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Final Exam
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2022-07-11 20:16:01
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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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