# MIT 18.03SC Differential Equations, Fall 2011

#### Differential equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Created by MIT OpenCourseWare.

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1: Separable Equations | MIT 18.03SC Differential Equations, Fall 2011

2: Exploration of the Amplitude and Phase: First Order Applet

3: Lec 1 | MIT 18.03 Differential Equations, Spring 2006

4: Exploration of the Isoclines Applet

5: Direction Fields | MIT 18.03SC Differential Equations, Fall 2011

6: Lec 2 | MIT 18.03 Differential Equations, Spring 2006

7: Exploration of the Euler's Method Applet

8: Euler's Method | MIT 18.03SC Differential Equations, Fall 2011

9: Lec 3 | MIT 18.03 Differential Equations, Spring 2006

10: Linear Equations | MIT 18.03SC Differential Equations, Fall 2011

11: Solutions of First-order Linear Equations | MIT 18.03SC Differential Equations, Fall 2011

12: Lec 6 | MIT 18.03 Differential Equations, Spring 2006

13: Complex Numbers and Euler's Formula | MIT 18.03SC Differential Equations, Fall 2011

14: Lec 8 | MIT 18.03 Differential Equations, Spring 2006

15: Sinusoidal Functions | MIT 18.03SC Differential Equations, Fall 2011

16: Lec 7 | MIT 18.03 Differential Equations, Spring 2006

17: First-order Constant Coefficient Linear ODE's | MIT 18.03SC Differential Equations, Fall 2011

18: Sinusoidal Inputs | MIT 18.03SC Differential Equations, Fall 2011

19: Lec 5 | MIT 18.03 Differential Equations, Spring 2006

20: Exploration of the Phase Lines Applet

21: Lec 9 | MIT 18.03 Differential Equations, Spring 2006

22: Autonomous Equations and Phase Lines | MIT 18.03SC Differential Equations, Fall 2011

23: Homogeneous Constant Coefficient Equations: Any Roots | MIT 18.03SC Differential Equations

24: Homogeneous Constant Coefficient Equations: Real Roots | MIT 18.03SC Differential Equations

25: Lec 10 | MIT 18.03 Differential Equations, Spring 2006

26: Exploration of the Damped Vibrations Applet

27: Damped Harmonic Oscillators | MIT 18.03SC Differential Equations, Fall 2011

28: Lec 11 | MIT 18.03 Differential Equations, Spring 2006

29: Lec 12 | MIT 18.03 Differential Equations, Spring 2006

30: Lec 13 | MIT 18.03 Differential Equations, Spring 2006

31: Forced Oscillations | MIT 18.03SC Differential Equations, Fall 2011

32: Gain and Phase Lag | MIT 18.03SC Differential Equations, Fall 2011

33: Undetermined Coefficients | MIT 18.03SC Differential Equations, Fall 2011

34: Lec 14 | MIT 18.03 Differential Equations, Spring 2006

35: Pure Resonance | MIT 18.03SC Differential Equations, Fall 2011

36: Exploration of the Amplitude and Phase: Second Order II Applet

37: Frequency Response | MIT 18.03SC Differential Equations, Fall 2011

38: Lec 15 | MIT 18.03 Differential Equations, Spring 2006

39: Lec 16 | MIT 18.03 Differential Equations, Spring 2006

40: Computing Fourier Series | MIT 18.03SC Differential Equations, Fall 2011

41: Exploration of the Fourier Coefficient Applet

42: Manipulating Fourier Series | MIT 18.03SC Differential Equations, Fall 2011

43: Lec 17 | MIT 18.03 Differential Equations, Spring 2006

44: Linear ODE's with Periodic Input | MIT 18.03SC Differential Equations, Fall 2011

45: Step and Delta Functions | MIT 18.03SC Differential Equations, Fall 2011

46: Unit Step and Impulse Response | MIT 18.03SC Differential Equations, Fall 2011

47: Lec 21 | MIT 18.03 Differential Equations, Spring 2006

48: Exploration of the Convolution Accumulation Applet

49: Convolution and Green's Formula | MIT 18.03SC Differential Equations, Fall 2011

50: Lec 19 | MIT 18.03 Differential Equations, Spring 2006

51: Lec 20 | MIT 18.03 Differential Equations, Spring 2006

52: Laplace Transform: Basics | MIT 18.03SC Differential Equations, Fall 2011

53: Partial Fractions and Laplace Inverse | MIT 18.03SC Differential Equations, Fall 2011

54: Laplace: Solving ODE's | MIT 18.03SC Differential Equations, Fall 2011

55: Pole Diagrams | MIT 18.03SC Differential Equations, Fall 2011

56: Lec 24 | MIT 18.03 Differential Equations, Spring 2006

57: Linear Systems of Equations | MIT 18.03SC Differential Equations, Fall 2011

58: Lec 25 | MIT 18.03 Differential Equations, Spring 2006

59: Lec 26 | MIT 18.03 Differential Equations, Spring 2006

60: Linear Systems: Complex Roots | MIT 18.03SC Differential Equations, Fall 2011

61: Linear Systems: Matrix Methods | MIT 18.03SC Differential Equations, Fall 2011

62: Lec 27 | MIT 18.03 Differential Equations, Spring 2006

63: Phase Portraits | MIT 18.03SC Differential Equations, Fall 2011

64: Trace-Determinant Diagram | MIT 18.03SC Differential Equations, Fall 2011

65: Lec 28 | MIT 18.03 Differential Equations, Spring 2006

66: Lec 29 | MIT 18.03 Differential Equations, Spring 2006

67: Matrix Exponentials | MIT 18.03SC Differential Equations, Fall 2011

68: Lec 30 | MIT 18.03 Differential Equations, Spring 2006

69: Lec 33 | MIT 18.03 Differential Equations, Spring 2006

70: Lec 31 | MIT 18.03 Differential Equations, Spring 2006

71: Linearization | MIT 18.03SC Differential Equations, Fall 2011

72: Lec 32 | MIT 18.03 Differential Equations, Spring 2006