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1. Course Number and Title: MA1100 Calculus
2. Semester Hours: 3
3. Classification of Course: Required
4. Prerequisite: MA1600 Precalculus or advanced placement
or permission of instructor
5. Enrollment Cap: 65tt tt>48h.
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ca, equation, graph, diagram, geometric figure.
Recognize what assumptions underlie a particular mathematical model and how those assumptions can affect the validity of the model, e.g., the implications of neglecting aspects of a biological or physical situation in developing a mathematical model of it.
Reason symbolically with parameters, diagrams, etc., in order to determine the influence of structural changes to a mathematical model.
2. Logical Reasoning
Formulate a conjecture or draw conclusions from a given set of results or observations.
Construct a valid argument to support or refute a conjecture or hypothesis.
Determine the validity of an argument or identify the flaw in an invalid argument.
3. Patterns and Similarities
Recognize patterns, trends, or symmetries; continue a pattern.
Identify relationships between alternate conceptions of mathematical ideas and processes, e.g., the relationship between the visual representation of changing slope and the rate of change of a (biological or physical) process.
4. Problem-Solving Strategies
Use intelligent guessing and conjecture to narrow the solution space and to inform a choice of solution strategy.
Reduce a problem to a simpler case, solve this case first, and then try to generalize.
Determine when a certain procedure is appropriate for solving a problem, e.g., computing an average, slope, or area.
5. Estimation and Approximation
Determine when estimation techniques are appropriate and determine the degree of accuracy in an estimate.
Recognize the reasonableness of a result through the use of an approximation or an appropriate validity check, e.g., correct order of magnitude, correct units, appropriate sign for a physical quantity such as time or distance.
11. Methods of Instruction:
Class-time is spent primarily in an interactive lecture/discussion/practice problem-solving format. Students are given a listing of materials to study and problems to work that correspond with each lecture/topic.
12. Grading and Examinations
The homework, quizzes, and examinations are formative/summative assessments of the ability outcomes with the following distribution of points:
Homework (practice for quizzes, not graded)
Eight Quizzes (10) 80 points
Midterm Exam 50 points
Final Exam 60 points
Total 190 points
.
Note that there will be one make-up bonus assignment worth 8 bonus points near the end of the semester, which is intended to bolster the lowest quiz score. However,
there is no other make-up for the individual quizzes.
Grading Scale:
A 93% & up B 83 86% C 73 76% D 63 66%
A 90 92% B 80 82% C 70 72% D 60 62%
B+ 87 89% C+ 77 79% D+ 67 69% F Below 60%
Students missing an exam with a legitimate absence will be allowed to make up the exam if it can be done within a reasonable length of time of the exam date. "Legitimate" and "reasonable length of time" will be determined by the instructor.
Attendance Policy:
Attendance is strongly encouraged and considered mandatory by the instructor. All classroom work, assignments, homework, exams and attendance are the responsibility of the individual student.
Examinations:
Exams consist mainly of problem solving, graphing, or interpreting graphs or tables and cover all lecture material, homework, handouts, and assigned reading material. Attendance at examinations is mandatory. Whether or not an absence from an exam is valid and excused will be determined by the instructor, and only if the student contacts the instructor on the day of the exam (or prior to) and with a valid excuse. Medical excuses will require documentation and verification by the students physician. In the event of an unexcused absence, a grade of zero will be given for that examination.
Academic and General Conduct:
All students are expected to behave in accordance with the policies stated in the Student Handbook and Code.
Policy on Academic Dishonesty:
All provisions of the St. Louis College of Pharmacy Student Code, section II, pp. vii-viii apply at all times.
13. Description of and Criteria for Assignments:
The course website has week-by-week assignments, worksheets, sample quizzes and solutions:
http://interactive-mathvision.com/CalcSpring2000/Syllabus/tentativeschedule.html
14-15. Texts & Other Learning Resources:
Required Texts:
Calculus Lite (CL), 3rd Edition, F. Morgan, A K Peters, Ltd, 2001.
Calculus for Kinetic Modeling (CKM), J. Pais, Interactive MathVision,
1997-2002, all materials are located on my website:
http://interactive-mathvision.com/CalcSpring2000/CKMAssignFrames.html
16. Schedule:
Note that the course website has links to worksheets, sample quizzes, and solutions listed in the week-by-week schedule below:
http://interactive-mathvision.com/CalcSpring2000/Syllabus/tentativeschedule.html
Week 1.
1. Review Assignment: Finding Zeroes of Polynomial Functions, Useful Facts
2. Check your work with Java Tools: Worksheet1 Applets
3. Quiz1 (10 points), Wednesday.
Fall 2001 Quiz1 Answers ,
Spring 2002 Quiz1.01 Answers , Spring 2002 Quiz1.02 Answers
Week 2 (+).
