# Math 421:01 - Advanced Calculus for Engineering

Instructor: Natalia Komarova, office hours M 1:30-2:30 and W 11:30-12:30, Hill 426; email: komarova@math

Place: SEC 204

Time: MW 5 (2:50-4:10)

Main text: Advanced Engineering Mathematics by Peter V. O'Neil.

Prerequisits: Primarily for mechanical engineering majors. CALC 4. Credit not given for both this course and 01:640:423

Course description: Laplace transforms, numerical solution of ordinary differential equations, Fourier series, and separation of variables method applied to the linear partial differential equations of mathematical physics (heat, wave, and Laplace's equation).

## Tentative syllabus

The grade will be decided on the basis of the two midterm exams (20% each), the final exam (40%), the homework (10%) and the quizzes (10%). The homework assignments are graded by a teaching assistant, who is asked to choose three problems at random for grading. The quizzes are graded by the professor. The worst homework and the worst quiz are not taken into account.

## Midterm 1 materials:

Date: Monday, March 1.

No calculators or books can be used on the midterm. A formula sheet will be provided.

• Sample problems for Midterm 1

• Some solutions for sample problems, and more solutions here.

• Solutions for Midterm 1 problems.

ATTENTION those who got 59 or less for the first midterm. On Monday, March 22, at 1:30-2:30, Hill 425, you can take a make-up test to gain up to 25 points to be added to your midterm result. In order to prepair for this test, please use the practice sheet. Also, study the Solutions for Midterm 1 problems, above.

## Midterm 2 materials:

Date: Monday, April 5.

No calculators or books can be used on the midterm. A list of useful matrix reduction facts will be provided.

• Sample problems for Midterm 2

• Some solutions for sample problems.

## Final exam materials:

Date: Thursday, May 6, 8:00-11:00 am

Place: SEC 204.

No calculators or books can be used on the final. A list of formulas will be provided.

• Sample problems for the Final exam, part 3

• Some solutions for sample problems.

Sample problems for the Final, parts 1 and 2 are the same as the sample problems for Midterms 1 and 2.

## Homework assignments

• Homework 1, due Mon Jan 26.

• Homework 2, due Mon Feb 2. Some solutions

• Homework 3, due Mon Feb 9. Some solutions

• Homework 4, due Mon Feb 16: Section 3.6: 1, 2, 12; Section 3.7: 2, 9. Some solutions

• Homework 5, due Mon Feb 23: Section 5.4: 1, 7; Section 5.5: 5, 17; Section 6.1: 11.

• Homework 6, due Wed Mar 3 (next class after the midterm!): Section 6.3: 1; Section 6.4: 5, 9; Section 6:5: 5, 7.

• Homework 7, due Wed Mar 10: Section 6.7: 1, 3, 5; Section 6.9: 17, 19

• Homework 8, due Mon Mar 22: Section 6.8: 5, 7; Section 7.1: 1, Section 7.2: 1, Section 7.4: 7, 9.

• Homework 9, due Mon Mar 29: Section 7.5: 13; Section 7.6: 1, Section 7.7: 7; Section 7.8: 5, 9; Section 8.1: 1(a,b), 7(a,b).

• Homework 10, due Mon Apr 5: Section 8.2: 3, 5, 7.

• Homework 11, due Mon Apr 19: Section 13.2: 1, 6, 7; Section 13.3: 5, 7 (for these problems, calculate Fourier Series, and then for N=5, 10, 15, 25 plot the Nth partial sum together with the function itself); Section 13.4: 1, 5.

• Homework 12, due Mon Apr 26: Section 16.2: 1, 5; Section 16.4: 1, 3, 5 (only write down the D'Alembert's solution).

## Quiz solutions

• Quiz 2

• Quiz 3

• Quiz 5

• Quiz March 29

Link to Math 421:02 taught by Stephen Greenfield.