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Syllabus - MA201
 

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)

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