2011-Shibberu, Yosi - MA211 Differential Equations. Class Notes
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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?”
Here is the Table of Contents
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
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