1 Functions 2 Limits 3 Derivatives 4 Applications Of The Derivative 5 Integration 6 Applications Of Integration 7 Logarithmic And Exponential, And Hyperbolic Functions 8 Integration Techniques 9 Differential Equations 10 Sequences And Infinite Series 11 Power Series 12 Parametric And Polar Curves 13 Vectors And The Geometry Of Space 14 Vector-valued Functions 15 Functions Of Several Variables 16 Multiple Integration 17 Vector Calculus A Proofs Of Selected Theorems B Algebra Review C Complex Numbers expand_more
9.1 Basic Ideas 9.2 Direction Fields And Euler's Method 9.3 Separable Differential Equations 9.4 Special First-order Linear Differential Equations 9.5 Modeling With Differential Equations Chapter Questions expand_more
Problem 1QC: Assuming solutions are unique (at most one solution curve passes through each point), explain why a... Problem 2QC Problem 3QC Problem 4QC: Notice that the errors in Table 9.1 increase in time for both time steps. Give a possible... Problem 1E: Explain how to sketch the direction field of the equation y(t) = f(t, y), where f is given. Problem 2E Problem 3E Problem 4E Problem 6E: Identifying direction fields Which of the differential equations ad corresponds to the following... Problem 7E: Direction fields A differential equation and its direction field are shown in the following figures.... Problem 8E Problem 9E: Direction fields with technology Plot a direction field for the following differential equation with... Problem 10E Problem 11E: Direction fields with technology Plot a direction field for the following differential equation with... Problem 12E: Sketching direction fields Use the window [2, 2] [2, 2] to sketch a direction field for the... Problem 13E: Sketching direction fields Use the window [2, 2] [2, 2] to sketch a direction field for the... Problem 14E: Sketching direction fields Use the window [2, 2] [2, 2] to sketch a direction field for the... Problem 15E: Sketching direction fields Use the window [2, 2] [2, 2] to sketch a direction field for the... Problem 16E: Sketching direction fields Use the window [2, 2] [2, 2] to sketch a direction field for the... Problem 17E: Increasing and decreasing solutions Consider the following differential equations. A detailed... Problem 18E: Increasing and decreasing solutions Consider the following differential equations. A detailed... Problem 19E: Increasing and decreasing solutions Consider the following differential equations. A detailed... Problem 20E: Increasing and decreasing solutions Consider the following differential equations. A detailed... Problem 21E: Logistic equations Consider the following logistic equations, for t 0. In each case, sketch the... Problem 22E: Logistic equations Consider the following logistic equations, for t 0. In each case, sketch the... Problem 23E: Logistic equations Consider the following logistic equations, for t 0. In each case, sketch the... Problem 24E: Logistic equations Consider the following logistic equations, for t 0. In each case, sketch the... Problem 25E: Two steps of Eulers method For the following initial value problems, compute the first two... Problem 26E: Two steps of Eulers method For the following initial value problems, compute the first two... Problem 27E: Two steps of Eulers method For the following initial value problems, compute the first two... Problem 28E: Two steps of Eulers method For the following initial value problems, compute the first two... Problem 29E: Errors in Eulers method Consider the following initial value problems. a.Find the approximations to... Problem 30E: Errors in Eulers method Consider the following initial value problems. a.Find the approximations to... Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E Problem 38E: Equilibrium solutions A differential equation of the form y(t) = f(y) is said to be autonomous (the... Problem 39E Problem 40E Problem 41E: Equilibrium solutions A differential equation of the form y(t) = f(y) is said to be autonomous (the... Problem 43E: Equilibrium solutions A differential equation of the form y(t) = f(y) is said to be autonomous (the... Problem 44E: Direction field analysis Consider the first-order initial value problem y(t)=ay+b,y(0)=A, for t ... Problem 45E: Eulers method on more general grids Suppose the solution of the initial value problem... Problem 46E: Analyzing models The following models were discussed in Section 9.1 and reappear in later sections... Problem 47E Problem 48E: Analyzing models The following models were discussed in Section 9.1 and reappear in later sections... Problem 49E: Convergence of Eulers method Suppose Eulers method is applied to the initial value problem... Problem 50E: Stability of Eulers method Consider the initial value problem y'(t) = ay, y(0) = 1, where a 0; it... format_list_bulleted