MA211 Calculus (part one)

• Methods of integration: substitution, integration by parts, partial fractions, reduction formulae
• Inverse functions
• Improper integrals (as limits of finite integrals)
• Differential equations: linear equations with constant coefficients, first order homogeneous equations.

MA212 Calculus (part two)

• Series: convergence, divergence, absolute convergence
• The Comparison, Integral and Ratio Tests
• Alternating series
• Power series, the Radius of convergence
• Functions of several variables, and vector-valued functions (in R² and R³): vectors, scalar product, cross product in R³, equations of lines and planes in parametric form
• Partial derivatives: gradients, tangent planes, maxima and minima of functions of 2 variables, Lagrange multipliers
• The Chain Rule

Texts

• G.B. Thomas & R.I. Finney, "Calculus and Analytic Geometry" (Addsison Wesley)
• S.L. Salas, E. Hille & J.T. Anderson, "Calculus, One and Several Variables" (Wiley)

Mathematics Department, Maths Physics Department, IT Department, Physics Department.
National University of Ireland, Galway, University Road, Galway, Ireland.
Phone: +353 (0)91 750442 (direct line) , +353 (0)91 524411 x2332 (via switchboard)
Fax No.: +353 (0)91 750542, E-mail: John.Burns@nuigalway.ie
Disclaimer
Copyright © 2003 National University of Ireland, Galway