Syllabus

MA320 Arts (pass)

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)

MA313/314 Linear Algebra

• Linear transformations: rank, kernel, image, eigenvectors, diagonalisation
• Diagonalisation of symmetric matrices
• Application to solution of linear differential equations
• The Gram-Schmidt Process, orthogonal matrices, orthogonal reduction of symmetric matrices
• Bilinear and quadratic forms
• Examples involving orthogonal polynomials and trigonometric polynomials
• Diagonalisation of a quadratic form by an orthogonal matrix, or by an arbitrary non-singular matrix
• Linear programming: simplex method, revised simplex method

Texts

• J.B. Fraleigh & R.A. Beauregard, "Linear Algebra" (Addison Wesley)

References

• F. Ayres, "Matrices" (Schaum Outline)
• F. Ayres, "Modern Algebra" (Schaum Outline)
• S. Lipschutz, "Linear Algebra" (Schaum Outline)
• S. Lipschutz, "Discrete Mathematics" (Schaum Outline)