Arthur Mattuck

Courses

1. 

   Differential Equations

   MIT / Mathematics
   Arthur Mattuck
   

Lectures

1. 
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   Non-Linear Systems and First-Order ODE's

   MIT /
   Arthur Mattuck
   
2. 
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   The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves

   MIT /
   Arthur Mattuck
   
3. 
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   Euler's Numerical Method for y'=f(x,y) and its Generalizations

   MIT /
   Arthur Mattuck
   
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   Solving First-order Linear ODE's; Steady-state and Transient Solutions

   MIT /
   Arthur Mattuck
   
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   First-order Substitution Methods: Bernouilli and Homogeneous ODE's

   MIT /
   Arthur Mattuck
   
6. 
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   First-order Autonomous ODE's: Qualitative Methods, Applications

   MIT /
   Arthur Mattuck
   
7. 
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   Complex Numbers and Complex Exponentials

   MIT /
   Arthur Mattuck
   
8. 
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   First-Order Linear with Constant Coefficients

   MIT /
   Arthur Mattuck
   
9. 
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   Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models

   MIT /
   Arthur Mattuck
   
10. 
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    Solving Second-Order Linear ODE's with Constant Coefficients

    MIT /
    Arthur Mattuck
    
11. 
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    Complex Characteristic Roots; Undamped and Damped Oscillations

    MIT /
    Arthur Mattuck
    
12. 
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    Second-Order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians

    MIT /
    Arthur Mattuck
    
13. 
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    Inhomogeneous ODE's; Stability Criteria for Constant-Coefficient ODE's

    MIT /
    Arthur Mattuck
    
14. 
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    Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials

    MIT /
    Arthur Mattuck
    
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    Interpretation of the Exceptional Case: Resonance

    MIT /
    Arthur Mattuck
    
16. 
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    Introduction to Fourier Series; Basic Formulas for Period 2(pi)

    MIT /
    Arthur Mattuck
    
17. 
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    More General Periods; Even and Odd Functions; Periodic Extension

    MIT /
    Arthur Mattuck
    
18. 
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    Finding Particular Solutions via Fourier Series; Resonant Terms

    MIT /
    Arthur Mattuck
    
19. 
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    Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's

    MIT /
    Arthur Mattuck
    
20. 
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    Convolution Formula: Proof, Connection with Laplace Transform, Application

    MIT /
    Arthur Mattuck