tut07 - The University of Sydney Math1003 Integral Calculus...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
The University of Sydney Math1003 Integral Calculus and Modelling Semester 2 Exercises for Week 7 2011 Assumed Knowledge Proportionality and inverse proportionality. Integration techniques. Taylor series expansion. Objectives (6a) Given a verbal description of a simple model, to be able to express it as a mathematical equation. (6b ) To be able to recognise an ordinary diFerential equation. (6c) To be able to sketch the solution curves for a ±rst-order diFerential equation from its direction ±eld. Preparatory Questions 1. ( i ) The diFerential equation dy dx = f ( x ) has a direction ±eld given by the diagram below. On the direction ±eld draw the graphs of two solutions of dy/dx = f ( x ), where one solution y = g ( x ) passes through the point (0 , 1) and the other solution y = h ( x ) satis±es the equation h (1) = 0. ( ii ) Do the graphs of y = g ( x ) and y = h ( x ) intersect? If not, why not? 1 2 3 1 1 2 3 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Practice Questions 2. Heat tends to fow From hot bodies to cold bodies. Newton observed that the rate at which temperature rises or Falls within a body is proportional to the temperature di±erence between the body and its surroundings.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

tut07 - The University of Sydney Math1003 Integral Calculus...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online