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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

Monday Sept 14th: Univariate Calculus 2

Integrals

ODEs

Exponential functions

differential equations
Differential equations

Algebraicequation: involves functions; solutions are numbers.

Differential equation: involves derivatives; solutions are functions.

INITIAL CONDITION

classification of odes
Classification of ODEs

Linearity:

Homogeneity:

Order:

superposition linear homogeneous equations
Superposition(linear, homogeneous equations)

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

slide22

ORDINARY differential equation (ODE): solutions are univariate functions

PARTIAL differential equation (PDE): solutions are multivariate functions

slide23

Exponential functions: start with ODE

Qualitative solution:

slope=1

1

properties of the exponential function
Properties of the exponential function

Taylor series:

Sum rule:

Power rule:

Derivative

Indefinite integral

homework
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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