## MA1S12: Calculus with applications for Scientists ### Hilary term, 2015 ---- #### Course outline: * Application of definite integrals in geometry (area between curves, volume of a solid, length of a plane curve, area of a surface of revolution). * Methods of integration (integration by parts, trigonometric substitutions, numerical integration, improper integrals). * Differential equations (separable DE, first order linear DE, Euler method). * Infinite series (convergence of sequences, sums of infinite series, convergence tests, absolute convergence, Taylor series). * Parametric curves and polar coordinates. There are two parts to MA1S12, the other part is Discrete Mathematics with [Prof. Colm &Oacute; D&uacute;nlaing](http://www.maths.tcd.ie/~odunlain/). Past exam papers can be found [here](http://www.tcd.ie/Local/Exam_Papers). #### Lecture times: * Monday 12pm (MacNeil Theatre) * Tuesday 12pm (MacNeil Theatre) * Tuesday 5pm (MacNeil Theatre) #### Assignments: * [Homework 1](homework01.pdf), date due: Week 2. [Tutorial 1](tut01.pdf). * [Homework 2](homework02.pdf), date due: Week 3. [Tutorial 2](tut02.pdf) ([Answers](tut02_sol.pdf)). * [Homework 3](homework03.pdf), date due: Week 4. [Tutorial 3](tut03.pdf) ([Answers](tut03_sol.pdf)). * [Homework 4](homework04.pdf), date due: Week 5. [Tutorial 4](tut04.pdf) ([Answers](tut04_sol.pdf)). * [Homework 5](homework05.pdf), date due: Week 6. [Tutorial 5](tut05.pdf) ([Answers](tut05_sol.pdf)). * [Homework 6](homework06.pdf), date due: Week 8. [Tutorial 6](tut06.pdf) ([Answers](tut06_sol.pdf)). * [Homework 7](homework07.pdf), date due: Week 9. [Tutorial 7](tut07.pdf). * [Homework 8](homework08.pdf), date due: Week 10. [Tutorial 8](tut08.pdf). * [Homework 9](homework09.pdf), date due: Week 11. [Tutorial 9](tut09.pdf). * [Homework 10](homework10.pdf), date due: Week 12. [Tutorial 10](tut10.pdf). <!-- ([Answers](https://cloud.sagemath.com/projects/4c226914-3876-4bf7-9296-367619f17668/files/Tutorial%204.sagews)). * [Homework 1](homework01.pdf), date due: Week 2. [Tutorial 1](tut01.pdf). * [Homework 2](homework02.pdf), date due: Week 3. [Tutorial 2](tut02.pdf). * [Homework 3](homework03.pdf), date due: Week 4. [Tutorial 3](tut03.pdf). * [Homework 4](homework04.pdf), date due: Week 5. [Tutorial 4](tut04.pdf). * [Homework 5](homework05.pdf), date due: Week 6. [Tutorial 5](tut05.pdf). * [Homework 6](homework06.pdf), date due: Week 8. [Tutorial 6](tut06.pdf). * [Homework 7](homework07.pdf), date due: Week 9. [Tutorial 7](tut07.pdf). * [Homework 8](homework08.pdf), date due: Week 10. [Tutorial 8](tut08.pdf). * [Homework 9](homework09.pdf), date due: Week 11. [Tutorial 9](tut09.pdf). * [Homework 10](homework10.pdf), date due: Week 12. [Solutions](sol_exam1_2013.pdf) to the exam 2013. [Sage worksheet](2014-03-31-calculus.sagews) (can be used from [SageMathCloud](https://cloud.sagemath.com)). [PDF](2014-03-31-calculus.pdf) version of the worksheet. --> <!--[Solutions](sol01.pdf) to Homework 1.--> #### Tutorials: Starting in week 2. Assignments and tutorial work will count for 20% of the marks. There will be final examination in May counting for the remaining 80%. <table width="400" class="table"> <tr><td>A1</td><td>Monday</td><td>14:00</td><td>M20</td><td>Leo</td></tr> <tr><td>A2</td><td>Thursday</td><td>16:00</td><td>ST107</td><td>Robert</td></tr> <tr><td>A3</td><td>Monday</td><td>14:00</td><td>Salmon</td><td>Gemma</td></tr> <tr><td>A4</td><td>Thursday</td><td>16:00 </td><td>M20</td><td>Dillon</td></tr> <tr><td>A5</td><td>Wednesday</td><td>13:00</td><td>Synge</td><td>Joy</td></tr> <tr><td>A6</td><td>Friday</td><td>13:00</td><td>Synge</td><td>Leo</td></tr> <tr><td>A7</td><td>Friday</td><td>13:00</td><td>CLLT</td><td>Laura</td></tr> </table> <!-- A1) Monday at 14:00 in M20 (Leo) A3) Monday at 14:00 in Salmon (Gemma) A5) Wednesday at 13:00 in Synge (Joy) A2) Thursday at 16:00 in ST107 (Robert) A4) Thursday at 16:00 in M20 (Dillon) A6) Friday at 13:00 in Synge (Leo) A7) Friday at 13:00 in CLLT (Laura) --> #### Recommended reading: * *Calculus, Late Transcendentals.* 9th edition by H. Anton, I. Bivens, S. Davis. <br> We will cover most of Chapters 5, 7, 8, 9, 10 and sections 13.1, 13.3. <br> Hamilton, Lending S-LEN 515 P23*8 P23*8;1 P23*8;5-10<br> Hamilton, Counter Reserve 515 P23*8;2-4 * *Calculus, Single Variable.* 9th edition by H. Anton, I. Bivens, S. Davis.<br> Hamilton 515 P2*8;4, S-LEN 515 P2*8<br> * *Calculus, Early Transcendentals.* 9th edition by H. Anton, I. Bivens, S. Davis. Links to the [Paperback](http://eu.wiley.com/WileyCDA/WileyTitle/productCd-1118092481,descCd-collegeEdNotes.html) and [E-book](http://eu.wiley.com/WileyCDA/WileyTitle/productCd-1118379314.html) versions at wiley.com. ----
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