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Differential Equations >> Content Detail



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Readings

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This section contains documents created from scanned original files, which are inaccessible to screen reader software. A "#" symbol is used to denote such documents.

Listed in the table below are reading assignments for each lecture session.

"EP" refers to the course textbook: Amazon logo Edwards, C., and D. Penney. Elementary Differential Equations with Boundary Value Problems. 5th ed. Upper Saddle River, NJ: Prentice Hall, 2003. ISBN: 013145773X.

The 4th edition (Amazon logo ISBN: 0130113018) differs slightly. If a reference to the Fourth Edition differs, I will indicate it by writing "IV: . . . ."

"SN" refers to the "18.03 Supplementary Notes" written by Prof. Miller.

"Notes" refers to the "18.03 Notes and Exercises" written by Prof. Mattuck.


SES #TOPICSREADINGS
I. First-order Differential Equations
L0Simple Models and Separable EquationsEP: 1.1 and 1.4
L1Direction Fields, Existence and Uniqueness of SolutionsEP: 1.2 and 1.3

Notes: G.1 (PDF)#

SN: 1 (PDF)
L2Numerical MethodsEP: 6.1 and 6.2

Notes: G.2 (PDF)#
L3Linear Equations: ModelsEP: 1.5

SN: 2 (PDF)
L4Solution of Linear Equations, Variation of ParameterEP: 1.5

SN: 3 (PDF)
L5Complex Numbers, Complex ExponentialsSN: 5 (PDF)

SN: 6 (PDF)

Notes: C.1-3 (PDF)
L6Roots of Unity; Sinusoidal FunctionsSN: 4 (PDF)

Notes: C.4 (PDF) and IR.6 (PDF)#
L7Linear System Response to Exponential and Sinusoidal Input; Gain, Phase LagSN: 4 (PDF)

Notes: IR.6 (PDF)#
L8Autonomous Equations; The Phase Line, StabilityEP: 1.7 and 7.1
L9Linear vs. Nonlinear
L10Hour Exam I
II. Second-order Linear Equations
L11The Spring-mass-dashpot Model; Superposition Characteristic Polynomial; Real Roots; Initial ConditionsEP: 2.1, 2.2, and 2.3 upto "Polynomial Operators"

SN: 9 (PDF)
L12Complex Roots; Damping ConditionsEP: 2.3 and 2.4
L13Inhomogeneous Equations, SuperpositionEP: 2.6, pp. 157-159 only, (See SN 7 (PDF) if you want to learn about beats)

Notes: O.1 (PDF)
L14Operators and Exponential SignalsEP: 2.6, pp. 165-167

SN: 10 (PDF)

Notes: O.1, 2, and 4 (PDF)
L15Undetermined CoefficientsEP: 2.5, pp. 144-153

SN: 11 (PDF)
L16Frequency ResponseSN: 14 (PDF)
L17Applications: Guest Appearance by EECS Professor Jeff Lang
L18Exponential Shift Law; ResonanceSN: 12 (PDF)

Notes: O.3 (PDF)
L19Hour Exam II
III. Fourier Series
L20Fourier SeriesEP: 8.1
L21Operations on Fourier SeriesEP: 8.2 and 8.3
L22Periodic Solutions; ResonanceEP: 8.3 and 8.4
IV. The Laplace Transform
L23Step Function and Delta FunctionSN: 17 (PDF)
L24Step Response, Impulse ResponseSN: 18 (PDF)

Notes: IR (PDF)#
L25ConvolutionEP: 4.1
L26Laplace Transform: Basic Properties
L27Application to ODEs; Partial FractionsEP: 4.2 and 4.3

SN: 20 (PDF)

Notes: H
L28Completing the Square; Time Translated FunctionsEP: 4.5-4.6

SN: 20 (PDF)
L29Pole DiagramSN: 22 (PDF)
L30Hour Exam III
V. First Order Systems
L31Linear Systems and MatricesEP: 5.1-5.3

SN: 24 (PDF)

Notes: LS.1 (PDF)
L32Eigenvalues, EigenvectorsEP: 5.4

Notes: LS.2 (PDF)
L33Complex or Repeated EigenvaluesEP: 5.4

Notes: LS.3 (PDF)
L34Qualitative Behavior of Linear Systems; Phase PlaneSN: 25 (PDF)
L35Normal Modes and the Matrix ExponentialEP: 5.7

Notes: LS.6 (PDF)
L36Inhomogeneous Equations: Variation of Parameters AgainEP: 5.8
L37Nonlinear SystemsEP: 7.2 and 7.3

Notes: GS (PDF)#
L38Examples of Nonlinear SystemsEP: 7.4 and 7.5

Notes: GS (PDF)#
L39Chaos
L40Final Exam

 








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