ADVANCED ENGINEERING MATH.>CUSTOM<
10th Edition
ISBN: 9781119480150
Author: Kreyszig
Publisher: WILEY C
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1) a) Determine which functions are solutions of the following
linear differential equation:
y"- 6y' + 9y=0
i) e³x
isė
зх
23x
ii) xe ³x iii) x² ³x iv) (x+3) e³x
3×
хе
b) Find the Wronskion
хе
the set of functions that you fand
for
as the solution of the differential equation above
from a)
c) What does the result that you found from b) imply?
conici
2) Perform a rotation of axes to eliminate the xy-term,
identify and sketch the graph of the following a
5x²-2xy + Sy²=24=0
Use the Chinese cube root algorithm to find the cube root
of 12,812,904.
Perform the calculations in Liu Hui's algorithm for deter-
mining л to find S2n for n = 6, 12, 24, 48, and 96.
Chapter 1 Solutions
ADVANCED ENGINEERING MATH.>CUSTOM<
Ch. 1.1 - Prob. 1PCh. 1.1 - Prob. 2PCh. 1.1 - Prob. 3PCh. 1.1 - Prob. 4PCh. 1.1 - Prob. 5PCh. 1.1 - Prob. 6PCh. 1.1 - Prob. 7PCh. 1.1 - Prob. 8PCh. 1.1 - Prob. 9PCh. 1.1 - Prob. 10P
Ch. 1.1 - Prob. 11PCh. 1.1 - Prob. 12PCh. 1.1 - Prob. 13PCh. 1.1 - Prob. 14PCh. 1.1 - 9–15 VERIFICATION. INITIAL VALUE PROBLEM...Ch. 1.1 - Prob. 16PCh. 1.1 - Half-life. The half-life measures exponential...Ch. 1.1 - Half-life. Radium has a half-life of about 3.6...Ch. 1.1 - Prob. 19PCh. 1.1 - Exponential decay. Subsonic flight. The efficiency...Ch. 1.2 - DIRECTION FIELDS, SOLUTION CURVES
Graph a...Ch. 1.2 - 1–8 DIRECTION FIELDS, SOLUTION CURVES
Graph a...Ch. 1.2 - DIRECTION FIELDS, SOLUTION CURVES
Graph a...Ch. 1.2 - Prob. 4PCh. 1.2 - DIRECTION FIELDS, SOLUTION CURVES
Graph a...Ch. 1.2 - Prob. 6PCh. 1.2 - DIRECTION FIELDS, SOLUTION CURVES
Graph a...Ch. 1.2 - Prob. 8PCh. 1.2 - Prob. 9PCh. 1.2 - Prob. 10PCh. 1.2 - Autonomous ODE. This means an ODE not showing x...Ch. 1.2 - Model the motion of a body B on a straight line...Ch. 1.2 - Prob. 13PCh. 1.2 - Prob. 14PCh. 1.2 - Prob. 15PCh. 1.2 - Prob. 16PCh. 1.2 - EULER’S METHOD
This is the simplest method to...Ch. 1.2 - EULER’S METHOD
This is the simplest method to...Ch. 1.2 - EULER’S METHOD
This is the simplest method to...Ch. 1.2 - EULER’S METHOD
This is the simplest method to...Ch. 1.3 - Prob. 1PCh. 1.3 - Prob. 2PCh. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - Prob. 17PCh. 1.3 - Prob. 18PCh. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - Prob. 20PCh. 1.3 - Radiocarbon dating. What should be the content...Ch. 1.3 - Prob. 22PCh. 1.3 - Prob. 23PCh. 1.3 - Prob. 24PCh. 1.3 - Prob. 25PCh. 1.3 - Prob. 26PCh. 1.3 - Prob. 27PCh. 1.3 - Prob. 28PCh. 1.3 - Prob. 29PCh. 1.3 - Prob. 30PCh. 1.3 - Prob. 31PCh. 1.3 - Prob. 32PCh. 1.3 - Prob. 33PCh. 1.3 - Prob. 36PCh. 1.4 - Prob. 1PCh. 1.4 - Prob. 2PCh. 1.4 - Prob. 3PCh. 1.4 - Prob. 4PCh. 1.4 - Prob. 5PCh. 1.4 - Prob. 6PCh. 1.4 - Prob. 7PCh. 1.4 - Prob. 8PCh. 1.4 - Prob. 9PCh. 1.4 - ODEs. INTEGRATING FACTORS
Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS
Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS
Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS
Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS
Test for exactness. If...Ch. 1.4 - Exactness. Under what conditions for the constants...Ch. 1.4 - Prob. 17PCh. 1.4 - Prob. 18PCh. 1.5 - CAUTION! Show that e−ln x = 1/x (not −x) and...Ch. 1.5 - Prob. 2PCh. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
7. xy′ =...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
9.
Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - Prob. 14PCh. 1.5 - Prob. 15PCh. 1.5 - Prob. 16PCh. 1.5 - Prob. 17PCh. 1.5 - Prob. 18PCh. 1.5 - Prob. 19PCh. 1.5 - GENERAL PROPERTIES OF LINEAR ODEs
These properties...Ch. 1.5 - Prob. 21PCh. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - Prob. 29PCh. 1.5 - MODELING. FURTHER APPLICATIONS
31. Newton’s law of...Ch. 1.5 - Prob. 32PCh. 1.5 - MODELING. FURTHER APPLICATIONS
33. Drug injection....Ch. 1.5 - MODELING. FURTHER APPLICATIONS
34. Epidemics. A...Ch. 1.5 - MODELING. FURTHER APPLICATIONS
35. Lake Erie. Lake...Ch. 1.5 - MODELING. FURTHER APPLICATIONS
36. Harvesting...Ch. 1.5 - Prob. 37PCh. 1.5 - Prob. 38PCh. 1.5 - Prob. 39PCh. 1.5 - Prob. 40PCh. 1.6 -
Represent the given family of curves in the form...Ch. 1.6 - Prob. 2PCh. 1.6 -
Represent the given family of curves in the form...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - APPLICATIONS, EXTENSIONS
11. Electric field. Let...Ch. 1.6 - Electric field. The lines of electric force of two...Ch. 1.6 - Prob. 13PCh. 1.6 - Conic sections. Find the conditions under which...Ch. 1.6 - Prob. 15PCh. 1.6 - Prob. 16PCh. 1.7 - Prob. 1PCh. 1.7 - Existence? Does the initial value problem (x −...Ch. 1.7 - Vertical strip. If the assumptions of Theorems 1...Ch. 1.7 - Change of initial condition. What happens in Prob....Ch. 1.7 - Prob. 5PCh. 1.7 - Maximum α. What is the largest possible α in...Ch. 1.7 - Prob. 8PCh. 1.7 - Common points. Can two solution curves of the same...Ch. 1.7 - Three possible cases. Find all initial conditions...Ch. 1 - Prob. 1RQCh. 1 - Prob. 2RQCh. 1 - Does every first-order ODE have a solution? A...Ch. 1 - What is a direction field? A numeric method for...Ch. 1 - What is an exact ODE? Is f(x) dx + g(y) dy = 0...Ch. 1 - Prob. 6RQCh. 1 - What other solution methods did we consider in...Ch. 1 - Can an ODE sometimes be solved by several methods?...Ch. 1 - Prob. 9RQCh. 1 - Prob. 10RQCh. 1 - Prob. 11RQCh. 1 - Prob. 12RQCh. 1 - Prob. 13RQCh. 1 - Prob. 14RQCh. 1 - Prob. 15RQCh. 1 - DIRECTION FIELD: NUMERIC SOLUTION
Graph a...Ch. 1 - Prob. 17RQCh. 1 - Prob. 18RQCh. 1 - Prob. 19RQCh. 1 - Prob. 20RQCh. 1 - Prob. 21RQCh. 1 - Prob. 22RQCh. 1 - Prob. 23RQCh. 1 - Prob. 24RQCh. 1 - Prob. 25RQCh. 1 - Prob. 26RQCh. 1 - Prob. 27RQCh. 1 - Prob. 28RQCh. 1 - Half-life. If in a reactor, uranium loses 10% of...Ch. 1 - Prob. 30RQ
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