MA 501 Advanced Mathematics for Engineers and Scientists I

You can find the Syllabus and General Course Information here.

More information can be found on the course Moodle page.

Textbook: Advanced Engineering Mathematics, 7th Ed., by Peter V. O’Neil

Fall 2026 Tentative Course Schedule

Week 1

08/18 Lecture 1: Welcome and Course Overview; Review of ordinary differential equations
– Sections 1.1 - 1.2
08/20 Lecture 2: Review of ordinary differential equations
– Sections 2.1 - 2.3, 2.5

Week 2

08/25 Lecture 3: Series Solutions of Ordinary Differential Equations
– Section 4.1
08/27 Lecture 4: Singular Points and the Method of Frobenius
– Section 4.2

** Homework 1 due Thursday

Week 3

09/01 Lecture 5: Singular Points and the Method of Frobenius continued
– Section 4.2
09/03 Lecture 6: The 1-D Heat Equation on a Finite Domain I
– Sections 17.1 - 17.2

Week 4

09/08 Lecture 7: The 1-D Heat Equation on a Finite Domain II
– Sections 17.2
09/10 Lecture 8: , Fourier Series of a Function, Fourier Cosine and Sine Series
– Sections 13.1 - 13.4

** Homework 2 due Thursday

Week 5

09/15 Lecture 9: Visualization of Fourier Series and the Gibbs Effect, Convergence of Fourier Series.
– Sections 13.5 - 13.6
09/17 Lecture 10: Complex Fourier Series, Fourier Integrals
– Sections 13.6, 14.1 - 14.2

Week 6

09/22 Lecture 11: Fourier Integrals
– Sections 13.6, 14.1 - 14.2
09/24 Lecture 12: Fourier Transform
– Sections 14.3

** Homework 3 due Friday

Week 7

09/29 Wellness Day; No Class
10/01 Lecture 13: Fourier Transform (ctd)
– Sections 14.3

Week 8

10/06 Lecture 14: The 1-D Heat Equation on Infinite Domain
10/08 Midterm

** Homework 4 due Wednesday at 4:30 pm

Week 9

10/13 Lecture 15: The 1-D Wave Equation on a Finite Domain
– Sections 16.1 - 16.2
10/15 Lecture 16: D’Alembert’s Solution to the 1-D Wave Equation
– Section 16.6

** Homework 5 due Thursday

Week 10

10/20 Fall Break: No Class.
10/22 Lecture 17: 1-D Wave Equation, Visualization of Solutions to the 1-D Wave Equations

Week 11

10/27 Lecture 18: Unbounded Domains
– Sections 16.3, 16.4
10/29 Lecture 19: Separation of Variables in Higher Dimensions, Visualization of Solutions to the 2-D Wave Equations
– Sections 16.9, 17.6

Week 12

11/03 Lecture 20: Vibrations of a Circular Membrane, Visualization of Vibrations on a Circular Membrane
– Sections 16.7 - 16.8
11/05 Lecture 21: Orthogonal functions and Sturm-Liouville theory

** Homework 6 due Thursday

Week 13

11/10 Lecture 22: Steady-State Temperature on a Metal Disc, Visualization of Steady State Temperature on a Disc
– Section 18.1, 18.3
11/12 Lecture 23: Laplace’s equation on rectangular domains, Laplace’s Equation in Spherical Coordinates
– Section 18.7, 18.8

Week 14

11/17 Lecture 24: First-order Linear PDEs
– Section 16.6
11/19 Lecture 25: Similarity Variables

** Homework 7 due Thursday

Week 15

11/24 Lecture 26: Intro to finite difference methods
11/26 Thanksgiving Holiday; No Class

Week 16

12/01 Lecture 27: Final Review
** Homework 8 due Tuesday

** 12/02: Reading Day