Lecture_24_E7_L24_Introduction_ODE

# Lecture_24_E7_L24_Introduction_ODE - Midterm 3 Results...

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E7 L24 1 Midterm 3 Results Midterm 3 Results (Statistics courtesy of Ken Hsu) mean = 72, stdev ≈ 16 (17%) Exam was not easy. particularly last problem Yet, most people did well. Good Job!

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E7 L24 2 Midterm 3 Results Midterm 3 Results (Statistics courtesy of Ken Hsu) Most people did not answer the last problem. 0 5 10 0 50 100 Problem 1 Score Number of Students Mean: 8.5621, Std: 1.5442 0 5 10 0 100 200 300 Problem 2 Score Mean: 8.7549, Std: 2.5367 0 5 10 0 50 100 150 Problem 3 Score Mean: 8.2092, Std: 2.3446 0 5 10 0 100 200 300 Problem 4 Score Mean: 9.3529, Std: 1.9535 0 5 10 0 100 200 300 Problem 5 Score Mean: 7.5458, Std: 4.0057 0 5 10 0 20 40 60 80 Problem 6 Score Mean: 7.1667, Std: 2.3723 0 5 10 0 50 100 150 Problem 7 Score Mean: 6.7418, Std: 3.4378 0 5 10 0 50 100 150 200 Problem 8 Score Mean: 7.4379, Std: 3.6598 0 5 10 0 50 100 150 200 Problem 9 Score Mean: 7.268, Std: 3.6736 0 5 10 0 100 200 300 Problem 10 Score Mean: 0.97059, Std: 2.6592 0 50 100 0 20 40 60 Total Score Mean: 72.0098, Std: 15.7608
E7 L24 3 E7: INTRODUCTION TO COMPUTER E7: INTRODUCTION TO COMPUTER PROGRAMMING FOR SCIENTISTS AND PROGRAMMING FOR SCIENTISTS AND ENGINEERS ENGINEERS Lecture Outline 1. Introduction to ordinary differential equations 2. Numerical solution of ordinary differential equations using Matlab 3. 3.Examples Copyright 2007, Horowitz, Packard. This work is licensed under the Creative Commons Attribution-Share Alike License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/2.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

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E7 L24 4 Introduction to differential equations Introduction to differential equations Applying the “conservation laws” that make up a scientific field often leads to differential equations: Mechanics: “rate of change of linear momentum of a mass particle” equals the forces applied to the particle. Thermodynamics: “rate of change of internal energy of a system” equals the net flow of energy into the system. Chemistry: “rate of change of concentration of a molecule” equals a sum of terms proportional to the products of concentrations of other molecules.
E7 L24 5 Introduction to differential equations Introduction to differential equations Applying the “conservation laws” that make up a scientific field often leads to differential equations: Rate of change means derivative. Notation: ( ) dy x dx ( ) ( ) dy t y t dt = & first derivative of y with respect to its argument ( x ) first derivative of y with respect to time t

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E7 L24 6 Introduction to differential equations Introduction to differential equations Applying the “conservation laws” that make up a scientific field often leads to differential equations: Rate of change means derivative. Notation: 2 2 ( ) ( ) d y t y t dt = && 3 3 ( ) ( ) d y t y t dt = &&& second derivative of y with respect to time t third derivative of y with respect to time t
E7 L24 7 Introduction to differential equations Introduction to differential equations Applying the “conservation laws” that make up a scientific field often leads to differential equations: Rate of change means derivative.

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## Lecture_24_E7_L24_Introduction_ODE - Midterm 3 Results...

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