- 7.1: (a) What is a differential equation? (b) What is the order of a dif...
- 7.2: What can you say about the solutions of the equation just by lookin...
- 7.3: What is a direction eld for the differential equation ?
- 7.4: Explain how Eulers method works.
- 7.5: What is a separable differential equation? How do you solve it?
- 7.6: (a) Write a differential equation that expresses the law of natural...
- 7.7: (a) Write the logistic equation. (b) Under what circumstances is th...
- 7.8: (a) Write Lotka-Volterra equations to model populations of food sh ...
- 7.9: Find the orthogonal trajectories of the family of curves.
- 7.10: Find the orthogonal trajectories of the family of curves.
- 7.11: A bacteria culture contains 200 cells initially and grows at a rate...
- 7.12: Cobalt-60 has a half-life of 5.24 years. (a) Find the mass that rem...
- 7.13: Let be the concentration of a drug in the bloodstream. As the body ...
- 7.14: A cup of hot chocolate has temperature in a room kept at . After ha...
- 7.15: (a) Write the solution of the initial-value problemand use it to nd...
- 7.16: (a) The population of the world was 5.28 billion in 1990 and 6.07 b...
- 7.17: The von Bertalanffy growth model is used to predict the length of a...
- 7.18: The Brentano-Stevens Law in psychology models the way that a subjec...
- 7.19: One model for the spread of an epidemic is that the rate of spread ...
- 7.20: A tank contains 100 L of pure water. Brine that contains 0.1 kg of ...
- 7.21: The transport of a substance across a capillary wall in lung physio...
- 7.22: Populations of birds and insects are modeled by the equationsdx dt ...
- 7.23: Suppose the model of Exercise 22 is replaced by the equationsdx dt ...
- 7.24: Barbara weighs 60 kg and is on a diet of 1600 calories per day, of ...
Solutions for Chapter 7: DIFFERENTIAL EQUATIONS
Full solutions for Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) | 4th Edition
Additive inverse of a real number
The opposite of b , or -b
Difference of two vectors
<u1, u2> - <v1, v2> = <u1 - v1, u2 - v2> or <u1, u2, u3> - <v1, v2, v3> = <u1 - v1, u2 - v2, u3 - v3>
Matrices that have the same order and equal corresponding elements.
See nth power of a.
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .
A function whose domain is the first n positive integers for some fixed integer n.
Identity involving a trigonometric function of u/2.
Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a - ƒ(x) = q.
Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1 - z1) 1x - i z 22 Á 1x - z n where the z1 are the zeros of ƒ
Linear regression equation
Equation of a linear regression line
A square matrix with nonzero determinant
A function whose graph is symmetric about the origin (ƒ(-x) = -ƒ(x) for all x in the domain of f).
The formula x = -b 2b2 - 4ac2a used to solve ax 2 + bx + c = 0.
Root of a number
See Principal nth root.
The distance from the center to a vertex of an ellipse.
Standard form of a complex number
a + bi, where a and b are real numbers
The line segment whose endpoints are the vertices of a hyperbola.
The y-value of the top of the viewing window.
The y-value of the bottom of the viewing window.