Mathematics
MA 312 GU Parametric Equations & Polar Coordinates Usage in Learning Calculus Exam Practice

MA 312

Grantham University

MA

Question Description

Can you help me understand this Calculus question?

needing each of the following questioned answered concerning calculus with 100-150 words. does not need to be to indepth just a generalized overview.

Unformatted Attachment Preview

1. Differential Equations think about how the solution to a differential equation compares to solutions of other algebraic equations you have solved in the past. How are solutions to differential equations similar or different to what you have done before? Do some research on the applications of differential equations, specifically the logistic equation. Where is the logistic equation most often used? 2. Applications of Integration sections that were covered focused on applications of integration. Of the applications that we studied, which did you find the most interesting, and why? Do some of your own research to find additional applications of integration. Compare what you found during your research to what was covered in the book. 3. Methods of Integration integration by parts, trigonometric integrals, and trigonometric substitution. Which of these methods made the most sense to you, and why? Which of these methods was the most confusing for you, and why? Share any tricks that you learned for recognizing when to use each of the method. 4. The Trapezoid Rule and Simpson's Rule The reality of many integrals is that we don’t have a good method to evaluate. This means that numerical methods become critical. This week, we studied two numerical methods for estimating definite integrals – the Trapezoid Rule and Simpson’s Rule. Which of these methods made more sense for you, and why? Do you research about other numerical methods that can be used to estimate the value of a definite integral. What did you find? How do other methods compare to the Trapezoid Rule and Simpson’s Rule? 5. Infinite Sequences and Infinite Series describe the similarities and differences between an infinite sequence and an infinite series. Do some research on your own about infinite sequences and series. Did you find any famously known sequences or series? Which ones? Why are they so well known? 6. Usefulness of Polynomials you learned a variety of different ways that polynomials can be used as approximations to functions. In your studies, what did you learn about why this might be so useful in mathematics? Using either your textbook or the Internet, search for the mathematicians who were historically instrumental in developing polynomial approximations. Who did you find and what were their contributions? 7. Parametric Equations and Polar Coordinates you studied both parametric equations and polar coordinates. Which of these topics do you see as being more useful in the study of Calculus and why? Which did you find easier to understand and why? ...
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Final Answer

Attached.

1. Differential Equations
think about how the solution to a differential equation compares to solutions of other algebraic
equations you have solved in the past. How are solutions to differential equations similar or
different to what you have done before? Do some research on the applications of differential
equations, specifically the logistic equation. Where is the logistic equation most often used?

Answer. The solution of an algebraic equation represents one or more points on a 2dimensional coordinates plane or ordered pairs e.g. (2,5), (3,0) etc. while the solution of a
differential equation represents an expression or relation between dependent variable and
independent variable(s), e.g. 𝑦 = 3𝑥 + (1 −

𝑘
2𝑥

) etc.

The relation between the dependent and independent variable can be linear e.g. y = mx+b
or non-linear e.g. 𝑦 = 2𝑥 2 + 5𝑥 − 10.
Differential equations are extensively used in the advanced studies of physical science,
medical science, social science, economics etc. The logistic equation has applications to
those problems where the rate of change in the dependent variable at given value of the
independent variable is directly proportional to the dependent variable and the dependent
variable is under a constraint.
For example, if dependent variable is N and independent variable is t then logistic
equation is

𝑑𝑁
𝑑𝑡

𝑁

= 𝑟𝑁 (1 − 𝑘 ) where k is the parameter or maximum value that N can

take. The logistic function is mostly used in the estimation of population of a nation or
global population.
2. Applications of Integration
sections that were covered focused on applications of integration. Of the applications that we
studied, which did you find the most interesting, and why? Do some of your own research to
find additional applications of integration. Compare what you found during your research to
what was covered in the book.

Answer. Integration is used to calculate the area between two curves, volume generated
by rotation of a curve about a straight line, to sum up a series and in solving many
scientific and economics problems. The application of integration to scientific problems
always impresses me. It is fascinated how complex and tedious problems are almost
correctly solved by the integration. In some cases, we derive relation between dependent
variable and independent variable(s). For example, the rate of change of velocity of a
moving body is proportional to the net force acting on the body.
This relation can be written ...

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