1. Assignment: TIFs & TSFs for Polynomial Functions , Background from CKM
Workspace, Finding Tangent Lines Examples
2. Check your work with Java Tools: Worksheet2 Applets
3. Quiz2 (10 points), Wednesday.
Sample Quiz2.01 , Sample Quiz2.02
Sample Quiz2.01 Answers , Sample Quiz2.02 Answers
Spring 2002 Quiz2.01 Answers , Spring 2002 Quiz2.02 Answers
Cubic Guesstimation
Week 3.
1. Assignment: TSFs and Graphical Reprsentations I
Worksheet3P1, Worksheet3P2, Worksheet3P3, Worksheet3P4, Worksheet3P5
2. Check your work with Java Tools: Worksheet3 Applets
3. Quiz3 (10 points), Wednesday. Fall 2001 Quiz3 Answers
Spring 2002 Quiz3.01 Answers , Spring 2002 Quiz3.02 Answers
Week 4 (+).
CL Assignment:
1. Read & Study Section 1: Limit Definition of Derivative.
Lecture Examples from CLExercises Sec. 1
2. Read & Study Section 3: The Product and Quotient Rules.
Do the odd Exercises 1-19 on pages 20-21 (2nd ed.), 19-21 (3rd ed.).
3. Read & Study Section 4: The Chain Rule,
Do the odd Exercises 1-21 on pages 25-26 (2nd ed.), 25-27 (3rd ed.).
4. Read & Study Section 5: The Extended Power Rule.
Do the odd Exercises 1-11 on pages 31-32 (2nd ed.), 33-34 (3rd ed.).
Sample solutions for some of this week's exercises (2nd ed. page numbering):
CLExercises Sec. 3, CLExercises Sec. 4, CLExercises Sec. 5
CKM Assignment:
CKM Internet Workspace: D-Rules & TSFs
4. Read & Study: D-Rules 1-4
There are worked out examples here that you will find helpful.
5. Quiz 4 (10 points), Wednesday.
Fall 2001 Quiz4 Sample Soln1 , Fall 2001 Quiz4 Sample Soln2
Week 5.
CL Assignment:
1. Note that we will use the formulas on page 215 (2nd ed.), 211 (3rd ed.) as
definitions: (28.3) for sin(x), (28.4) for cos(x), and (28.2) for exp(x).
2. Read & Study Section 6: Derivatives of Sines and Cosines.
Do the odd Exercises 1-15 on pages 39-40 (2nd ed.), 40-41 (3rd ed.).
3. Read & Study Section 9: Derivatives of Exponentials and Logarithms.
Do the odd Exercises 23-55 on pages 83-84 (2nd & 3rd ed.).
CKM Assignment:
CKM Internet Workspace: D-Rules & TSFs
4. Read & Study: D-Rules 5-7
There are worked out examples here that you will find helpful.
5. Click on the More Handouts button at left to get some more practice exercises
with answers.
6. Assignment: TIFs and Graphical Representations I
Quiz3.1tif, Quiz3.2tif (Note: For additional practice, use the Week 3 Worksheets)
7. Sample Solutions:
Quiz3.1tifsoln, Quiz3.2tifsoln
Midterm Exam (50 points), Wednesday.
Week 6.
CL & CKM Assignments:
1. Read these notes on Exponential & Logarithmic Functions: Exps & Logs
2. Finish off the CL & CKM Assignments for Week 5 involving Log functions,
using 1. to help you understand and see how to do the exercises.
3. Quiz 5 (10 points), Wednesday.
Fall/Spring Break.
Week 7.
CL Assignment: none.
CKM Assignment:
CKM Internet Workspace: Dissolution Models
1. Read & Study: Flow Diagram, DM Definition 1
2. Written Homework: DM Worksheet and DM Exercises 3-4.
(click on link above to find copies of these worksheets)
You can use DM Interactive to help you when you
get stuck and to check your answers.
Note that this is a Maple V R5 Interactive Problem Solver,
and to open it you need to browse using MS Internet Explorer
(Netscape doesn't work!) and you need to have Maple V R5
on your computer. StLCOP's MLL, Room 410M, has both.
DMExercise3soln
3. Quiz 6 (10 points), Wednesday.
Fall 2001 Quiz6 Sample Soln
Week 8.
CL Assignment:
1. Read & Study Section 12: Antidifferentiation
Do all Exercises 1-17 on pages 107-108 (2nd & 3rd ed.), and
Exercise 27 on pages 122-123(2nd & 3rd ed.).
2. Read & Study Section 15: Area and the Riemann Integral.
No Exercises.
3. Read & Study Section 16: The Fundamental Theorem of Calculus.
Do the odd Exercises 1-19 on pages 136-138 (2nd & 3rd ed.).
