Engineering Mathematics I (Michalemas term 18/19) **NOT CURRENT ACADEMIC YEAR**
Index
Jump to:
- Organization
- Assesment
- Help with math questions
- Textbook
- List of lectures
- Tutorials
- Ideas for projects
- Project Evaluation
- Model Exams
Organization
The module runs for the first half (12 weeks) of the academic year and comprises of three lectures and one tutorial per week (total of 44 hours contact time).
Lectures take place Mondays, Tuesdays and Thursdays at 11:00 in McNeil theater.
Assessment
Weekly continuous assessment together with a team project contributes 20% towards the final grade with the end-of-year final written two-hour examination contributing 80%.
Projects
The final year group project is mandatory in order to have any grade in the continuous assessment (i.e without a project, one gets a 0 in CA no matter the tutorial grades).
The project should be about something that goes beyond what has been covered in class (just explaining something that has already been covered is not enough). Here you have some ideas. When you decide the title of your project make sure to let me know (to see if this is appropriate) by email. You should also attach a list of the members of the group.
Obviously you are encouraged to ask me any doubts or help with your project. I will try to provide some guidelines if you are interested in something in particular.
Tutorials assessment
Each week exercises will be available in this web page. You have to solve the exercises and hand them to your tutor before the tutorial starts. During the tutorials you are encouraged to ask any questions about the difficulties you found while doing the exercises.
The names of the tutors are:
- Laura Hayes <HAYESLA_at_tcd.ie>: Wed./Fri 9am @Museum building (M20)
- Dovydas Mickus <MICKUSD_at_tcd.ie>: Wed. 9am @Museum building (M21)
- Mario Galante <GALANTEM_at_tcd.ie>: Wed. 3pm and Fri. 9am @Museum building (M21)
Written exam
The final year written exam consists on 4-5 exercises that have to be solved without any calculator/books/tables.
Help with math questions
Of course, every student is encouraged to ask any question during or after the or directly in my office in the Lloyd building 2.20.
Textbook
- Main text for the course: Calculus, by Howard Anton, Irl Bivens, Stephen Davis.
There are several copies in the Hamilton library. There exist different versions and editions of the same book or parts of it, with different subtitles. Some of them only contain the first 8 or 9 chapters and are subtitled “Single Variable”. This is sufficient for the course I am teaching, but some material needed for the second semester (1E2) is missing. If you intend to buy the book probably is better that you make sure to buy an edition that covers both 1E1 and 1E2. There is also the possibility to buy an on-line version.
- Additional interesting reference books:
- Calculus - An Intuitive and Physical Approach, by Morris Kline.
- Calculus, by M. Spivak.
- Mathematics Its Content, Methods, and Meaning, by M. A. Lavrent’ev, A. D. Aleksandrov, A. N. Kolmogorov.
- The cartoon guide to Calculus, by Larry Gonick.
Lectures
A brief overview of what has been covered in each class.
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Week 1
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Week 2
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Week 3
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Week 4
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Week 5
- 8.10.2017: (Chapter 2) Limit definition of derivative.
- 9.10.2017: (Chapter 2) Computation of derivatives.
- 11.10.2017: (Chapter 2) More derivatives and implicit diferentiations.
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Week 6
- 15.10.2017: (chapter 2.7, 2.8): Implicit differentiation, linear approximation of functions.
- 16.10.2017: (chapter 3.1): Finding maxima or minima of functions.
- 18.10.2017: (chapter 3.2,3.4): More maxima and minima of functions.
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Week 7
- Study week
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Week 8
- 29.10.2017: Bank Holiday.
- 30.10.2017: (chapter 3.3): Rational functions and asymptotes. functions.
- 1.11.2017: (chapter 3.5): Maximum/minimum problems.
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Week 9
- 5.11.2017: (chapter 3.8): Rolle’s theorem, Mean value theorem.
- 6.11.2017: (chapter 4.1): The area problem.
- 8.11.2017: (This is better explained in M. Spivak, chapter 13): Upper and lower sums. Definition of definite integral.
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Week 10
- 12.11.2017: (chapter 4.4): Integrals and areas.
- 13.11.2017: (chapter 4.2): Techniques of integration I.
- 15.11.2017: (chapter 4.3): Techniques of integration II.
Recap
Small sumaries of the important content of the course.
- Limits: Download PDF.
- Minimum principles: Download PDF.
Tutorials
- Week 1: There are no tutorials the first week. Tutorials starts week 2, so the week of 16th September.
- Week 2: Functions, domain and range of a function. Operations with functions. Problem set.
- Week 3: Elementary functions. Inverse functions. Problem set.
- Week 4: Limits. Problem set.
- Week 5: More limits, continuity, sequences. Problem set.
- Week 6: Derivatives. Problem set.
- Week 8: Minimum principles. Problem set.
- Week 9: Minimum principles. Problem set.
- Week 10: Mean value theorem. Areas and partitions. Problem set.
- Week 11: Techniques of integration. Problem set.
- Week 12: Applications of integrals. No problem set this week, but please let the tutors know any doubts you have.
