Kristen Darling
Mr. Tumin
AP Calculus
11/8/12
Pharmacokinetics
According to the Medical dictionary the definition of “Pharmacokinetics is, sometimes abbreviated as PK, the word coming from Ancient Greek pharmakon "drug" and kinetikos "to do with motion,” is a branch of pharmacology dedicated to the determination of the fate of substances administered externally to a living organism. The substances of interest include pharmaceutical agents, hormones, nutrients, and toxins.” Pharmacokinetics is the study of the rate of drug absorption and disposition in the body. So, differential calculus is an important part in the development of many of the equations used. There are four pharmacokinetic processes to which every drug is subject in the body: Absorption, Distribution, Metabolism, and Excretion Absorption is the process by which a drug is made available to the fluids of distribution of the body. (i.e. blood or plasma) Most orally-administered drugs reach a maximum or peak level blood concentration within 1-2 hours. Once a drug has been absorbed from the stomach and/or intestines into the blood, it is circulated to some degree to all areas of the body to which there is blood flow and that is the process of distribution. Metabolism is the complex of physical and chemical processes occurring within a living cell or organism that are necessary for the maintenance of life. In metabolism some substances are broken down to yield energy for vital processes while other substances, necessary for life, are produced. Drugs are often eliminated by biotransformation, the alteration of a substance within the body, or excretion into the urine or the fluid that is made by the liver, also known as bile. The liver is the major location for drug metabolism, but specific drugs may experience biotransformation in other tissues. The metabolic transformation of drugs is catalyzed by enzymes, and most of the reactions obey Michaelis-Menten kinetics (a method of...

...Portfolio in Calculus
Submitted by:
Chloe Regina C. Paderanga
Submitted to:
Sir Ferdinand Corpuz
Journal for the Month of June
WHAT I LEARNED?
I learned many things this month. It was good that our teacher repeated the topics in basic math to strengthen our foundation. Even if we had a hard time, I don’t see any reason why we should complain because I understand that our wanted to master these topics to be able to move to a higher math. The topics tackled this month are namely:
Inequalities
Rational Inequalities
Circles
Distances
Slopes
Angles of Incidence
WHAT IS THE HARDEST TOPIC?
For me, the hardest topic to master was the inequalities, which I know I should master to be able to understand the next topics.
HOW DID I LEARN?
I reviewed my wrong answers in our summative tests because I don’t want to be left behind with the topics.
REFLECTION
When Sir Corpuz said that we are going to have a double program in Math, I was excited because we are not just advancing but are reviewing in the same time.
APPLICATION TO LIFE
A lot of advance technologies are product of such very simple concepts in math as long as it is utilized in a very good way. For example the distance formula, this is not just used in Math but also in Physics, Science and many other fields.
Journal for the Month of July
WHAT I LEARNED?
This month, I learned that there are also ‘other’ versions of circles. Namely:
Parabola
Ellipse...

...1
Reflective Paper
MTH 157
July 2, 2013
Gina Loscalzo
Evan Schwartz
Reflective Paper 2
Math for Elementary Teachers II is the second part in a two part series. The mathematical concepts that were focused on throughout the second part of Math for Elementary Teachers were on measurement, geometry, probability, and data analysis. Just like part one of Math for Elementary Teachers, part two also address the relationship of the course concepts to the National Council of Teachers of Mathematics Standards for K-8 instruction.
The first two weeks of this course, the main concepts that were explored was data analysis and probability. When learning about data analysis, A Problem Solving Approach to Mathematics for Elementary School Teachers taught students that data analysis is the measures of Central Tendency, Statistics, and Variation. During data analysis students also reviewed that different ways data can be presented; bar graphs, circle graphs, line graphs, or scatter plots. Probability taught theorem and tree diagrams/geometry probabilities. Both of these mathematical concepts were cover throughout chapters 9 and 10 of A Problem Solving Approach to Mathematics for Elementary School Teachers.
The mathematical concepts covered during week three and four was Introduction to Geometry. During these two weeks, the concepts of geometry that were covered were; angles, basic...

...
Calculus in Medicine
Calculus in Medicine
Calculus is the mathematical study of changes (Definition). Calculus is also used as a method of calculation of highly systematic methods that treat problems through specialized notations such as those used in differential and integral calculus. Calculus is used on a variety of levels such as the field of banking, data analysis, and as I will explain, in the field of medicine. Medicine is defined as the science and/or practice of the prevention, diagnosis, and treatment of physical or mental illness (Definition). The term medicine can also mean a compound or a preparation applied in treatment or control of diseases, mostly in form of a drug that is usually taken orally (Definition). Calculus has been widely used in the medical field in order to better the outcomes of both the science of medicine as well as the use of medicine as treatment. (Luchko, Mainardi & Rogosin, 2011). There has been a strong movement towards the inclusion of additional mathematical training throughout the world for future researchers in biology and medicine. It can be hard to develop new courses as well as alter major requirements, but institutions should consider the importance of a clear understanding of the function of mathematics in science. However, scientists who have not had the level of mathematical training needed to work in...

