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MATHS 102 Mathematics 2

MATHS 102 Mathematics 2. Module 0 Models & Functions Lecture 3 Formal Functions. MATHS 102 – Introductory Module In this third lecture we will discuss one of the key concepts of mathematics, that of a function.

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MATHS 102 Mathematics 2

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  1. MATHS 102 Mathematics 2 Module 0 Models & Functions Lecture 3 Formal Functions

  2. MATHS 102 – Introductory Module In this third lecture we will discuss one of the key concepts of mathematics, that of a function. The idea of a function is used repeatedly in mathematics. You will already have met many functions, or mathematical relationships which can be expressed as functions.

  3. but first … your work: • Cost of running a flat …... • Braking distance of a car …... • Final 102 mark …... • Post-Lecture Exercise …...

  4. Factory Production

  5. Factory Production

  6. MATHS 102Lecture 3/0 • Administration • An Example • Formal Functions • Types of Functions

  7. Administration • Reminders • Assumed knowledge • Sources of help / Office hours David: MTWTh 8-9 Bill: MTWTh 9-10 Ye Yoon: MTWTh 10-11 • New Items • Class Reps • Computer access

  8. MATHS 102Lecture 3/0 • Administration • An Example • Formal Functions • Types of Functions

  9. Preliminary Exercise • x • x + 16 • 2(x + 16) • 2(x + 16) – 14 • 2{2(x + 16) – 14} • 2{2(x + 16) – 14} – x • [2{2(x + 16) – 14} – x]/3 – x • [2{2(x + 16) – 14} – x]/3 – x + 4 • √([2{2(x + 16) – 14} – x]/3 – x + 4)

  10. Preliminary Exercise • √([2{2(x + 16) – 14} – x]/3 – x + 4) • √([2{2x + 32 – 14} – x]/3 – x + 4) • √([2{2x + 18} – x]/3 – x + 4) • √([4x + 36 – x]/3 – x + 4) • √([3x + 36]/3 – x + 4) • √(x + 12 – x + 4) • √(16) • 4

  11. Surface area of a cylinder of height 10cmS = 2πr2 + 20πr Radius Surface Area 2cm 150.8cm2 4cm 351.9cm2 6cm cm2 8cm 10cm

  12. MATHS.102Lecture 3/0 • Administration • An Example • Formal Functions • Types of Functions

  13. Domains & Games • The domain is a set (of numbers) which is the starting set. • The second part of a function is the rule which associates a particular value with every member of the domain. • What are sensible domains for: • The cost of n tomatoes ? • The cost of n kilos of tomatoes ? • The length of a piece of metal at a given temperature ? • The function g(x) = 100/x

  14. Algebraic formulations ... • S = 2πr2 + 20πr • S: r —> 2πr2 + 20πr • S(r) = 2πr2 + 20πr

  15. MATHS.102Lecture 3/0 • Administration • An Example • Formal Functions • Types of Functions

  16. Functions can be expressed ... • Algebraically • Graphically • As a Table.

  17. Functions with which you may be familiar.What shape are they ? • linear • quadratic • cubic & other polynomial • exponential & logarithmic • periodic (sines, cosines) • hyperbolic

  18. Lecture 3/0 – Summary • Functions are a key idea in mathematics. • The idea of a function can be used in many different situations • Functions map objects (numbers) from one set (the domain) to another (the range).

  19. MATHS 102 Lecture 3/0 • Before the next lecture........ Go over Lecture 3/0 in your notes Do the Post-Lecture exercise p13 Do the Preliminary Exercise p14 • See you tomorrow ........

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