1 Functions And Models 2 Limits And Derivatives 3 Differentiation Rules 4 Applications Of Differentiation 5 Integrals 6 Applications Of Integration 7 Techniques Of Integration 8 Further Applications Of Integration 9 Differential Equations 10 Parametric Equations And Polar Coordinates 11 Sequences, Series, And Power Series 12 Vectors And The Geometry Of Space 13 Vector Functions 14 Partial Derivatives 15 Multiple Integrals 16 Vector Calculus A Numbers, Inequalities, And Absolute Values B Coordinate Geometry And Lines C Graphs Of Second-degree Equations D Trigonometry E Sigma Notation F Proofs Of Theorems G The Logarithm Defined As An Integral expand_more
9.1 Modeling With Differential Equations 9.2 Direction Fields And Euler's Method 9.3 Separable Equations 9.4 Models For Population Growth 9.5 Linear Equations 9.6 Predator-prey Systems Chapter Questions expand_more
Problem 1CC: (a) What is a differential equation? (b) What is the order of a differential equation? (c) What is... Problem 2CC: What can you say about the solutions of the equation y' = x2 + y2 just by looking at the... Problem 3CC: What is a direction field for the differential equation y' = F(x, y)? Problem 4CC: Explain how Euler's method works. Problem 5CC: What is a separable differential equation? How do you solve it? Problem 6CC: What is a first-order linear differential equation? How do you solve it? Problem 7CC: (a) Write a differential equation that expresses the law of natural growth. What does it say in... Problem 8CC: (a) Write the logistic differential equation. (b) Under what circumstances is this an appropriate... Problem 9CC: (a) Write Lotka-Volterra equations to model populations of food-fish (F) and sharks (S). (b) What do... Problem 1TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 2TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 3TFQ Problem 4TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 5TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 6TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 7TFQ Problem 8TFQ Problem 9TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 1E: (a) A direction field for the differential equation y' = y(y 2)(y 4) is shown. Sketch the graphs... Problem 2E: (a) Sketch a direction field for the differential equation y' = x/y. Then use it to sketch the four... Problem 3E: (a) A direction field for the differential equation y' = x2 y2 is shown. Sketch the solution of the... Problem 4E: (a) Use Euler's method with step size 0.2 to estimate y(0.4), where y(x) is the solution of the... Problem 5E: Solve the differential equation. 5. y=xesinxycosx Problem 6E: Solve the differential equation. 6. dxdy=1t+xtx Problem 7E: Solve the differential equation. 7. 2yey2y=2x+3x Problem 8E: Solve the differential equation. 8. x2yy=2x3e1/x Problem 9E: Solve the initial-value problem. 9. drdt+2tr=r,r(0)=5 Problem 10E: Solve the initial-value problem. 10. (1 + cos x) y' = (1 + ey) sin x, y(0) = 0 Problem 11E: Solve the initial-value problem. 11. xy' y = x ln x, y(1) = 2 Problem 12E: Solve the initial-value problem y' = 3x2ey, y(0) = 1 , and graph the solution. Problem 13E: Find the orthogonal trajectories of the family of curves. 13. y = kex Problem 14E: Find the orthogonal trajectories of the family of curves. 14. y = ekx Problem 15E: (a) Write the solution of the initial-value problem dPdt=0.1P(1P2000)P(0)=100 and use it to find the... Problem 16E Problem 17E: The von Bertalanffy growth model is used to predict the length L(t) of a fish over a period of time.... Problem 18E: A tank contains 100 L of pure water. Brine that contains 0.1 kg of salt per liter enters the tank at... Problem 19E: One model for the spread of an epidemic is that the rate of spread is jointly proportional to the... Problem 20E: The Brentano-Stevens Law in psychology models the way that a subject reacts to a stimulus. It states... Problem 21E: The transport of a substance across a capillary wall in lung physiology has been modeled by the... Problem 22E: Populations of birds and insects are modeled by the equations dxdt=0.4x0.002xydydt=0.2y+0.000008xy... Problem 23E: Suppose the model of Exercise 22 is replaced by the equations... Problem 24E: Barbara weighs 60 kg and is on a diet of 1600 calories per day, of which 850 are used automatically... Problem 1PP: Find all functions f such that f' is continuous and [f(x)]2=100+0x{[f(t)2]+[f(t)2]}dtforallreadx Problem 2PP: A student forgot the Product Rule for differentiation and made the mistake of thinking that (fg)' =... Problem 3PP: Let f be a function with the property that f(0) = 1, f'(0) = 1, and f(a + b) = f(a) f(b) for all... Problem 4PP: Find all functions f that satisfy the equation (f(x)dx)(1f(x)dx)=1 Problem 5PP: Find the curve y = f(x) such that f(x) 0, f(0) = 0, f(1) = 1, and the area under the graph of f... Problem 6PP: A subtangent is a portion of the x-axis that lies directly beneath the segment of a tangent line... Problem 7PP: A peach pie is taken out of the oven at 5:00 pm. At that time it is piping hot, 100C. At 5:10 pm its... Problem 8PP: Snow began to fall during the morning of February 2 and continued steadily into the afternoon. At... Problem 9PP Problem 10PP: (a) Suppose that the dog in Problem 9 runs twice as fast as the rabbit. Find a differential equation... Problem 11PP: A planning engineer for a new alum plant must present some estimates to his company regarding the... Problem 12PP: Find the curve that passes through the point (3, 2) and has the properly that if the tangent line is... Problem 13PP: Recall that the normal line to a curve at a point P on the curve is the line that passes through P... Problem 14PP: Find all curves with the properly that if the normal line is drawn at any point P on the curve, then... Problem 15PP: Find all curves with the property that if a line is drawn from the origin to any point (x, y) on the... format_list_bulleted