...in a teacup after t seconds is given by M =10.5-0.4t2
(a) When will all the sugar dissolve?
0=10.5-0.4t2
0.4t2=10.5
t2=26.25
t=5.12 sec
(b) Find the average rate of change in the interval 0 ≤ t ≤ 1
M(0) = (0, 10.5); M(1)= (1, 10.1)
= (10.1-10.5) / (1-0)
= -0.4 g/s
(Please make sure to include word answers or concluding statements, and to specify units. We are marking for communication and presentation, as well as for correct answers.)
(c) Draw on graphing paper a graph of M with respect to t and use the secant method to approximate the instantaneous rate of change at t = 2 seconds
M(1.5) = (1.5, 9.6); M(2)= (2, 8.9)
= (8.9-9.6)/(2-1.5) = -1.4
instantaneous rate of change at t = 2 seconds is -1.4
(Again, you must choose a value for t that is within ± 0.1 seconds. When t = 1.9, the IROC is -1.56 g/s, which is closer to the true value of -1.6 g/s)
3. 4.5/5
As a car moves from a traffic light, the distance in metres of the car from the traffic light after t seconds is given by d(t)=2t2.
(a) Draw a graph on graphing paper of the distance versus time
(b) Calculate the average speed when 4 ≤ t ≤ 7
d(4)= (4,32); d(7)=(7,98)
= (98-32)/(7-4)
= 22m/s √
(c) Use the secant method to approximate the instantaneous velocity at t = 4 seconds
d(3.5)= (3.5, 24.5); d(4)= (4,32)
= (32-24.5)/(4-3.5)
= 15m/s
(A value of t = 3.9 will result in an IROC of 15.8 m/s. The true rate is 16.0 m/s)
4. 6/6 (a) Describe in your own words how you...

...functions to be resulted at representation of other functions. Its uses are:
1. Evaluating definite Integrals, for functions without antiderivative.
2. Understanding asymptotic behaviour, how a function behaves in an important part of its domain.
3. Estimating approximate values, such as sin x and e.
The Taylor Series is also used in power flow analysis of electrical power systems (Newton-Raphson method). It is widely used in calculators to estimate approximate values. Thus, the Taylor Series is used by occupations such as Mathematicians & Electrical Engineers. It has limitations that it is only available for a small domain and it is challenging to find the nth term of the derivative.
RESOURCES
http://en.wikibooks.org/wiki/Calculus/Taylor_series
https://www.efunda.com/math/taylor_series/taylor_series.cfm
http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/series/appsTaylor.html
...

...No 1. 2. 3. 4. 5. 6. 7. 8. Code: UCCM1153 Status: Credit Hours: 3 Semester and Year Taught:
Information on Every Subject Name of Subject: Introduction to Calculus and Applications
Pre-requisite (if applicable): None Mode of Delivery: Lecture and Tutorial Valuation: Course Work Final Examination 40% 60%
9. 10.
Teaching Staff: Objective(s) of Subject: • Review the notion of function and its basic properties. • Understand the concepts of derivatives. • Understand linear approximations. • Understand the relationship between integration and differentiation and continuity. Learning Outcomes: After completing this unit, students will be able to: 1. describe the basic ideas concerning functions, their graphs, and ways of transforming and combining them; 2. use the concepts of derivatives to solve problems involving rates of change and approximation of functions; 3. apply the differential calculus to solve optimization problems; 4. relate the integral to the derivative; 5. use the integral to solve problems concerning areas.
11.
12.
Subject Synopsis: This unit covers topics on Functions and Models, Limits and Derivatives, Differentiation Rules, Applications of Differentiation and Integrals.
13.
Subject Outline and Notional Hours: Topic Learning Outcomes 1 L 4 T 1.5 P SL 6.25 TLT 11.75
Topic 1: Functions and Models
• • • • • • Functions Models and curve fitting Transformations, combinations, composition and graphs of...

...
Calculus:
Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, Differential Calculus and Integral Calculus, which are related by the fundamental theorem of calculus.
Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.
Application of Calculus in Various Fields:
Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired. It allows one to go from (non-constant) rates of change to the total change or vice versa, and many times in studying a problem we know one and are trying to find...

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