Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 107. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | Systems of Differential Equations 1041 PROBLEMS FOR SECTION 1. Let x x i be the number of hundreds of animals of species A at time i. Let y y i be the number of hundreds of animals of species B at time i. For each system of differential equations describe the nature of the interaction between the two species. What happens to each species in the absence of the other a c - - - - - - b - For each system of differential equations in Problems 2 through 4 find the nullclines and identify the equilibrium solutions. 2. 3. 4. - - Éf - - - - - Suppose 5. Let x x i be the number of thousands of animals of species A at time i. Let y y i be the number of thousands of animals of species B at time i. t x - y - . a Is the interaction between species A and B symbiotic competitive or a predatorprey relationship b What are the equilibrium populations c Find the nullclines and draw directed horizontal and vertical tangent lines in the phase-plane as in Figures and . d The nullclines divide the flrst quadrant of the phase-plane into four regions. In each region determine the general direction of the trajectories. e If x 0 what happens to y i How is this indicated in the phase-plane If y 0 what happens to x i How is this indicated in the phase-plane f Use the information gathered in parts b through e to sketch representative solution trajectories in the phase-plane. Include arrows indicating the direction the trajectories are traveled. g For each of the initial conditions given below describe how the number of species of A and B change with time and what the situation will look like in the long run. i. x 0 2 y 0 ii. x 0 2 y 0 iii. x 0 y 0 2 1042 CHAPTER 31 Differential Equations h Does this particular model support