Ideas for projects
Here are some ideas for the projects
Some ideas for projects
- The Kepler laws: What do they say? How do they derive from the laws of motion and the law of gravity?. Guidelines.
- The fundamental theorem of algebra: A polynomial of degree n has exactly n complex roots (if one counts the multiplicity). Guidelines.
- Galois theory: There is no explicit formula for the roots of a polynomial of degree 5 or higher!. Guidelines
- Linear regression: Using polynomials to estimate/model the relationship between variables. Guidelines
- Fourier analysis: Representing a function as a sum of trigonometric functions. Guidelines
- The hyperreal line: Extending the real line to fit infinite(simals). Guidelines
- Fixed point theorem’s: Brouwer fixed-point theorem, Banach fixed-point theorem, and its amazing consequences. Guidelines
- Propagation of errors: Using linear approximations of functions to “propagate” uncertainties. Guidelines
Project Evaluation
Rules
- Material: Bring your poster/slides/whatever printed, and tape to put it on the wall.
- e-mail me the material (<alberto.ramos_at_maths.tcd.ie>) BEFORE 29.11. Add in the subject your poster number and in the body of the mail the Names/IDs of all members of the group.
- Date: Thursday the 29th of November
- Hour: 1-3pm (sharp).
- Place: Goldsmith Hall.
Group List
A list of the project groups with their corresponding number
- Group 100 (The Kepler laws): Adam Carty, Andrew Tobin, Nathan Carney, Fergal Murray and Conrad Opperman.
- Group 110 (Game theory): Lauryn Mckay, Michelle Gaughan, Elaine Murphy, Aoife McDonnell, Daira Beirnat
- Group 115 (The Kepler laws): Mark Donegan, Donal Cotter, Oisin Cousins, Claire Lemass and Darragh Kelly.
- Group 120 (Applications of Snell laws): Shana Ngai, Meabh Doran, Sarah Clyne, Donal Murray, Andrew Webb.
- Group 125 (Euler Identity): Karen O’Flynn, Claire O’Brien, Aoife Roche, Sarah Lavelle, Louise O’Connor.
- Group 130 (Minimum principleas and the Brachistochrone Curve): Oisin McCay, Donal Walsh, Naoise Tobin and Rory Meighan.
- Group 135 (Galois theory): Liam Coman, Ciaran marren, Sam Hartshorn, Julia borel
- Group 140 (Fractals): Casey, Ciara, Riley.
- Group 145 (Kepler Laws): Stephen Cushen, Con Murphy, Adam Keating.
- Group 150 (The fundamental theorem of algebra): Ronan Quinn, Michael O Callaghan, Matthew Martin, Harvey Gallagher.
- Group 155 (Mathematics of music): David Cluff, Gabi Matczuk, Nicholas Orr.
- Group 160 (Bernoulli trials): Lauryn Blair, Any Heatley, Ben O’Sullivan, David Morrin
- Group 170 (Game theory): Anna Quinn, Rita Ryan, Nada Mostafa.
- Group 175 (An Exploration Into The Concept and Applications of Exponential Functions): Joe Cedrick Linogao, Jule Loescher, Daniel Nathan Forrester, Arna Roy.
- Group 180 (Fundamental Theory of Algebra): Sinead McGetrick, Aoife Gardiner, Caoimhe Shanahan, Sorcha Tiernan, Aisling Smith.
- Group 185 (Fourier Analysis): James Connon, Thomas Grant, Philip Healy, Michael Haskins, Jason Yang, Robert Campion Kennedy..
- Group 190 (Golden Ratio): Gavin Taylor, Christopher Masterson, Raghav Ahuja.
- Group 195 (Linear regression): Rose Connolly, Ranjana Singh, Ed Donovan, Owen Buckley, Harry O Brien.
- Group 200 (Calculus of variations): Michael o’dolan, Helen Elliot, Jonathan O Rourke, Hugo Zieg, Emer Lyster.
- Group 205 (Kepler Laws): Benjamin Zelent, Paddy Flanagan, Josh Doyle, Ryan Champion, Conor Mccarry.
- Group 210 (Different Proofs and Variations of Pythagoras): Robert Teeling, Evan Mitchell, Oisin Fullam, Kevin Quinn, Domhnall O’Maonaigh,
- Group 215 (Linear regression): Amelia Stanley, Gwen McArdle.
- Group 220 (Kepler Laws): Ciarán Oflannagáin, Michael Leahy, Conor Kennedy, Liam Gibbons.
- Group 225 (Fundamental theorem of Algebra): Mark Gilsenan, Cian O Shea, John Toner and Patrick White.
- Group 230 (Linear Programming): Daniel Carroll, David Rohu, Oisin Mackin.
- Group 235 (Probability density function): Daniil Denisovich Markin, Saul Xavier Yu, Alexandr Goultiaev.
- Group 240 (Counting past infinity): Nina Trivedi, Ahfad Mehdï.
- Group 245 (Golden ratio): Robert McCarthy, James Nolan, James Murphy, Aaron Stenson.
