The Lecture Notes:
- Lecture 1 (Intro to first term),
- Lecture 2 (Numbers in different bases),
- Lecture 3 (Computater related issues),
- Lecture 4 (Fractions ),
- Lecture 5 (problems with solutions),
- Lecture 6 (Review questions),
- Lecture 7 (Intro to Mathematica),
- Lecture 8 (Solve, defining functions and Plot;
tutorial Q's at the end),
- Lecture 9 (Sum, Matrix, DSolve),
- Lecture 10 (Mathematica at work),
- Lecture 11 (Went through past papers),
- Lecture 12 (Link to Mathematica commands, incomplete),
- Lecture 13 (Recap),
- Lecture 14 (Went through 2 more past papers),
- Lecture 15 (Some Coord geometry,Slope and derivative, Problem with slope at a point),
- Lecture 16 (The line, Slope, application to
max/min and Newton-Raphson),
- Lecture 17 (limits, derivative, concave up and down, max/min, Newton-Raphson),
- Lecture 18 (max/min, Newton-Raphson),
- Questions for Tutorial 2 here,
- The course description
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Summary of what we've done:
Summary of what we are doing:
- Computers work with bits. Groups of these in fact (32-bit is common at the
moment). We though are not particularly interested in bits.
- Using bits we can represent numbers, which we are interested in.
- Storing numbers in binary is the natural thing to do BUT this is limited
- The largest number we can store is only around 4 billion which is not
- We are unable to represent fractions.
- We can write numbers in scientific notation. Where we break them into
a mantissa and an exponent. Using this approach we can allocate some of our
32 bits for the mantissa and the rest for the exponent. Then we can represent
VERY LARGE NUMBERS and FRACTIONS.
- Using floating points(the mantissa and exponent approach) we only
actually have the first 7-8 decimal places of a number. For example
if you add one to 10 billion on your calculator and then subtract
10 billion you get zero and not one(in many cases). So things are not
as good as they might seem, but they really aren't too bad.
- Otherwise we looked at how you can convert to octal and hex from
binary quickly and how to express fractions in binary.
- Intro to mathematica, overblown calculators. Basically it can perform
a vast array of operations. In maths, classic questions involve finding
roots to polynomials, differentiating and integration things, working
with matrices and vectors and more. Mathematica can help in doing these
which means that you don't have to worry as much about learning how to
them(If you are a non-mathematician that is).
What you should be able to do:
- Determine what a number written in some base is equal to in base 10.
- Express numbers given in base 10 in other bases.
- Know how numbers are stored on computers(integers and floating points).
- Know how binary numbers can be converted to octal and hex, and vice versa.
- Express fractions in binary.