Handbook
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ISBN 0 7492 6647 3
88 pages
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Handbook
Content:
- The Greek alphabet
- SI units
- Mathematical modelling
- Some useful graphs
- Notation
- Glossary
- Background material for MST121 and MS221
- Definitions and results in MST121 and MS221
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Block A: Mathematical Exploration
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ISBN 0 7492 9324 1
47 pages
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Chapter A1
Exploring sequences
Content:
- The golden ratio
- Fibonacci numbers and their properties
- Linear second-order recurrence sequences
- Exploring linear second-order recurrence sequences with the computer
- Proving identities
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ISBN 0 7492 9329 2
60 pages
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Chapter A2
Conics
Content:
- What is a conic?
- Conics in standard position
- The focus-directrix property
- Quadratic curves
- Parametrising conics
- Conics on the computer
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ISBN 0 7492 9334 9
60 pages
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Chapter A3
Functions from geometry
Content:
- Functions
- Isometries
- Trigonometric formulas
- Quadratic curves revisited
- Isometries on the computer
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Block B: Exploring Iteration
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ISBN 0 7492 3998 1
60 pages
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Chapter B1
Iteration
Content:
- Iterating real functions
- Classifying fixed points
- Composition of functions
- Iterating real functions with the computer
- The Binomial Theorem
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ISBN 0 7492 4032 6
68 pages
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Chapter B2
Matrix transformations
Content:
- Vectors and matrices
- Linear transformations
- Composite and inverse transformations
- Affine transformations
- Visualising affine transformations
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ISBN 0 7492 4035 1
63 pages
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Chapter B3
Iteration with matrices
Content:
- Fixed points and invariant lines
- Eigenvalues and eigenlines
- Using eigenvalues and eigenlines
- Iterating linear transformations
- Iterating linear transformations with the computer
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Block C: Calculus
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ISBN 0 7492 2293 2
63 pages
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Chapter C1
Differentiation
Content:
- Differentiation
- Differentiating combinations of functions
- Graph sketching
- Newton-Raphson method
- Differentiation with the computer
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ISBN 0 7492 5560 9
64 pages
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Chapter C2
Integration
Content:
- Integration
- Integration by parts
- Integration by substitution
- Volumes of solids of revolution
- Integration with the computer
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ISBN 0 7492 5561 7
60 pages
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Chapter C3
Taylor polynomials
Content:
- Linear and quadratic Taylor polynomials
- Taylor polynomials
- Taylor series
- Manipulating Taylor series
- Taylor series with the computer
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Block D: Structure in mathematics
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ISBN 0 7492 6652 X
55 pages
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Chapter D1
Complex numbers
Content:
- The origins of complex numbers
- Complex numbers
- The geometry of complex numbers
- Roots of polynomials
- Complex exponentials
- Complex numbers and Mathcad
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ISBN 0 7492 6653 8
48 pages
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Chapter D2
Number theory
Content:
- Congruence
- Divisibility tests
- Modular arithmetic
- Cryptography
- Number theory and Mathcad
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ISBN 0 7492 6654 6
60 pages
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Chapter D3
Groups
Content:
- Symmetry
- Groups
- Isomorphic groups
- Groups in action
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ISBN 0 7492 2296 3
48 pages
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Chapter D4
Proof and reasoning
Content:
- Aspects of proof
- Implication and deduction
- Proof by mathematical induction
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Computer Books
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ISBN 0 7492 6651 1
35 pages
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Computer Book A
Mathematical Exploration
Content:
- Exploring linear second-order recurrence sequences with the computer
- Conics on the computer
- Isometries on the computer
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ISBN 0 7492 6648 1
36 pages
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Computer Book B
Exploring Iteration
Content:
- Iterating real functions with the computer
- Visualising affine transformations
- Iterating linear transformations with the computer
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ISBN 0 7492 6649 X
30 pages
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Computer Book C
Calculus
Content:
- Differentiation with the computer
- Integration with the computer
- Taylor series with the computer
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ISBN 0 7492 6650 3
28 pages
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Computer Book B
Structure in Mathematics
Content:
- Complex numbers and Mathcad
- Number theory and Mathcad
- Symmetry
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