Lecture 9 Notes

Lecture 9 Notes - Today Introduction to systems of...

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Today • Introduction to systems of equations • Direction Felds • Eigenvalues and eigenvectors • ±inding the general solution (distinct e-value case) • Return midterm 1
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Introduction to systems of equations
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Introduction to systems of equations • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function.
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Introduction to systems of equations • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples:
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Introduction to systems of equations • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v:
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Introduction to systems of equations mx °° + γ x ° + kx =0 • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v:
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Introduction to systems of equations mx °° + γ x ° + kx =0 x ° = v • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v:
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Introduction to systems of equations mx °° + γ x ° + kx =0 x °° = v ° x ° = v • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v:
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Introduction to systems of equations mx °° + γ x ° + kx =0 x °° = v ° x ° = v mv ° + γ v + • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v:
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Introduction to systems of equations mx °° + γ x ° + kx =0 x °° = v ° x ° = v mv ° + γ v + v ° = γ m v k m x • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v:
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Introduction to systems of equations mx °° + γ x ° + kx =0 x °° = v ° x ° = v mv ° + γ v + v ° = γ m v k m x • So far, we’ve only dealt with equations with one unknown function. Sometimes, we’ll be interested in more than one unknown function. • Examples: • position of object in one dimensional space in terms of x, v: x ° = v v ° = k m x γ m v
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Introduction to systems of equations mx °° + γ x ° + kx =0 x °° = v ° x ° = v mv ° + γ v + v ° = γ m v k m x • So far, we’ve only dealt with equations with one unknown function.
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Lecture 9 Notes - Today Introduction to systems of...

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