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

Spring 2025 Tentative Course Schedule

Week 1

  • 01/07 Lecture 1: Welcome and Course Overview; Review of ordinary differential equations
    – Sections 1.1 - 1.2

  • 01/09 Lecture 2: Review of ordinary differential equations
    – Sections 2.1 - 2.3, 2.5

Week 2

  • 01/14 Lecture 3: Nonhomogeneous ODEs, Series Solutions of ODEs
    – Sections 2.3, 4.1

  • 01/16 Lecture 4: Singular Points and the Method of Frobenius
    – Section 4.2

** Homework 1 due Thursday

Week 3

  • 01/21 Lecture 5: Singular Points and the Method of Frobenius continued
    – Section 4.2

  • 01/23 Lecture 6: The 1-D Heat Equation on a Finite Domain I
    – Sections 17.1 - 17.2

Week 4

  • 01/28 Lecture 7: The 1-D Heat Equation on a Finite Domain II
    – Sections 17.2

  • 01/30 Lecture 8: Fourier Series of a Function, Fourier Cosine and Sine Series
    – Sections 13.1 - 13.4

** Homework 2 due Thursday

Week 5

  • 02/04 Lecture 9: Visualization of Fourier Series and the Gibbs Effect, Convergence of Fourier Series.
    – Sections 13.5 - 13.6

  • 02/06 Lecture 10: Complex Fourier Series, Fourier Integrals
    – Sections 13.6, 14.1 - 14.2

Week 6

  • 02/11 Wellness Day; No class

  • 02/13 Lecture 11: Fourier Integrals
    – Sections 13.6, 14.1 - 14.2

** Homework 3 due Friday

Week 7

  • 02/18 Lecture 12: Fourier Transform
    – Sections 14.3

  • 02/20 Lecture 13: Fourier Transform (ctd)
    – Sections 14.3

Week 8

  • 02/25 Lecture 14: The 1-D Heat Equation on Infinite Domain

  • 02/27 Midterm

** Homework 4 due Thursday

Week 9

  • 03/04 Lecture 15: The 1-D Wave Equation on a Finite Domain
    – Sections 16.1 - 16.2

  • 03/06 Lecture 16: D’Alembert’s Solution to the 1-D Wave Equation
    – Section 16.6

** Homework 5 due Thursday

Week 10

  • 03/11, 03/13 Spring Break: No Classes.

Week 11

  • 03/18 Lecture 17: 1-D Wave Equation, Visualization of Solutions to the 1-D Wave Equations

  • 03/20 Lecture 18: Unbounded Domains
    – Sections 16.3, 16.4

Week 12

  • 03/25 Lecture 19: Separation of Variables in Higher Dimensions, Visualization of Solutions to the 2-D Wave Equations
    – Sections 16.9, 17.6

  • 03/27 Lecture 20: Vibrations of a Circular Membrane, Visualization of Vibrations on a Circular Membrane
    – Sections 16.7 - 16.8

** Homework 6 due Thursday

Week 13

  • 04/01 Lecture 21: Orthogonal functions and Sturm-Liouville theory

  • 04/03 Lecture 22: Steady-State Temperature on a Metal Disc, Visualization of Steady State Temperature on a Disc
    – Section 18.1, 18.3

Week 14

  • 04/08 Lecture 23: Laplace’s equation on rectangular domains, Laplace’s Equation in Spherical Coordinates
    – Section 18.7, 18.8

  • 04/10 Lecture 24: First-order Linear PDEs
    – Section 16.6

** Homework 7 due Thursday

Week 15

  • 04/15 Lecture 25: Similarity Variables

  • 04/17 Lecture 26: Intro to finite difference methods

Week 16

  • 04/22 Lecture 27: Final Review

** Homework 8 due Tuesday

** 04/23 Reading Day

Final Exam: Tuesday, April 29, 12:00 pm - 2:30 pm