## 2011-Shibberu, Yosi - MA211 Differential Equations. Class Notes

SIMIODE, Chardon OH USA

#### Abstract

Shibberu, Yosi. 2011. MA211 Differential Equations. Class Notes. PowerPoint. 426 slides.

https://www.rose-hulman.edu/~shibberu/MA211/Slides.pdf . Accessed 1 September 2017

This is a very good set of course slides and the Table of Contents is given here. Since this is a mathematics course taught at an engineering school., Rose-Hulman Institue of Technology, there are many examples from engineering, e.g., circuits and spring mass systems. The material is a mix of exposition (no proofs) of techniques and modeling opportunities with solutions. We give one example here. Example 105 (Minimum Sized Tank) from Slide 255.

“A food processing plant has a problem. Ideally, all the jars of pickled fruit produced by the plant should have the same salt concentration. However, the concentration of the salt solution pumped into jars at 100 gal/hr is observed to vary with time. Assume the salt concentration pumped into the jars is approximated by the function cin(t) = 0.1 sin(t) + 0.2 lbs/gal where t is measured in hours. What should be done to fix this problem?”

Mathematical Models

Physical vs Mathematical Models

Dynamical Systems and Differential Equations

Parameter Identification

Slope Fields and Integral Curves

2 Separable Differential Equations

Solution Method: Separate and Integrate

3 Linear Differential Equations

Linear vs Nonlinear

DE Classification

Solution Method: Integrating Factor

Structure of Solutions to Linear Equations

4 Salt Tank Systems

5 Electrical Circuits

6 Nonlinear Differential Equations

Stability Analysis

Trajectory Flow

Population Models

7 Euler’s Method

8 Linearity

9 Trigonometry

10 Method of Undetermined Coefficients

11 Gain Function

12 Spring-Mass-Damper

13 Second Order Differential Equations

14 Complex Numbers

15 Free Oscillations

16 Undamped Forced Oscillations

17 Damped Forced Oscillations

18 Introduction to Laplace Transforms

19 Definition of the Laplace Transform

20 Linearity II

21 Laplace of Derivatives

22 Switching Functions

23 Impulse Functions

24 Inverse Laplace Transforms

25 Shifting Theorems

26 Convolution

27 Transfer Function

28 Laplace Transform Proofs

Keywords: differential equation, engineering, oscillation, notes, slides, circuits, spring, Laplace transform, tank, mixing, stability

#### Cite this work

Researchers should cite this work as follows:

• Brian Winkel (2017), "2011-Shibberu, Yosi - MA211 Differential Equations. Class Notes," https://simiode.org/resources/3981.