- Group 250 (The maths behind machine learning algorithms): Isaiah Isijola, Angeliki Parisi-Ploumpi
- Group 255 (Superpermutations and De Bruijn Sequences): Dara O’Boyle, Oliver Juchnevicius, David Ryan, Sean Hawkshaw, Daniel Boyle.
- Group 260 (
\pi
exceeds 22/7): Isabel Moulton, Rebecca Lee, Conor Gallagher, Ross King - Group 265 (The Doppler effect): Brian Hastings, Kate Finnegan, Aoife McLoughlin and Lizzie Collins.
- Group 270 (Chaos theory): Niamh Cowan, Katie Kilroy, Shauna Gurhy and Lucy Daly.
- Group 275 (Propagation of errors): José Miguel Recuero Hernandez, Brian McCarthy.
- Group 280 (Primes of Lunar Arithmetic): Euan Carroll, Jack Murphy, Michael Kwok.
- Group 285 (Fourier analysis): Cornell Castelino and Seamus Wade
- Group 290 (Fibonacci sequences): Bold-Erdene Ganbaatar, Duaij Alqallaf, Abdullah Azam, Brian Burke.
- Group 295 (Sierpinksi triangle): Naoh McCarthy, Sam Mchugh, Sean Good, Luka Corrocher.
- Group 300 (Taylor series): Emily harte, Ciara byrne, Manus Mcauliffe.
- Group 305 (The napkin ring problem): Joe Marron, Patrick Hutton and Richard O’Rahilly.
- Group 310 (Special relativity): Neal manning, Kostantinos Lekkas, Cillian thomas and Daniel tamas koevesi.
- Group 315 (The golden ratio): Emmet Murphy, Roisin O’Farrell, Eoghan O’Leary, Maghnus Shaw and Niamh Rafter.
- Group 320 (The Fibonacci sequence and golden ratio and how it relates to the world of design and mathematics): Megan Fitzgerald, …
- Group 325 (Fourier’s Analysis): Victor Nwali, Richard Vanukevich, Addam Reyes, Charbel Nebo, Olajuwon Dele.
- Group 330 (The napkin ring paradox): Josh warren, Conor Little, Emily Cullen, Jack flynn.
- Group 335 (Fundamental theorem of algebra): Inga Bourke Mullaney, Louise McKiernan.
- Group 340 (Pascal’s Triangle): Oluwaseyi Adekoje, James Gooding, Olivia Butler, David Gillespie.
- Group 345 (Complex numbers, quaternions and rotations): Desmond McCarthy, Charlie Allen, Tom McManus, Tom Brennan, Adam Peat.
- Group 350 (Fixed point theorems): Hugo Bolger, Tom Shanahan.
- Group 355 (Dragon Curve): Coleman Toner, Shane Walsh, Lochlann Hackett, Cian O Gaora, Cillian Isdell.
- Group 360 (Pythagorean Theorem Definition and history): Koushik Kodukula, Ronan Reehil, Oliver Allen, Liam Mcfall.
- Group 365 (Fourier analysis): Scott Talbot, Klaudius kolaszewski, Michael colwell, Cormac Graham, Paul Twomey.
- Group 370 (Golden Ratio): Newman, Dan Smith.
- Group 375 (Fixed Point Theorem): Gavin MacDonnell, Shuang Xie, Nicholas Kelly, Hok Man Raymond Yeung, Wei Ying Chang, Ahad Khalil.
- Group 380 (Transcendental numbers): David McKenna, Jack Goodwin.
- Group 385 (Linear regression): Josephine De Bellefroid, Aedi D’Arcy.
- Group 390 (Propagation of Errors): Matthew Jordan, Jack Manning, Ciaran Lynch, Ben Mannion.
- Group 395 (The rate of growth of a blooming flower): Sarah Long, Ninna Montes, Muireann Ní, Rucha Benare.
- Group 400 (Regular solids): Heather Murphy, Orla Charters, Trudy O Hare.
- Group 405 (Fibonacci sequence): Stephen Foley, Patrick Duffy, Ted Regan, David Rooney, Jamie Collins, Jack McCarthy.
- Group 410 (Bernoulli numbers): Sam Butler.
- Group 415 (Game Theory): Aoife Igoe, Colin Hart, Linda Robinson, Luke Guerin, Thomas Darragh Clark.
- Group 420 (What is Pi): Hekmatullah Safi.
- Group 425 (Fixed point theorems): Daniel O’Donovan, Jack O’Caoimh, Luke McKay.
- Group 430 (Special relativity): Kostantinos Lekkas, Cillian Thomas, Neal Manning, Daniel Koevesi.
- Group 435 (Banach-tarski paradox): Rosa Hickey, Sean Moran, Niall Groves, Caoimhe Corcoran, Katherine Hardgrave.
- Group 440 (Golden ratio and Fibonacci sequence): Gavin Taylor, Christopher Masterson, Raghav Ahuja.
- Group 445 (Propagation of Errors): Rory Gallagher, Davin Breathnach, John Moore.
- Group 450 (The fundamental theorem of algebra): Andrew Worth, Aidan Murphy.
- Group 455 (Galois theory): James Cooper, Alex Cooper.