MATH 1500X/Y

**Handouts:**

- Homework 1 | Solutions
- Homework 2 | Solutions
- Homework 3 | Solutions
- Homework 4 | Solutions
- Midterm 1 practice questions | Solutions
- Some calculus problems
- Homework 5
- Homework 6 | Solutions
- Homework 7
- Homework 8 | Solutions
- Practice questions for midterm 2
- Homework 9: For your practice only, do not hand in.

Section 5.3: 13,14,17.

Section 5.5: 1-22 (selection), 36, 39-44.

Section 5.6: 1-44 (selection)

- Practice sheet for the final exam
- Final exam 1 | Solutions
- Homework 10 | Solutions
- Homework 11 | Solutions
- Homework 12 | Solutions
- Homework 13 | Solutions
- Homework 14 | Solutions
- An example of Romberg integration (Richardson extrapolation)
- Sample questions for midterm 3
- Homework 15, due Monday 8 March: Section 9.1 (8,10,22,25,28,35)

Section 9.2 (6,8,9,10,11,14,21)

- Homework 16 | Solutions
- Homework 17 | Solutions
- Bonus question: hand in anytime just before the final exam. | Solutions
- Review questions for midterm 4 | Solutions
- The motion of a hanging chain | Maple worksheet with animation

**Course outline.** A tenative list of topics is given below. It is
subject to change.

- Completeness of real numbers, limits, delta-epsilon arguments
- Derivatives, graph sketching, optimization
- Logistic map, discrete dynamical systems
- Integration, fundamental theorem of calclulus
- Applications of integrals
- Numerical methods: root finding, differentiation, integration, error estimates, Richardson extrapolation
- Parametric curves, polar coordinates
- Complex numbers: Fundamental theorem of Algebra, Euler's formula
- Sequences and series
- Fourier series, Gibbs phenomenon
- Differential equations: exact solutions, stability analysis, applications.

**Relation to other Calculus courses:** Math 1500X/Y is a
two-semester Calculus course which is an enriched version of Math
1000/1010. This stream is recommended for students who did well in high
school Math 12 and would like a more challenging experience. You have
the option of transferring to Math 1000 in the first three weeks of the
class without any penalty.

** Textbook:** Adams,
* Calculus, 7-th edition* is available at the bookstore.
A copy has been placed on reserve in the library.

** Evaluation **

The final exam grade (F) is taken to be the best of

F = 0.5 F1 + 0.5 F2

F = 0.25 F1 + 0.75 F2

where F1 and F2 are the final exam grades for first and second half, respectively.

The midterm grade M is taken to be the average of the four midterms; similar for the homework grade H.

The overall grade will be taken to be the best of:

0.25 H + 0.25 M + 0.5 F

0.125 H + 0.125 M + 0.75 F