University Differential Equations Worksheets

Which sets match your course code

University Differential Equations is not one course with one number. The material is split across different courses in the public calendars of Montreal universities, and each orders and weights it its own way. Find your code below for the sets that cover its material, then check your own outline for what your exam includes.

• ENGR 213 — Differential Equations and Direction Fields, First-Order Solution Methods, Modelling with First-Order Equations, Constant-Coefficient Linear Equations, Nonhomogeneous and Variable-Coefficient ODEs, Mechanical Vibrations and Electric Circuits, Power Series Solutions, Systems of Linear Differential Equations
• MAT2115 — Differential Equations and Direction Fields, Constant-Coefficient Linear Equations, Systems of Linear Differential Equations
• MAT265 — Differential Equations and Direction Fields, First-Order Solution Methods, Modelling with First-Order Equations, Constant-Coefficient Linear Equations, Nonhomogeneous and Variable-Coefficient ODEs, Mechanical Vibrations and Electric Circuits, The Laplace Transform, Power Series Solutions, Systems of Linear Differential Equations
• MATH 263 — Differential Equations and Direction Fields, First-Order Solution Methods, Constant-Coefficient Linear Equations, Nonhomogeneous and Variable-Coefficient ODEs, The Laplace Transform, Power Series Solutions, Systems of Linear Differential Equations
• MATH 315 — Differential Equations and Direction Fields, The Laplace Transform, Power Series Solutions

What University Differential Equations covers

CEGEP Calculus II solves one kind of differential equation, the separable one, and checks a solution by substituting it back. This course asks the question the other way round: given an equation, what kind is it, and which method does that kind call for? First-order equations come first — linear, exact, Bernoulli, homogeneous, and the separable ones revisited where they get subtle — then the models they describe: cooling, mixing, circuits and logistic growth. Much of the work in the first half is recognising the equation before solving it.

The second half is linear equations of second and higher order. The characteristic equation settles the homogeneous case, with complex numbers brought in for the roots that need them; undetermined coefficients, variation of parameters, Cauchy-Euler equations and reduction of order handle the rest; and springs and circuits show what the three kinds of root mean physically. The last three sets stand on their own and can be taken in any order: the Laplace transform, which turns an initial value problem with a switched-on or impulsive force into algebra; power series solutions about an ordinary point; and systems of linear equations solved by eigenvalues.

The course stands on CEGEP Calculus I and II and CEGEP Linear Algebra. Integration techniques, partial fractions, power series, determinants and row reduction are used here, not re-taught. Fourier series and partial differential equations are not part of this course, and numerical work stops at Euler's method. The courses that carry this material at university differ most in their last chapters — some teach the Laplace transform and some leave it to a later course; some reach series solutions or systems and some do not. The list of course codes on this page says which sets each one covers.