Introductory Mathematics and Applied Mathematics

2011

Syllabus

Mathematics MA 1003

Instructor

Benjamin McKay
b.mckay{@skip.this.part)ucc.ie
School of Mathematical Sciences
University College Cork
Cork, Ireland

Telephone	353 21 490 2434
Fax	353 21 427 0813
Secretary	353 21 490 2542

Students with disabilities

University College Cork seeks to provide equal access to its programs, services and activities for people with disabilities. If you will need accomodations in this class, reasonable prior notice needs to be given to the instructor and to the college to make arrangements for accomodations. All written information in this course can be made available in alternative format with prior notification.

What you know already

Functions, linear equations, algebra, quadratic formula, graphing of elementary functions, trigonometry.

Course objectives

By the end of this course, you should be able to

1. demonstrate knowledge of the real number system, in particular the decimal system
2. manipulate numbers in scientific notation
3. simplify algebraic expressions and use basic algebraic identities
4. apply correctly the algebraic rules for manipulating equations
5. demonstrate knowledge of functions and their notation
6. determine the domain and range of a given function
7. find the equation of a given line in the cartesian plane
8. demonstrate knowledge of quadratic graphs
9. solve quadratic equations using the quadratic formula
10. demonstrate knowledge of radian measure for angles
11. find basic trigonometric functions of angles measured in radians and, conversely, find solutions for angles in a given range, given the value of the trigonometric function, using a scientific calculator
12. demonstrate knowledge of the properties of power functions of the form ax, (with a > 0 constant), in particular the exponential function e^x
13. plot graphs of power functions with positive and negative exponent
14. use correctly the properties of logarithmic functions
15. apply the techniques of differentiation to find the derivatives of polynomial functions, trigonometric functions, logarithmic and exponential functions, and their application to graph sketching
16. demonstrate knowledge of derivatives as rates of change in scientific contexts
17. apply the techniques of integration to evaluate the indefinite integrals of a range of functions
18. apply the methods of substitution and integration by parts to evaluate indefinite integrals
19. use definite integration to find the area under the graph of a given function
20. solve first order ODEs by direct integration or by separation of variables
21. incorporate given initial values into solutions (initial value problems)
22. be aware of a range of scientific contexts which use this mathematical model
23. demonstrate knowledge of finding curves of best fit to given sets of data and determining the most suitable type
24. apply least-squares analysis to find the line of best fit for a given set of data
25. use methods of numerical integration: Euler's method; the trapezium rule; Simpson's rule
26. display knowledge of various mathematical models used in science
27. set up mathematical models in simple cases of uniform growth and exponential growth or decay
28. solve the resulting equations and make inferences from the solution (e.g. using population growth models).

The textbook

• J. Stewart, Calculus: Early Transcendentals, 6th edition, Brooks Cole, 2007

Some other excellent calculus books:

• Frank Morgan, Calculus Lite, A K Peters, Ltd., 2001. (Short, quick and clear.)
• Michael Spivak, Calculus, Cambridge University Press, 2006. (For very smart people only! But everyone should try it.)

Some equally good free books available online legally:

• Gil Strang, Calculus,

  http://euclid.ucc.ie/pages/staff/Mckay/calculus/Strang/Calculus.pdf

• Hugo Rossi, Calculus,

  http://euclid.ucc.ie/pages/staff/Mckay/calculus/Rossi/

Equipment

Students may employ a scientific calculator in tests and in the final exam, but no computers or other electronics, or tables. Neither notes nor tapes of lectures may be permitted for purposes of sale.

Marking

There will be two tests, each worth 10% of the final mark. The remaining 80% of the final mark will come from the final exam. Tests and exams are to be completed independently by each student; only original work of the student whose name is on the assignment may be submitted for marking. Missed tests (or final exam) can not be rescheduled. Attendance will not count toward the final mark, however the instructor reserves the right to refuse marking of any student's final exam if the student has (in the instructor's opinion) a poor attendance record.

Lectures

Day	Time	Room
Tuesday	11am-12pm	Boole LL 3
Wednesday	11am-12pm	Brookfield BHSC G01
Thursday	11am-12pm	Western Gateway WGB G05

Sections

Acronym	Full title	Instructor	Number of tutorial groups
BL	Biological and Chemical Science	M. Quirke	3
GN	Genetics	M. Quirke	part of 3rd BL group
EV	Environmental and Earth Systems Science	B. McKay	2
CM	Chemical Science	B. McKay	1
CS	Computer Science	B. McKay	1
Biomed	Biomedical Science (joint course with CIT)	B. McKay	1
NT	Nutritional Science including Food Science	B. McKay	2

Tutorials

Section	Your last name starts with	Day	Time	Semester	Room
BL	A-H	Thursday	17:00-18:00	Autumn	Connelly S3
				Spring	Connelly J5
	H-O	Wednesday	16:00-17:00	Autumn and Spring	O'Rahilly 132
	O-Z	Monday	17:00-18:00	Autumn and Spring	Brookfield 122
Chem Sc	anything	Friday	10:00-11:00	Autumn	Western Gateway G08
				Spring	Western Gateway G14
CS	anything	Wednesday	14:00-15:00	Autumn	Cavanagh Pharmacy LG52
				Spring	Brookfield G05
EV	anything	Friday	14:00-15:00	Autumn and Spring	O'Rahilly 101
GN	anything	Monday	17:00-18:00	Autumn and Spring	Brookfield 122
NT	anything	Thursday	16:00-17:00	Autumn	O'Rahilly 101
				Spring	Connelly A
Biomed	anything	Tuesday	16:00-17:00	Autumn and Spring	Kane B10A

Test Dates

There will be a test Friday November 25, 6-8pm, in Boole 1,2,3 and 4, and a test on Monday, February 13, 6-8pm also in Boole 1,2,3 and 4. Each test will cover all material since the previous test.

Missed Tests

Students who miss a test for a medical emergency should take a medical certificate from their doctor to the School of Mathematical Sciences office, Western Gateway Building, 1st floor. Students who miss for other emergencies should contact their instructor, preferably in advance if possible. Should the student be excused from a test, due to medical or other emergency, the final exam per cent mark will be used by the instructor as the student's per cent mark in the missed test.

Calendar

This calendar tells you which chapter and section is covered on each day.

Problems

You are responsible for solving the concept check problems for chapters 1 to 11, and also the homework problems listed on the calendar above. These will be the source of all of the problems on the tests and the final exam.

Office hours

I will be in my office, Western Gateway room G39, Fridays 9:30-11:30am, and you can drop by then to ask questions. The schedule may be changed; if so you will be notified in class.

Holidays

Students who anticipate the necessity of being absent from class due to the observation of a major religious observance must provide advance notice of the dates to the instructor in writing.

Old exams and tests

Exams and tests not collected by students will be kept by the instructor for a period of three months after the termination of the course, at which time they will be destroyed.