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Unit 1: First Order Differential Equations

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  • Conventions
  • Basic DE's
  • Geometric Methods
  • Numerical Methods
  • Linear ODE's
  • Integrating Factors
  • Complex Arithmetic
  • Sinusoidal Functions
  • Constant Coefficient
  • Exponential Input
  • Autonomous Equations
  • Linear VS NonLinear

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  • Unit 1: First Order Differential Equations
    • Conventions
    • Basic DE's
    • Geometric Methods
    • Numerical Methods
    • Linear ODE's
    • Integrating Factors
    • Complex Arithmetic
    • Sinusoidal Functions
    • Constant Coefficient
    • Exponential Input
    • Autonomous Equations
    • Linear VS NonLinear
  • Unit 2: Second Order Constant Coefficient Linear Equation
    • Characteristic Equation
    • Damped Oscillators
    • Exponential Response
    • Gain and Phase Lag
    • Undetermined Coefficients
    • Linear Operators
    • Pure Resonance
    • Frequency Response and Practical Response
    • Applications
    • Exams 2
  • Unit 3: Fourier Series And Laplace Transform
    • Fourier Series: Basics
    • Operations
    • Periodic Input
    • Step and Delta
    • Impulse Response
    • Convolution
    • Laplace Transform
    • Partial Fractions
    • Solving IVP's
    • Transfer Functions
    • Poles
    • Exams 3
  • Unit 4: First-Order Systems
    • Linear Systems
    • Matrix Methods
    • Phase Portraits
    • Matrix Exponentials
    • NonLinear Systems
    • Linearization
    • Limit Cycles And Chaos
  • Final Exam
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