At the end of each week the problems and solutions of the tutorials will be posted here:
tutorial 1 (12-14 October 2011):
problems and
solutions
tutorial 2 (19-21 October 2011):
problems and
solutions
tutorial 3 (26-28 October 2011): problems and
solutions
tutorial 4 (2-4 November 2011): problems and
solutions
tutorial 5 (16-18 November 2011): problems and
solutions
tutorial 6 (23-25 November 2011): problems and
solutions
tutorial 7 (30 November - 1 December 2011): problems and
solutions
tutorial 8 (7-9 December 2011):
problems and solutions
tutorial 9 (14-16 December 2011):
problems and
solutions
Further help with maths questions:
Of course, you may ask me directly after class or call into my office (2.46 in the Lloyd building).
In addition, the School of Mathematics runs a help room Monday, Tuesday Friday 1-2pm and Wednesday, Thursday 12-2pm in Room 2.6
which is located on the 2nd floor of the School of Maths. Here you can ask specific maths questions and more advanced students
will try to answer them.
About this module MA1S11:
This module is divided in two parts, covering calculus and discrete mathematics (mostly linear algebra), respectively. I am teaching calculus, Prof. Timoney is teaching the discrete mathematics part. The official course information can be found here. In the second semester this will be followed by MA1S12 (pdf) . You may also have a look at last year's course page . There will be a single exam and a single mark for MA1S11, which means that half of the exam paper will be about calculus and the other half about linear algebra/discrete mathematics. The final mark for MA1S11 will be 80 percent based on the exam and 20 percent on continuous assessments, i.e. the tutorials and labs. You can find past exam papers here .
- Synopsis
Functions. Limits and Continuity. The Derivative. The Derivative in Graphing and Applications. Integration.
- Textbook
Calculus, by Howard Anton, Irl Bivens, Stephen Davis, (9th edition; publisher Wiley, New York)
You can find it in the Hamilton library [515 P2*8;4,6,7, S-LEN 515.P2*8;1-3]
Unfortunately, there exist different versions of the same book or parts of it, with different subtitles. The library has a few hardbound copies which only contain the first 8 or 9 chapters and are subtitled "Single Variable". While this is sufficient for the course I am teaching, some material needed for the second semester (MA1S12) is missing. Therefore, if you intend to buy the book it is probably best to go with the paperback edition pictured below.
 |
Calculus Late Transcendentals, 9th Edition Howard Anton, Irl Bivens, Stephen Davis ISBN: 978-0-470-39874-6 Wiley 2009, (1168 pages + appendices) |
- Feedback
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- Covered so far:
| Lecture | Topics covered | Textbook chapter |
|---|---|---|
| 1 | Functions, graphs and some examples, vertical line test | 0.1 |
| 2 | Graphs, functions defined piece-wise, open and closed intervals, domain range of a function. | 0.1 |
| 3 | Natural domain of a function. New functions from old: sum, difference, product and ratio of functions, corresponding domains. | 0.2 |
| 4 | New functions from old: composition of functions. Translations and reflections, horizontal and vertical stretches and compressions of the graph of a function | 0.2 |
| 5 | New functions from old: Translations and reflections, horizontal stretches and compressions, symmetry about x-axis, about y-axis and about origin. Even and odd functions. | 0.2 |
| 6 | New functions from old: vertical stretches and compressions, symmetry of curves in the xy-plane about x-axis, about y-axis and about origin, symmetry test in algebraic expressions. | 0.2-0.3 |
| 7 | Families of functions indexed by a parameter, e.g. y=mx+b with b fixed and parameter m. Power functions, y=x^n with non-negative integer n. Inverse functions, example of Fahrenheit-Celsius conversion. | 0.3-0.4 |
| 8 | Inverse functions. How to obtain them. When do they exist? | 0.4 |
| 9 | Inverse functions cont'd. Increasing and Decreasing functions. Horizontal line test. Graph of inverse functions. Motivation for limits: tangent line to a curve from secant lines. | 0.4, 1.1 |
| 10 | Limits, an intuitive approach, informal and formal (epsilon-delta) definition of limits. One-sided limits | 1.1,1.4 |
| 11 | Limits, relationship between (two-sided) limit and one-sided limits. Infinite limits. | 1.1,1.4 |
| 12 | Infinite limits. Limits of a sum, difference, product and ratio of functions. | 1.2,1.4 |
| 13 | Limits at infinity, end behaviour of a function. Infinite limits at infinity. | 1.4 |
| 14 | Continuity of a function at a point, continuity on open and closed intervals | 1.5 |
| 15 | Continuous functions. Continuity on open and closed intervals. Continuity of sum/difference/product/ratio of functions. The intermediate value theorem. The derivative: motivation. | 1.5,2.1 |
| 16 | The derivative, tangent line to a curve, slope of the tangent line from secant lines, slope of a tangent line and rate of change. The derivative function. Differentiability at a point or in an open interval. When is a function not differentiable? Corner points and lines of vertical tangency. | 2.1,2.2 |
| 17 | Relationship between differentiability and continuity: differentiability implies continuity. Differentiability in a closed interval. Other derivative notations. Proof of power rule for positive integer exponents using binomial formula. | 2.2,2.3 |
| 18 | Techniques of differentiation: power rule for real exponents. Higher derivatives. Linearity of differentiation: (af+bg)'= af'+bg'. Product/Leibniz rule and quotient rule. | 2.3,2.4 |
| 19 | Techniques of differentiation: power rule for real exponents. Linearity of differentiation: (af+bg)'= af'+bg'. Product/Leibniz rule and quotient rule. | 2.4 |
| 20 | Techniques of differentiation: chain rule, examples. | 2.6 |
| 21 | Techniques of differentiation: chain rule, implicit differentiation | 2.6,2.7 |
| 22 | Analysis of functions: increasing and decreasing functions, concavity up and down, inflection points, relative maxima and minima | 3.1 |
| 23 | Relative extrema: first and second derivative tests; critical points, stationary points, points of non-differentiability | 3.2 |
| 24 | Absolute extrema. Extreme value theorem | 3.4 |
| 25 | Finding zeros of functions: Newton's method. Mean value theorem. | 3.7,3.8 |
| 26 | Integration: area under a curve, rectangle method, example of f(x)=x^2, square pyramidal number. | 4.1 |
| 27 | The indefinite integral. Antiderivative of a function. integral notation, power rule, trigonometic functions. Linearity of the antiderivative. Integration from the point of view of differential equations. | 4.2 |
| 28 | The indefinite integral. More examples. Slope fields as guides to picture solution without explicitly calculating it. Integration by substitution. | 4.2,4.3 |
| 29 | Guidelines for u-substitution, examples. The definite integral. Partitioning into subintervals of different widths. Riemann sums. The definite integral as limit of Riemann sums, (Riemann-) integrability of a function. Net signed area under a curve, properties of the definite integral: exchange of limits of integration is compensated by a factor (-1), linearity of the definite integral, integral over [a,a] vanishes. | 4.5 |
| 30 | The fundamental theorem of calculus (part 1), Relationship definite <-> indefinite integral | 4.6 |
| 31 | The fundamental theorem of calculus (part 2). Mean value theorem for integrals. u-substitution in definite integrals. | 4.6,4.9 |