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MA1002 Calculus Applications of
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MA1002 Calculus Applications of
Contents
Contents
List of Figures
Applications
Rates of Change
Introduction
Questions 1 (Hints and solutions start on page
.)
Worked Examples
Questions 2 (Hints and solutions start on page
.)
Velocity and Acceleration
Velocity
* Motion in Space
Questions 3 (Hints and solutions start on page
.)
Optimisation
Introduction
Critical Points
Maxima and Minima
Questions 4 (Hints and solutions start on page
.)
Being Careful
Questions 5 (Hints and solutions start on page
.)
The Second Derivative Test
Questions 6 (Hints and solutions start on page
.)
Justification of the Test
Practical Problems
Questions 7 (Hints and solutions start on page
.)
Curve Sketching
Introduction
Methods
Some Common Graphs
Quadratics
Questions 8 (Hints and solutions start on page
.)
*Cubics
Questions 9 (Hints and solutions start on page
.)
The function
f
(
x
) =
x
n
, Even and Odd Functions
Questions 10 (Hints and solutions start on page
.)
Functions that `blow up'
Questions 11 (Hints and solutions start on page
.)
Worked Examples
Questions 12 (Hints and solutions start on page
.)
Approximation and Taylor Series
Introduction
Accuracy
Questions 13 (Hints and solutions start on page
.)
Linear Approximation
Questions 14 (Hints and solutions start on page
.)
Small Changes
Questions 15 (Hints and solutions start on page
.)
Solving Equations--Approximately
Newton's Method
Questions 16 (Hints and solutions start on page
.)
Higher Approximations
Second Approximation
Higher Approximations
Questions 17 (Hints and solutions start on page
.)
* l'Hôpital's Rule
Questions 18 (Hints and solutions start on page
.)
Taylor Series
Infinite Series
Geometric Series
Taylor Series
The Binomial Series
Questions 19 (Hints and solutions start on page
.)
Solutions to Exercises
Solutions for Questions 1 (page
).
Solutions for Questions 2 (page
).
Solutions for Questions 3 (page
).
Solutions for Questions 4 (page
).
Solutions for Questions 5 (page
).
Solutions for Questions 6 (page
).
Solutions for Questions 7 (page
).
Solutions for Questions 8 (page
).
Solutions for Questions 9 (page
).
Solutions for Questions 10 (page
).
Solutions for Questions 11 (page
).
Solutions for Questions 12 (page
).
Solutions for Questions 13 (page
).
Solutions for Questions 14 (page
).
Solutions for Questions 15 (page
).
Solutions for Questions 16 (page
).
Solutions for Questions 17 (page
).
Solutions for Questions 18 (page
).
Solutions for Questions 19 (page
).
About this document ...
Ian Craw 2000-01-20
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