Brooks Emerick

maTH 305 — Applied Mathematics for Engineers

Spring Semester 2025 — University of Delaware

Course Materials, Websites, and apps:

• Syllabus is on Canvas

• Graded Assignments are on WileyPLUS, which is accessed through Canvas

• Registering for WileyPLUS

• Slopes App for iPad or iPhone

DESMos Templates and other Resources

• Desmos — Exponential Growth/Decay

• Desmos — Newton’s Law of Cooling

• Desmos — Logistic Growth

• Desmos — Gompertz Growth

• Desmos — Slope Field Generator

• Desmos — Implicitly Defined Solutions

• Desmos — Pond Problem and Steady-State

• Youtube — Bifurcations in Linear Systems

Lecture Notes and Videos

• Chapter 1 — Introduction (complete)

• Chapter 2 — First Order ODEs (complete)

• Feb 12 Snow Day Lecture

• Chapter 3 — Two Dimensional Linear Systems (complete for now)

• Chapter 4 — Second Order Linear ODEs (updated 4/2)

Worksheets

• Chapter 1 Worksheets

• Chapter 2 Worksheets

• S.3.1.P1: Systems of Two Linear Algebraic Equations (solutions)

• S.3.1.P2: Eigenvalues and Eigenvectors (solutions)

• S.3.2.P1: The Geometry of Systems (solutions)

• S.3.2.P2: Linear Systems of Two ODEs (solutions)

• S.3.3.P1: Homogeneous, Constant Coefficient, Linear Systems (solutions)

• S.3.3.P2: Real, Distinct, Nonzero Eigenvalues (solutions)

• S.3.3.P3: One Zero Eigenvalue (solutions)

• S.3.4: Complex Eigenvalues (solutions)

• S.3.5: Repeated Eigenvalues (solutions)

• S.3.6.P1: The Trace-Determinant Plane (solutions)

• S.4.1: Mechanical Oscillators (solutions)

Additional PRoblems

• Chapter 1 — Introduction (solutions)

• Chapter 2 — First Order ODEs (solutions)

• Chapter 3 (part 1) — First Order Systems (solutions)

• Chapter 3 (part 2) — First Order Systems (coming soon)

• Chapter 4 — Second Order Linear ODEs (coming soon)