MA 501 Advanced Mathematics for Engineers and Scientists I
You can download the syllabus here.
More information can be found on the course Moodle page.
Textbook: Advanced Engineering Mathematics, 7th Ed., by Peter V. O’Neil
Fall 2024 Tentative Course Schedule
Week 1

08/20 Lecture 1: Welcome and Course Overview; Review of ordinary differential equations
– Sections 1.1  1.2 
08/22 Lecture 2: Review of ordinary differential equations
– Sections 2.1  2.3, 2.5
Week 2

08/27 Lecture 3: Series Solutions of Ordinary Differential Equations (Zoom lecture)
– Section 4.1 
08/29 Lecture 4: Singular Points and the Method of Frobenius (Zoom lecture)
– Section 4.2
** Homework 1 due Thursday
Week 3

09/03 Lecture 5: Singular Points and the Method of Frobenius continued
– Section 4.2 
09/05 Lecture 6: The 1D Heat Equation on a Finite Domain I
– Sections 17.1  17.2
Week 4

09/10 Lecture 7: The 1D Heat Equation on a Finite Domain II
– Sections 17.2 
09/12 Lecture 8: , Fourier Series of a Function, Fourier Cosine and Sine Series
– Sections 13.1  13.4
** Homework 2 due Thursday
Week 5

09/17 Wellness Day; No Class

09/19 Lecture 9: Visualization of Fourier Series and the Gibbs Effect, Convergence of Fourier Series.
– Sections 13.5  13.6
Week 6

09/24 Lecture 10: Complex Fourier Series, Fourier Integrals
– Sections 13.6, 14.1  14.2 
09/26 Lecture 11: Fourier Integrals
– Sections 13.6, 14.1  14.2
** Homework 3 due Friday
Week 7

10/01 Lecture 12: Fourier Transform
– Sections 14.3 
10/03 Lecture 13: Fourier Transform (ctd)
– Sections 14.3
Week 8

10/08 Lecture 14: The 1D Heat Equation on Infinite Domain

10/10 Midterm
** Homework 4 due Wednesday at 4:30 pm
Week 9

10/15 Fall Break: No Class.

10/17 Lecture 15: The 1D Wave Equation on a Finite Domain
– Sections 16.1  16.2
** Homework 5 due Thursday
Week 10

10/22 Lecture 16: D’Alembert’s Solution to the 1D Wave Equation
– Section 16.6 
10/24 Lecture 17: 1D Wave Equation, Visualization of Solutions to the 1D Wave Equations
Week 11

10/29 Lecture 18: Unbounded Domains
– Sections 16.3, 16.4 
10/31 Lecture 19: Separation of Variables in Higher Dimensions, Visualization of Solutions to the 2D Wave Equations
– Sections 16.9, 17.6
Week 12

11/05 Lecture 20: Vibrations of a Circular Membrane, Visualization of Vibrations on a Circular Membrane
– Sections 16.7  16.8 
11/07 Lecture 21: Orthogonal functions and SturmLiouville theory
** Homework 6 due Thursday
Week 13

11/12 Lecture 22: SteadyState Temperature on a Metal Disc, Visualization of Steady State Temperature on a Disc
– Section 18.1, 18.3 
11/14 Lecture 23: Laplace’s equation on rectangular domains
Week 14

11/19 Lecture 24: Firstorder Linear PDEs
– Section 16.6 
11/21 Lecture 25: Similarity Variables
** Homework 7 due Tuesday
Week 15

11/26 Lecture 26: Special topics

11/28 Thanksgiving Holiday; No Class
** Homework 8 due Tuesday
Week 16
 12/03 Lecture 27: Review
** 12/04: Reading Day