ENGR 495/695
Advanced Topics in Engineering Mathematics

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2026–2027 Bucknell University Course Catalog Description

"Applications of linear algebra (including least-squares optimization), ordinary and partial differential equations, and finite difference methods to engineering problems. Exploration of how mathematical methods reveal unique insights."

Detailed Description

This course will help you develop the skills and understanding required to apply mathematical methods to practical problems drawn from the realm of the engineering sciences (also known as applied physics). Many such problems are expressed as systems of linear equations or as partial differential equations (PDEs). Thus, considerable class time is devoted to solution methods for matrix equations and understanding what a PDE is and how they can be solved. PDEs in particular are rather complex mathematical entities, so the course covers many mathematical details and methods that need to be brought together in order to find solutions. Because of the broad range of topics covered, the course is primarily introductory in nature and is meant to give you a good start toward developing comprehensive solutions to problems that you might encounter in your graduate work and your professional career.

Specific goals for this course are to:

• Review basic concepts of linear algebra.
• Apply linear-algebraic methods to the solution of applied problems.
• Develop the concept of an eigenvalue problem in both linear algebra and differential equations.
• Work with important analytical and numerical methods useful in the solution of partial differential equations.
• Develop proficiency with a structured programming language to solve problems that cannot be addressed using analytical methods.

All but the last topic are standard fare for a first-semester graduate math course that you might find in any engineering school. The last item has been added to prepare you for a separate computational and/or numerical methods course or to give you a starting point for computational work in your own studies. However, this is not a course on numerical methods.

The application examples and assigned projects have historically made use of the MATLAB mathematical analysis software package. Beginning with the Fall 2026 semester, the Python programming language may be used as an alternative for some or all of the assignments.

Recommended Preparation

There are no explicit prerequisites for this course other than permission of the instructor. However, students should possess the following knowledge and skills developed through previous formal course instruction:

• Calculus, including differentiation and integration, and some vector calculus
• At least one course in ordinary differential equations
• Matrix-based solutions of systems of linear equations
• Proficiency with a computer for numerical calculations. Expert status in a language is not required, but familiarity with MATLAB and/or Python could be very helpful.

Class Meetings

The lecture portion of this course is scheduled to meet 1:00–1:50 pm Monday, Wednesday, and Friday in Breakiron 066. The lab section meeting time (1 to 1.5 hours in duration) will be determined by class agreement during the first week of the semester.