CKM Assignment:
CKM Internet Workspace: Integrals, Area & Reversing D-Rules
4. Read & Study: Integrals 1-3
There are worked out examples here that you will find helpful.
5. Written Homework: IA Worksheet 1.
Make sure to use IA Interactive to help you when you
get stuck and to check your answers.
Note that IA Interactive is a Maple V R5 Interactive Problem Solver,
and to open it you need to browse using MS Internet Explorer
(Netscape doesn't work!) and you need to have Maple V R5
on your computer. StLCOP's MLL, Room 410M, has both.
6. Read, Study & Work through: AOC/AUC Ex 1
7. Written Homework: IA Worksheet 2.
Note that you should use the answers from IA Worksheet 1
to do IA Worksheet 2.
Make sure to use IA Interactive to help you when you
get stuck and to check your answers.
IA Worksheet 2: Answers 1-6
IA Worksheet 2: Answers 7-10
IA Worksheet 2: Answers 11-14
8. Quiz 7 (10 points), Wednesday.
Fall 2001 Quiz7 Answers
Weeks 9 & 10.
CL Assignment: None.
Precalculus Review Assignment:
1. Review Precalculus Week 8 Assignment:
CKM Internet Workspace: Velocity, Acceleration & Reaction Kinetics
Review RK Definitions 3-4 (Buttons on left) and
RK Exercises 3-4 (Buttons on left). You need this material
to do AM Exercises 1-2 below.
CKM Assignment:
CKM Internet Workspace: Absorption Models
2. Read and Study: AM Definitions 1-2 (Buttons on left)
3. Written Homework: AM Exercises 1-2 (First complete Review above.)
Help for AM Exercise 2 Part 5
4. Written Homework: More Handouts (Button on left) contains data from
the Drug Dose Generator for the first 2 doses. By hand calculation, verify
these values for both doses: calculate ymin, ymax, and yave, yourself,
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1. Course Number and Title: MA1100 Calculus
2. Semester Hours: 3
3. Classification of Course: Required
4. Prerequisite: MA1600 Precalculus or advanced placement
or permission of instructor
5. Enrollment Cap: 65
6. When Offered: Fall and Spring
7. Alternative Configurations: 3 hours of lecture/discussion per week
8. Instructor: John Pais
9. Description/Purpose:
This course focuses on the reasoning and technical skills necessary for students to become proficient in applying the mathematical concepts and tools of calculus. In keeping with the goals of the current reform movement, a primary goal of this course is to improve student mastery of the concept of function. This mastery is an essential ingredient of the effective use of mathematics to identify, represent, and solve a wide variety of problems that arise in other disciplines. In order for the learner to achieve this mastery, it is necessary that he/she acquire the ability to move fluidly among the various human-readable representations of functions. Consequently, this course addresses a multi-representation mastery including written descriptions in ordinary English, graphical representations, computational representations, and symbolic representations.
In addition, the learning goals, content, assessment, and implementation of this course have been refocused and redesigned to ensure that pharmacy students will find their calculus experience both appealing and useful. In order to address this pedagogical challenge, I have developed an Internet text "Calculus for Kinetic Modeling (CKM)." This interactive text has been designed to emphasize the introduction of precalculus and calculus concepts using exploratory problem-solving and visualization. A primary goal and innovation of this project has been to provide pharmacy students the opportunity to acquire a mathematical understanding of the basics of kinetic modeling, including an introduction to reaction kinetics, Michaelis-Menten enzyme kinetics, Makoid-Banakar drug dissolution, and several first-order drug absorption models.
10. Ability Outcomes:
Thinking and Decision-Making
1. Gather and comprehend information from reading texts, handouts, and lecture notes. 2. Analyze the structure of a problem situation and (when possible) translate it into a variety of useful mathematical representations.
Mathematical Reasoning
The following five numbered categories specify the mathematical reasoning abilities that are the targeted abilities for each student to acquire/develop by the end of the course. Beneath each ability category are general performance criteria indicating the type of content-specific performances that are necessary to demonstrate mastery of the related skills and knowledge.
1. Mathematical Modeling
Express, in ordinary (natural) language, model specifications and relationships that are presented mathematically and/or visually using a graph, diagram, or geometric figure.
Recognize whether a mathematical model applies to a given situation, e.g., a linear function, a quadratic function, an exponential growth, a first-order kinetic process, etc.
Develop a mathematical model from an ordinary language specification, including an appropriate visual representation, e.g., formululations up for homework.
5. Optional Computer Lab Exercise: AM Interactive, Drug Dose Generator
Work through enough consecutive doses so that the drug in the
blood curve reaches steady state. Write out a short description
of what you did and what happened.
Note that AM Interactive is a Maple V R5 Interactive Problem Solver,
and to open it you need to browse using MS Internet Explorer
(Netscape doesn't work!) and you need to have Maple V R5
on your computer. StLCOP's MLL, Room 410M, has both.
