Section                           Questions
8.1                                    2, 3, 4
8.1                                    12, 13, 14 (Use the Taylor Series Method)
8.2                                    1, 2
8.3                                    17, 27, 30
 
6.2                                    1, 2, 4, 8, 12, 18, 27, 29, 30, 32
 
5.2                                    1-16      
5.4                                    1-6
5.5                                    1-6
 
3.1                                     16, 25, 33, 39, 40
3.3                                    7, 18, 19, 26, 35
3.5                                    3, 4, 13, 20, 55, 54
 
2.4                                    7
 
1.1                                    5, 7, 22, 34 
1.2                                    5, 9, 17
1.3                                    1, 23
1.4                                    5, 13, 21
1.5                                    3, 5, 9, 17, 35
1.6                                    31, 33, 35, 37

 

Maple Assignment 4: due date 10th of November. Can be submitted through email.

Use Variation of Parameters to solve 5.6) 30 and 31.  Then use Euler and Runge Kutta approximations, 10 steps each, to obtain solutions when time = 1.  Compare your answers at time = 1 with the actual solutions.  Compute Errors for both approximations.

 

Maple Assignment 3: due date 27th of October.  Can be submitted through email.

Use Maple to solve the following problems:

Section 5.4  10, 14, 20, 22.

Section 5.5  7, 8.

Useful Maple commands are array, exponential, evalm, eigenvects, and eigenvals.

 

Maple Assignment 2: due date 28 of September.  Can be submitted through email.

Use the Euler, Improved Euler, and Runge-Kutta Maple Worksheets to answer these questions.

1)       Consider the D.E dy/dx = sin(x) – y, y(0) = 1.

Find the value, using five steps, of y(1) with the different approximating methods.  Draw a table with the following columns: step, x value, y value (Euler), y value (Improved Euler), y value (Runge-Kutta), y value (actual), Euler error, Improved Euler error, Runge-Kutta error.

 

Maple Assignment 1: due date 21 of September.  Can be submitted through email.

Use the Direction Field Maple Worksheet to answer these questions.

1)       Consider the D.E dy/dx = e^(-x^2).

a)       Suppose y(0) = 0.  What will be value (approximately) of y(7)?

b)       Suppose y(0) = 3.  What will be value (approximately) of y(-10)?

2)       Consider the D.E dy/dx = sin(x) – y^2.

a)       Suppose y(-4) = 0.  What will be value (approximately) of y(-7), y(3), y(-9)?

b)       Why do solution curves tend to oscillate around y=0?