12.5 Differentiable Equations

12.5.1 Antiderivatives

A slightly different look at antiderivatives and introducing some new terminology: The indefinite integral.

Resources:

  • Notes
  • Antiderivative/Integral formulas

Assignment:

  • p312 #1-23, 45, 47

 

Attachments:
FileDescriptionFile size
Download this file (5.1.notes.pdf)5.1.notes.pdf 156 kB
Download this file (5.1b.formulas.pdf)5.1b.formulas.pdf 84 kB

12.5.4 Separable Differential Equations

When a derivative is expressed with both variables, it is very likely to have been differentiated using implicit differentiation.  It becomes important to separate the variables and differentiate each side separately.  Then, you may, or may not be able to write the resulting equation using function notation, depending on the equation itself.

Resources

  • Warmup: indefinite integrals
  • Notes: Separable differential equations

Assignment:

  • p322 #39-44

Things you should be able to do after today:

  • integrate derivatives that are expressed in terms of both x and y
  • use separable differentiable equations to integrate derivatives  in terms of both x and y where substitution may be needed
Attachments:
FileDescriptionFile size
Download this file (5.4.notes.pdf)5.4.notes.pdf 301 kB

Login Form