Hyperbolic Functions Who Needs Them?

1
Hyperbolic FunctionsWho Needs Them?

• Chapter 6.9

2
The gentle arc of a suspension bridge or the
complex geometry of Einsteins Theory of
Relativity provide us with real-life examples of
Hyperbolic Functions!
3
Basic Definitions

• The hyperbolic functions are built out of the
  exponential function
• We can form other hyperbolic functions

4
Contrasting Circular Functions with Hyperbolic
Functions
5
Review Identities

• Pg 478 Basic Relations
• Pg 479 - Derivative Patterns
• Pg 481 - Inverse and Derivative of Inverse
  Patterns
• Pg 483 Integral Patterns

6
Compare and Contrast

• The hyperbolic functions, their inverses and
  derivatives often appear very similar to the
  circular functions (sin, cos etc)
• So how do I remember all this stuff?
• You dont! Just be sure to understand that these
  are a new set of functions with some important
  similarities and differences with the ordinary
  circular functions. You will learn some of the
  easier patterns but in general it is fair to rely
  on Tables or Computer Algebra Systems.

7
Samples

• Pg 484 11, 21, 27, 47, 69