6. MakeUp Bonus Exercise (8 bonus points), AM Exercises 1-2,
Due Wednesday 4-24-2002.
NOTE: This is the only makeup option for missing quizzes.
If you get full credit for completing this assignment, then you will
receive 8 extra bonus points added to your total number of points.
7. Quiz 8 (10 points), Friday.
Fall 2001 Quiz8 Answers
Final Exam (60 points).
/=all materials are located on the instructors 1. 2. Fall 2001 Quiz1 Answers Spring 2002 Quiz1.01 Answers& TSFs for Polynomial Functions Sample Quiz2.01 Answers Spring 2002 Quiz2.01 Answers Spring 2002 Quiz3.01 Answers Fall 2001 Quiz4 Sample Soln1
More Practice Problems1.
Practice Problems 1KMOm|~02572468=?gh
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6. When Offered: Fall and Spring
7. Alternative Configurations: 3 hours of lecture/discussion per week
8. Instructor: John Pais
9. Description/Purpose:
This course focuses on the reasoning and technical skills necessary for students to become proficient in applying the mathematical concepts and tools of calculus. In keeping with the goals of the current reform movement, a primary goal of this course is to improve student mastery of the concept of function. This mastery is an essential ingredientDocumentSummaryInformation8 of the effective use of mathematics to identify, represent, and solve a wide variety of problems that arise in other disciplines. In order for the learner to achieve this mastery, it is necessary that he/she acquire the ability to move fluidly among the various human-readable representations of functions. Consequently, this course addresses a multi-representation mastery including written descriptions in ordinary English, graphical representations, computational representations, and symbolic representations.
In addition, the learning goals, content, assessment, and implementation of this course have been refocused and redesigned to ensure that pharmacy students will find their calculus experience both appealing and useful. In order to address this pedagogical challenge, I have developed an Internet text "Calculus for Kinetic Modeling (CKM)." This interactive text has been designed to emphasize the introduction of precalculus and calculus concepts using exploratory problem-solving and visualization. A primary goal and innovation of this project has been to provide pharmacy students the opportunity to acquire a mathematical understanding of the basics of kinetic modeling, including an introduction to reaction kinetics, Michaelis-Menten enzyme kinetics, Makoid-Banakar drug dissolution, and several first-order drug absorption models.
10. Ability Outcomes:
Thinking and Decision-Making
1. Gather and comprehend information from reading texts, handouts, and lecture notes. 2. Analyze the structure of a problem situation and (when possible) translate it into a variety of useful mathematical representations.
Mathematical Reasoning
The following five numbered categories specify the mathematical reasoning abilities that are the targeted abilities for each student to acquire/develop by the end of the course. Beneath each ability category are general performance criteria indicating the type of content-specific performances that are necessary to demonstrate mastery of the related skills and knowledge.
1. Mathematical Modeling
Express, in ordinary (natural) language, model specifications and relationships that are presented mathematically and/or visually using a graph, diagram, or geometric figure.
Recognize whether a mathematical model applies to a given situation, e.g., a linear function, a quadratic function, an exponential growth, a first-order kinetic process, etc.
Develop a mathematical model from an ordinary language specification, including an appropriate visual representation, e.g., formululations up for homework.
5. Optional Computer Lab Exercise: AM Interactive, Drug Dose Generator
Work through enough consecutive doses so that the drug in the
blood curve reaches steady state. Write out a short description
of what you did and what happened.
Note that AM Interactive is a Maple V R5 Interactive Problem Solver,
and to open it you need to browse using MS Internet Explorer
(Netscape doesn't work!) and you need to have Maple V R5
on your computer. StLCOP's MLL, Room 410M, has both.
6. MakeUp Bonus Exercise (8 bonus points), AM Exercises 1-2,
Due Wednesday 4-24-2002.
NOTE: This is the only makeup option for missing quizzes.
If you get full credit for completing this assignment, then you will
receive 8 extra bonus points added to your total number of points.
7. Quiz 8 (10 points), Friday.
Fall 2001 Quiz8 Answers
Final Exam (60 points).
/=all materials are located on the instructors 1. 2. Fall 2001 Quiz1 Answers Spring 2002 Quiz1.01 Answers& TSFs for Polynomial Functions Sample Quiz2.01 Answers Spring 2002 Quiz2.01 Answers Spring 2002 Quiz3.01 Answers Fall 2001 Quiz4 Sample Soln1
More Practice Problems1.
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5. Assignment: TIFs and Graphical Representations I
Quiz3.1tif, Quiz3.2tif (Note: For additional practice, use the Week 3 Worksheets)
Quiz3.1tifsoln, Quiz3.2tifsoln you handouts, and lecture notes.
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5. Assignment: TIFs and Graphical Representations I
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