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Rules of differentiationPowerPoint Presentation

Rules of differentiation

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Rules of differentiation

REVIEW:

Antiderivative (indefinite integral)

Antiderivative (indefinite integral)

Integrating data: the trapezoidal rule

Very similar!

Another angle: the upper limit as an argument

Another angle: the upper limit as an argument

Another angle: the upper limit as an argument

Differential equations

Algebraicequation: involves functions; solutions are numbers.

Differential equation: involves derivatives; solutions are functions.

INITIAL CONDITION

Superposition(linear, homogeneous equations)

Can build a complex solution from the sum of two or more simpler solutions.

Superposition(linear, inhomogeneous equations)

Superposition(linear, inhomogeneous equations)

Superposition(nonlinear equations)

ORDINARY differential equation (ODE): solutions are univariate functions

PARTIAL differential equation (PDE): solutions are multivariate functions

Exponential functions: start with ODE

Analytical solution

Exponential functions: start with ODE

Analytical solution

Differentiation, integration

(chain rule)

Properties of the exponential function

Taylor series:

Sum rule:

Power rule:

Derivative

Indefinite integral

Homework:

- Do exercises for section 2.6, 2.8 and 2.9. Omit 2.9, #1.
- This will include:
- Exercise with antiderivatives and classifying ODEs.
- Carbon dating (for Thursday field trip)
- Derive further well-known functions from f’’=-f

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