Number of lectures per week: 2 + 1 tutorial
Assessment: 20 homeworks; 2-hour tests at beginning of Hilary and
End-of-year Examination: One 3-hour paper
Coordinate geometry. Lines in 2 dimensions. Points, vectors, and displacements in 2 dimensions. Scalar products. Bases of coordinate systems. Vectors in 3 dimensions. Planes. Linear maps. Cross products. Rotations in 3 dimensions. Gauss-Jordan elimination. Invertible matrices. Bases and coordinate systems. Permutations and signatures. Determinants. Cofactor expansions. Adjoint form of inverse. Cramer's Rule. Row space, column space, kernel. Product rule for determinants.
Limits and continuity. Derivatives. Differentiation rules. Tangent line. Graph sketching. Taylor's series. Taylor's Theorem. Integration.
Ordinary differential equations (separable and linear). Recurrences. Linear recurrences. Second order differential equations and recurrences.
Newton-Raphson method with error estimates. Approximate integration: Trapezoidal formula and Simpson's Rule.
Textbook. Elementary Linear Algebra, by Howard Anton. (Not a required text.)
Oct 11, 2000