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# Rules of differentiation - PowerPoint PPT Presentation

Rules of differentiation. REVIEW:. The Chain Rule. Taylor series. Approximating the derivative. Monday Sept 14th: Univariate Calculus 2. Integrals ODEs Exponential functions. Antiderivative (indefinite integral). Antiderivative (indefinite integral).

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REVIEW:

### Monday Sept 14th: Univariate Calculus 2

Integrals

ODEs

Exponential functions

Antiderivative (indefinite integral)

Antiderivative (indefinite integral)

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

Algebraicequation: involves functions; solutions are numbers.

Differential equation: involves derivatives; solutions are functions.

INITIAL CONDITION

Linearity:

Homogeneity:

Order:

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

Qualitative solution:

slope=1

1

Analytical solution

Analytical solution

(chain rule)

Taylor series:

Sum rule:

Power rule:

Derivative

Indefinite integral

• 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