 9.1.1: In 110 use the improved Eulers method to obtain a fourdecimal appr...
 9.1.2: In 110 use the improved Eulers method to obtain a fourdecimal appr...
 9.1.3: In 110 use the improved Eulers method to obtain a fourdecimal appr...
 9.1.4: In 110 use the improved Eulers method to obtain a fourdecimal appr...
 9.1.5: In 110 use the improved Eulers method to obtain a fourdecimal appr...
 9.1.6: In 110 use the improved Eulers method to obtain a fourdecimal appr...
 9.1.7: In 110 use the improved Eulers method to obtain a fourdecimal appr...
 9.1.8: In 110 use the improved Eulers method to obtain a fourdecimal appr...
 9.1.9: In 110 use the improved Eulers method to obtain a fourdecimal appr...
 9.1.10: In 110 use the improved Eulers method to obtain a fourdecimal appr...
 9.1.11: Consider the initialvalue problem y (x y 1)2 , y(0) 2. Use the imp...
 9.1.12: Although it might not be obvious from the differential equation, it...
 9.1.13: Consider the initialvalue problem y 2y, y(0) 1. The analytic solut...
 9.1.14: Repeat using the improved Eulers method. Its global truncation erro...
 9.1.15: Repeat using the initialvalue problem y x 2y, y(0) 1. The analytic...
 9.1.16: Repeat using the improved Eulers method. Its global truncation erro...
 9.1.17: Consider the initialvalue problem y 2x 3y 1, y(1) 5. The analytic ...
 9.1.18: Repeat using the improved Eulers method, which has a global truncat...
 9.1.19: Repeat for the initialvalue problem y ey , y(0) 0. The analytic so...
 9.1.20: Repeat using the improved Eulers method, which has global truncatio...
 9.1.21: Answer the question Why not? that follows the three sentences after...
Solutions for Chapter 9.1: EULER METHODS AND ERROR ANALYSIS
Full solutions for A First Course in Differential Equations with Modeling Applications  10th Edition
ISBN: 9781111827052
Solutions for Chapter 9.1: EULER METHODS AND ERROR ANALYSIS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. Since 21 problems in chapter 9.1: EULER METHODS AND ERROR ANALYSIS have been answered, more than 41530 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. Chapter 9.1: EULER METHODS AND ERROR ANALYSIS includes 21 full stepbystep solutions.

Circular functions
Trigonometric functions when applied to real numbers are circular functions

Closed interval
An interval that includes its endpoints

Conversion factor
A ratio equal to 1, used for unit conversion

Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.

Exponent
See nth power of a.

Fundamental
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).

Instantaneous rate of change
See Derivative at x = a.

Limit
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

Lower bound of f
Any number b for which b < ƒ(x) for all x in the domain of ƒ

Parallelogram representation of vector addition
Geometric representation of vector addition using the parallelogram determined by the position vectors.

Period
See Periodic function.

Polar equation
An equation in r and ?.

Right triangle
A triangle with a 90° angle.

Sequence of partial sums
The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

Sine
The function y = sin x.

Speed
The magnitude of the velocity vector, given by distance/time.

Standard position (angle)
An angle positioned on a rectangular coordinate system with its vertex at the origin and its initial side on the positive xaxis

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

Unit circle
A circle with radius 1 centered at the origin.

xaxis
Usually the horizontal coordinate line in a Cartesian coordinate system with positive direction to the right,.