MA301 Advanced Calculus (part one)

• Taylor series
• Double integrals, change of variables, Jacobians
• Fourier series:  as an inner product, Fourier series of simple functions.and Fourier series of simple functions
• Line integrals, Green's Theorem

MA302 Calculus (part two)

• Complex functions, the Cauchy-Riemann equations, standard complex functions
• Linear functions, linear fractional transformations
• Complex integration: Cauchy's Integral Theorem, Taylor and Laurent expansions, residues, the Residue Theorem and applications

Texts

• S.L. Salas, E. Hille & J.T. Anderson, "Calculus, One and Several Variables" (Wiley)

References

• J.B. Fraleigh, "Calculus and Analytic Geometry" (Addison Wesley)
• M. Spiegel, "Advanced Calculus" (Schaum Outlines)

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