Course for first-year students, given in the second semester, 3 hours lecture + 1 hour recitation each week.

- Vector analysis
- Algebra of vectors, components, scalar and vector fields
- Scalar and vector products, triple product
- Derivatives of vectors, continuity and differentiability, partial derivatives of vectors, differential geometry
- Gradient, divergence, and curl
- Integration of vectors: line, surface, and volume integrals
- Gauss' Theorem, Green's and Stokes' Theorems
- Curvilinear coordinates: unit vectors, gradient, divergence, and curl
- Differential equations
- First order equations
- Linear vs. non-linear first-order equations
- Solution of linear equations
- Separable equations
- Exact differentials and integration factors
- Substitutions and scale invariance
- Second-order equations
- Homogeneous linear equations and linear independence
- Reduction of order
- Constant coefficients
- Particular solutions to inhomogeneous equations
- Systems of linear equations

- M. R. Spiegel,
*Vector Analysis*(Schaum's Outline) - F. Ayres,
*Differential Equations*(Schaum's Outline)

- G. B. Thomas,
*Calculus and Analytic Geometry*(any edition) - W. E. Boyce and R. C. DiPrima,
*Elementary Differential Equations*(any edition)

Exams for 1998 can be found at the course Web page in GIF format. There is also Postscript: mo'ed a, mo'ed b.