Arthur Mattuck

Professor of Mathematics

1 course · 21 total lectures · 17h recorded

Mathematics Engineering, Control & Robotics Physics & Cosmology

Courses by Arthur Mattuck

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Complete university lecture series taught by Arthur Mattuck.

MIT 18.03: Differential Equations

MIT · 18.0321 lectures · 17h

Mathematics·undergraduate

Differential Equations

Prof. Arthur Mattuck·MIT

Direction fields, first-order and second-order linear ODEs, complex exponentials, resonance, Fourier series, Laplace transforms, Dirac delta impulses, and linear systems.

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All lectures by Arthur Mattuck

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Direction Fields and Integral Curves (MIT 18.03, Lecture 1)

Direction Fields and Integral Curves (MIT 18.03, Lecture 1)

18.03 · Lec 1 · Arthur Mattuck · MIT

Arthur Mattuck MIT

48:56

Euler's Numerical Method for y'=f(x,y) and its Generalizations (MIT 18.03, Lecture 2)

Euler's Numerical Method for y'=f(x,y) and its Generalizations (MIT 18.03, Lecture 2)

18.03 · Lec 2 · Arthur Mattuck · MIT

Arthur Mattuck MIT

50:45

First-order Linear ODEs: Steady-state and Transient Solutions (MIT 18.03, Lecture 3)

First-order Linear ODEs: Steady-state and Transient Solutions (MIT 18.03, Lecture 3)

18.03 · Lec 3 · Arthur Mattuck · MIT

Arthur Mattuck MIT

50:22

First-order Autonomous ODEs: Qualitative Methods and Applications (MIT 18.03 Differential Equations, Lecture 5)

First-order Autonomous ODEs: Qualitative Methods and Applications (MIT 18.03 Differential Equations, Lecture 5)

18.03 · Lec 5 · Arthur Mattuck · MIT

Arthur Mattuck MIT

45:46

Complex Numbers and Complex Exponentials (MIT 18.03, Lecture 6)

Complex Numbers and Complex Exponentials (MIT 18.03, Lecture 6)

18.03 · Lec 6 · Arthur Mattuck · MIT

Arthur Mattuck MIT

45:28

First-order Linear Differential Equations with Constant Coefficients (MIT 18.03, Lecture 7)

First-order Linear Differential Equations with Constant Coefficients (MIT 18.03, Lecture 7)

18.03 · Lec 7 · Arthur Mattuck · MIT

Arthur Mattuck MIT

41:10

First-Order Substitution Methods: Bernoulli and Homogeneous ODEs (MIT 18.03, Lecture 4)

First-Order Substitution Methods: Bernoulli and Homogeneous ODEs (MIT 18.03, Lecture 4)

18.03 · Lec 4 · Arthur Mattuck · MIT

Arthur Mattuck MIT

50:14

Lecture 19: Introduction to the Laplace Transform; Basic Formulas (18.03)

Lecture 19: Introduction to the Laplace Transform; Basic Formulas (18.03)

18.03 · Lec 18 · Arthur Mattuck · MIT

Arthur Mattuck MIT

47:40

Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases (18.03)

Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases (18.03)

18.03 · Lec 9 · Arthur Mattuck · MIT

Arthur Mattuck MIT

50:01

Lecture 15: Introduction to Fourier Series; Basic Formulas for Period 2π (18.03)

Lecture 15: Introduction to Fourier Series; Basic Formulas for Period 2π (18.03)

18.03 · Lec 15 · Arthur Mattuck · MIT

Arthur Mattuck MIT

49:32

Lecture 11: Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians (18.03)

Lecture 11: Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians (18.03)

18.03 · Lec 11 · Arthur Mattuck · MIT

Arthur Mattuck MIT

50:32

Lecture 8: Applications to Temperature, Mixing, RC-Circuit, Decay, and Growth Models (18.03)

Lecture 8: Applications to Temperature, Mixing, RC-Circuit, Decay, and Growth Models (18.03)

18.03 · Lec 8 · Arthur Mattuck · MIT

Arthur Mattuck MIT

50:36

Lecture 10: Complex Characteristic Roots; Undamped and Damped Oscillations (18.03)

Lecture 10: Complex Characteristic Roots; Undamped and Damped Oscillations (18.03)

18.03 · Lec 10 · Arthur Mattuck · MIT

Arthur Mattuck MIT

46:24

Lecture 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's (18.03)

Lecture 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's (18.03)

18.03 · Lec 19 · Arthur Mattuck · MIT

Arthur Mattuck MIT

51:08

Lecture 21: Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems (18.03)

Lecture 21: Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems (18.03)

18.03 · Lec 20 · Arthur Mattuck · MIT

Arthur Mattuck MIT

44:20

Lecture 13: Finding Particular Solutions to Inhomogeneous ODE's: Operator and Solution Formulas Involving Exponentials (18.03)

Lecture 13: Finding Particular Solutions to Inhomogeneous ODE's: Operator and Solution Formulas Involving Exponentials (18.03)

18.03 · Lec 13 · Arthur Mattuck · MIT

Arthur Mattuck MIT

47:56

Lecture 12: General Theory for Inhomogeneous ODE's; Stability Criteria for Constant-coefficient ODE's (18.03)

Lecture 12: General Theory for Inhomogeneous ODE's; Stability Criteria for Constant-coefficient ODE's (18.03)

18.03 · Lec 12 · Arthur Mattuck · MIT

Arthur Mattuck MIT

46:24

Lecture 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds (18.03)

Lecture 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds (18.03)

18.03 · Lec 17 · Arthur Mattuck · MIT

Arthur Mattuck MIT

45:47

Lecture 16: More General Periods; Even and Odd Functions; Periodic Extension (18.03)

Lecture 16: More General Periods; Even and Odd Functions; Periodic Extension (18.03)

18.03 · Lec 16 · Arthur Mattuck · MIT

Arthur Mattuck MIT

49:29

Lecture 14: Interpretation of the Exceptional Case: Resonance (18.03)

Lecture 14: Interpretation of the Exceptional Case: Resonance (18.03)

18.03 · Lec 14 · Arthur Mattuck · MIT

Arthur Mattuck MIT

44:26