MIT Concourse 18.03  Ordinary Differential Equations  Supplementary Materials
18.03 Notes (Arthur Mattuck)  Exercises and Solutions  
D. Definite Integral Solutions G. Graphical and Numerical Methods O. Linear Differential Operators S. Stability 
LS.1. Linear Systems: Review of Linear Algebra LS.2. Homogeneous Linear Systems with Constant Coefficients LS.3. Complex and Repeated Eigenvalues LS.4. Decoupling Systems LS.5. Theory of Linear Systems LS.6. Solution Matrices GS.16. Graphing ODE Systems GS.78. Structural stability LC. Limit Cycles 
1. First Order ODE's Solutions 2. Higher Order ODE's Solutions 
18.03 Supplementary Notes (Haynes Miller, Spring 2010) These notes (Spring 2010 version) were written by Prof. Haynes Miller and were designed to supplement the Edwards & Penney textbook. They are available as individual chapters below or compiled into a complete set. (PDF  1.5MB) 

Preface (PDF)  Chapter 1: Notation and Language (PDF) 1.1. Dependent and Independent Variables 1.2. Equations and Parametrizations 1.4. Parametrizing the Set of Solutions of a Differential Equation 1.5. Solutions of ODEs 
Chapter 2: Modeling by First Order Linear ODEs (PDF) 2.1. The Savings Account Model 2.2. Linear Insulation 2.3. System, Signal, System Response 
Chapter 3: Solutions of First Order Linear ODEs (PDF) 3.1. Homogeneous and Inhomogeneous; Superposition 3.2. Variation of Parameters 3.3. Continuation of Solutions 3.4. Final Comments on the Bank Account Model 
Chapter 4: Sinusoidal Solutions (PDF) 4.1. Periodic and Sinusoidal Functions 4.2. Periodic Solutions and Transients 4.3. Amplitude and Phase Response 
Chapter 5: The Algebra of Complex Numbers (PDF) 5.1. Complex Algebra 5.2. Conjugation and Modulus 5.3. The Fundamental Theorem of Algebra 
Chapter 6: The Complex Exponential (PDF) 6.1. Exponential Solutions 6.2. The Complex Exponential 6.3. Polar Coordinates 6.4. Multiplication 6.5. Roots of Unity and Other Numbers 
Chapter 7: Beats (PDF) 7.1. What Beats Are 7.2. What Beats Are Not 
Chapter 8: RLC Circuits (PDF) 8.1. Series RLC Circuits 8.2. A Word About Units 8.3. Implications 
Chapter 9: Normalization of Solutions (PDF) 9.1. Initial Conditions 9.2. Normalized Solutions 9.3. ZSR/ZIR 
Chapter 10: Operators and the Exponential Response Formula (PDF) 10.1. Operators 10.2. LTI Operators and Exponential Signals 10.3. Sinusoidal Signals 10.4. Damped Sinusoidal Signals 10.5. Time Invariance 
Chapter 11: Undetermined Coefficients (PDF) 
Chapter 12: Resonance and the Exponential Shift Law (PDF) 12.1. Exponential Shift 12.2. Product Signals 12.3. Resonance 12.4. Higher Order Resonance 12.5. Summary 
Chapter 13: Natural Frequency and Damping Ratio (PDF) 
Chapter 14: Frequency Response (PDF) 14.1. Driving Through the Spring 14.2. Driving Through the Dashpot 14.3. Second Order Frequency Response Using Damping Ratio 
Chapter 15: The Wronskian (PDF) 
Chapter 16: More on Fourier Series (PDF) 16.1. Symmetry and Fourier Series 16.2. Symmetry about Other Points 16.3 The Gibbs Effect 16.4. Fourier Distance 16.5. Complex Fourier Series 16.6 Harmonic Response 
Chapter 17: Impulses and Generalized Functions (PDF) 17.1. From Bank Accounts to the Delta Function 17.2. The Delta Function 17.3. Integrating Generalized Functions 17.4. The Generalized Derivative 
Chapter 18: Impulse and Step Responses (PDF) 18.1. Impulse Response 18.2. Impulses in Second Order Equations 18.3. Singularity Matching 81.4. Step Response 
Chapter 19: Convolution (PDF) 19.1. Superposition of Infinitesimals: The Convolution Integral 19.2. Example: The Build Up of a Pollutant in a Lake 19.3. Convolution as a Product 
Chapter 20: Laplace Transform Technique: Coverup (PDF) 20.1. Simple Case 20.2. Repeated Roots 20.3. Completing The Square. Suppose 20.4. Complex Coverup 20.5. Complete Partial Fractions 
Chapter 21: The Laplace Transform and Generalized Functions (PDF) 21.1. Laplace Transform of Impulse and Step Responses 21.2. What the Laplace Transform Doesn't Tell Us 21.3. Worrying about t = 0 21.4. The tderivative Rule 21.5. The Initial Singularity Formula 21.7. The Initial Value Formula 21.8. Initial Conditions 
Chapter 22: The Pole Diagram and the Laplace Transform (PDF) 22.1. Poles and the Pole Diagram 22.2. The Pole Diagram of the Laplace Transform 22.3. The Laplace Transform Integral 22.4. TranLaplace Transform 
Chapter 23: Amplitude Response and the Pole Diagram (PDF) 
Chapter 24: The Laplace Transform and more General Systems (PDF) 22.1. Zeros of the Laplace Transform: Stillness in Motion 22.2. General LTI Systems 
Chapter 25: First Order Systems and Second Order Equations (PDF) 25.1. The Companion System 25.2. Initial Value Problems 
Chapter 26: Phase Portraits in Two Dimensions (PDF) 26.1. Phase Portraits and Eigenvectors 26.2. The (tr, det) Plane and Structural Stability 26.3. The Portrait Gallery 
Appendices Appendix A. The KermackMcKendrick Equation (PDF) Appendix B. The Tacoma Narrows Bridge: Resonance vs Flutter (PDF) Appendix C. Linearization: The Phugoid Equation as Example (PDF) 
Notes ©Arthur Mattuck and M.I.T. 1988, 1992, 1996, 2003, 2007.
Suppementary Notes
©Haynes Miller and M.I.T. 2004, 2006, 2008, and 2010.
Concourse 18.03 Lecture Notes
©Robert Winters 20132019.