Schedule & Homework

Schedule & Homework

Week 1, Jan 23-29

Problem sheet 1.

(This homework will not be graded. Solutions will be discussed during the lecture of Wednesday Jan 25.)

Week 2, Jan 30 - Feb 5

Review: definition of integrals §§ 1.9, 1.12, 1.16, 1.17 in [A]

the Fundamental Theorem of Calculus §§ 5.1-5.3 in [A]

complex numbers §§ 9.1-9.7 in [A]

Notes: Notes1

Reading: vectors, dot product, norm: §§ 12.1-12.9 in [A]

polar coordinates: §§ 2.9-2.10 in [A]

parametrized curves: Appendix to Chapter 12 in [S]

Homework: HW1 (due on Feb 6 at the recitation meeting)

Week 3, Feb 6 - Feb 12

Reading: uniform continuity and integrability: §§ 3.17-3.18 in [A]

parametrized curves and their length: pp. 135-137 in [R]

curvature: §§ 2.1-2.3 in [P]

For a reference to the topics on curves (length, curvature and the Isoperimetric Inequality) we are studying you can have a look at sections 1.1, 1.2, 1.3, 2.1, 2.2, 3.1 and 3.2 of

[P] Elementary Differential Geometry, by A. Pressley, Springer Undergraduate Mathematics Series.

Homework: HW2 (due on Feb 13 at the recitation meeting)

Week 4, Feb 13 - Feb 19

Reading: the Isoperimetric Inequality: §§ 3.1-3.2 in [P]

sequences: §§ 10.2-10.3 in [A] and Chapter 3 in [R]

Homework: HW3 (due on Feb 20 at the recitation meeting)

Week 5, Feb 20 - 26

Review and First Midterm Exam

Week 6, Feb 27 - Mar 5

Reading: Newton’s Method: exercises 16-17-18 on p. 81 in [R]

Uniform convergence: §§11.1-11.4 in [A] and pp. 143-154 in [R]

Homework: HW4 (due on Mar 6 at the recitation meeting)

Week 7, Mar 6-12

Reading: Uniform convergence: Chapter 7, pp. 143-160 in [R]

Notes: Notes4

Homework: HW5 (due on Mar 20 at the recitation meeting)

Week 8, Mar 20-26

Reading: Weierstrass Approximation Theorem: Chapter 7, pp. 159-160 in [R]

Taylor polynomials: Chapter 7, §§ 7.1-7.8 in [A]

Series of functions: Chapter 11, §§ 11.6-11.16 in [A]

Notes: Notes4

Homework: HW6 (due on Mar 27 at the recitation meeting)

Week 9, Mar 27 - Apr 2

Reading: Power series, Taylor series: Chapter 11, §§ 11.6-11.13 in [A]

Homework: HW7 (due on Apr 3 at the recitation meeting)

Week 10, Apr 3-9

Second Midterm Exam

Reading: First-order differential equations. Notes5 provides a guide to readings and exercises and contains detailed references to sections in Chapter 8 of [A].

Homework: problems 1, 2.(a), 2.(b).iv, 2.(c) in Notes5

(due on Apr 9 at the recitation meeting)

Week 11, Apr 10-16

Reading: First-order differential equations. Notes5 provides a guide to readings and exercises and contains detailed references to sections in Chapter 8 of [A].

Homework: problems 10-11 in §8.5 in [A], 2 and 10 in §8.24 in [A], 4.(d) and 5 in Notes5

(due on Apr 17 at the recitation meeting)

Week 12, Apr 17-23

Reading: First and second-order differential equations. Notes5 provides a guide to readings and exercises and contains detailed references to sections in Chapter 8 of [A].

Homework: problems 6.(e), 7.(a) and (c) for exercises 3 and 5 in §8.22 of [A], 7.(b) for exercise 6 in §8.26 of [A], 8 in Notes5

(due on Apr 24 at the recitation meeting)

Week 13, Apr 24-30

Reading: Second-order differential equations. Notes5 provides a guide to readings and exercises and contains detailed references to sections in Chapter 8 of [A].

Homework: exercises 15, 17, 19, 20 in §8.14 of [A]

exercises 6, 7, 12, 22 in §8.17 of [A]

problems 14.(b) and 14.(c) in Notes5

(due on May 1 at the recitation meeting)

Week 14, May 1-7

Reading: §14.20 in [A].

Review.