Rules of differentiation

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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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Monday Sept 14th: Univariate Calculus 2

Integrals

ODEs

Exponential functions

Differential equations

Algebraicequation: involves functions; solutions are numbers.

Differential equation: involves derivatives; solutions are functions.

INITIAL CONDITION

Classification of ODEs

Linearity:

Homogeneity:

Order:

Superposition(linear, homogeneous equations)

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

ORDINARY differential equation (ODE): solutions are univariate functions

PARTIAL differential equation (PDE): solutions are multivariate functions

Qualitative solution:

slope=1

1

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