guide but not exactly right. • SOLVE:

5. Order of Operations: • SOLVE (NOW USE A CALCULATOR): • The answer is 9. Unfortunately this equation is written very poorly and it is difficult to understand the authors intention. • RULE 1: Use lots of parentheses especially when putting in equations in a calculator. • RULE 2: Write equations appropriately so they can easily be read. • Isn’t this easier to read: • = ?

6. Order of Operations: • RULE 3: Solve read equations from left to right. • RULE 4: Solve Exponents after parentheses. • It is extremely important that you put exponents into parentheses when inputting them into your calculator (especially when dividing). • The required calculator for this course (TI-30XIIS) has a button that looks like this ^. So when inputting it into your calculator you will write it as: • Multiplying:

7. Order of Operations: • RULE 5: Multiplication and Division come after exponents. Multiplication and Division are equal to one another. • This means that if you encounter multiplication before division, you do the multiplication first. • 2 x 10 / 5 • It also means that you encounter division before multiplication, you do the division first. • 20 / 4 x 2 • Again: Write the equations in a readable format using parentheses as much as possible.

8. Order of Operations: • RULE 6: Addition and Subtraction come after Multiplication and Division. Just as with Multiplication and Division, Addition and Subtraction are equal. • If Addition comes first, you do the addition. If subtraction comes first, you do the subtraction. • (3 x 9) – (2 x 6) + (4 / 2)

9. Order of Operations – Forgive me:

10. Algebra – Graphing: • I won’t be reviewing all of your algebra and certainly not all of the graphing rules. You do need to read at least the basics of graphing such as when something is linear, exponential, increasing, decreasing, etc. • You especially need to know what I am talking about when I talk about things being on the horizontal (x-axis) and on the vertical (y-axis).

11. Algebra – Graphing:

12. Algebra – Check Point 1: • Identify the function? (A) (B) (C)

13. Algebra – Solve for x: • Equation is extremely important in physics, engineering, chemistry, accounting, computers, finances, scheduling, anything to do with management. So the sooner you get the hang of it, the better off you will be. • In algebra you commonly see equations like: • or • In physics, you are going to have to solve equations such as: • or

14. Algebra – Proportionality: • Proportionality is the relationship between two “substances” in a system. • In equations, we will see that variables are either Directly Proportional or Indirectly Proportional. • The proportionality symbol is:  it looks like a cut off infinity symbol.

15. Algebra – Direct Proportionality: • Directly proportionality is when one amount increases, another amount increases. • Take the ideal gas law: • n and R are constants which means they will not change. • p (pressure), V (volume), and T (temperature) are all subject to change. • What does this equation mean? • We see that as temperature increases, either pressure, volume, or both will increase with it.

16. Algebra – Indirect Proportionality: • Indirect proportionality is when one amount increases, another amount decreases, and vice versa. • Take the ideal gas law again and isolate pressure p: • What does this equation mean? • We see that as pressure increases, volume decreases, and temperature increases. • It also means that as pressure decreases, volume increases, and temperature decreases.

17. Algebra – Check Point: • Solve the equation to find x: • What type of relationship does Force (F) have with Acceleration (a) in the equation below? Explain what that means? • F = ma • What type of relationship does current I have resistance R in the equation below? Explain what that means? • V = IR

18. Trigonometric Operations: • We won’t go in depth on this right now but here are some basics. • First off, learn to set your calculator into degree mode. We most likely will never use radian mode in this class (although it is good to know when to use degree and radian). • On the TI-30XIIS, you click DRG and you will be given the options of DRG RAD GRD. DRG stands for Degree, RAD stands for Radian, and GRD stands for Gradian. Make sure DRG is underlined.

19. Trigonometric Operations: • You should know sine, cosine, and tangent. • Sine:

20. Trigonometric Operations: • You should know sine, cosine, and tangent. • Sine:

21. Trigonometric Operations: • Cosine:

22. Trigonometric Operations: • Cosine:

23. Trigonometric Operations: • Tangent:

24. Trigonometric Operations: • Tangent:

25. Trigonometric Operations: • Pythagorean Theorem:

26. Vectors: • Vectors utilize the Pythagorean Theorem, sinθ, cosθ, and tanθ a lot. We will not get that in this class yet, but we will get there. • If you are in Calculus or Pre-Calculus, I was told my methodology for teaching vectors helped out a lot in those classes so do pay attention.

27. Trigonometric Operations: • One thing you will also need to familiarize yourself with is the unit circle and what the different degrees mean. • Please keep the handout that I give you of the unit circle, they will be useful in this class and in other classes.

28. Trigonometric Operations:

29. Decimal Places:

30. The Greek Alphabet:

31. Exit Ticket: • Solve for acceleration a in if • What is the relationship between Work and Distance in W= Fd? • What is the relationship between velocity and distance in v = d / t ? • What is the relationship between acceleration and time in a = v / t ?