- 1.4.1E: In 1–4, use Euler’s method to approximate the solution to the given...
- 1.4.1TWE: Select four fields (for example, astronomy, geology, biology, and e...
- 1.4.2E: In 1–4, use Euler’s method to approximate the solution to the given...
- 1.4.2TWE: Compare the different types of solutions discussed in this chapter—...
- 1.4.3E: ?3E 1–4, use Euler’s method to approximate the solution to the give...
- 1.4.4E: In 1–4, use Euler’s method to approximate the solution to the given...
- 1.4.5E: Use Euler’s method with step size h = 0.1 to approximate the soluti...
- 1.4.6E: ?6E Euler’s method with step size h = 0.2 to approximate the soluti...
- 1.4.7E: Use Euler’s method to find approximations to the solution of the in...
- 1.4.8E: Use Euler’s method to find approximations to the solution of the in...
- 1.4.9E: Use Euler’s method with h = 0.1 to approximate the solution to the ...
- 1.4.10E: Use the strategy of Example 3 to find a value of h for Euler’s meth...
- 1.4.11E: Use the strategy of Example 3 to find a value of h for Euler’s meth...
- 1.4.12E: In Example 2 we approximated the transcendental number e by using E...
- 1.4.13E: Prove that the “rate of convergence” for Euler’s method in is compa...
- 1.4.14E: ?14E Euler’s method with the spacings h = 0.5, 0.1, 0.05, 0.01 to a...
- 1.4.15E: Newton’s Law of Cooling. Newton’s law of cooling states that the ra...
- 1.4.16E: Stefan’s Law of Radiation. Stefan’s law of radiationstates that the...
Solutions for Chapter 1.4: Fundamentals of Differential Equations 8th Edition
Full solutions for Fundamentals of Differential Equations | 8th Edition
Axis of symmetry
See Line of symmetry.
See Compound fraction.
The behavior of a graph of a function as.
The terms of the Fibonacci sequence.
General form (of a line)
Ax + By + C = 0, where A and B are not both zero.
Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2 - x 1, y2 - y19>
Increasing on an interval
A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.
See Polynomial function in x.
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)
Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b
See Additive inverse of a real number and Additive inverse of a complex number.
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle
Projection of u onto v
The vector projv u = au # vƒvƒb2v
Secant line of ƒ
A line joining two points of the graph of ƒ.
Shrink of factor c
A transformation of a graph obtained by multiplying all the x-coordinates (horizontal shrink) by the constant 1/c or all of the y-coordinates (vertical shrink) by the constant c, 0 < c < 1.
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data
Sum of an infinite geometric series
Sn = a 1 - r , |r| 6 1
See Horizontal translation, Vertical translation.
See Weighted mean.