MTH102: Analysis in one variable

[Cr:3, Lc:2, Tt:1, Lb:0]

Course Outline

• The real number system, completeness axiom, complex numbers.
• Sequences, limits, convergence, series.
• Polynomials, rational functions, continuous functions.
• Trigonometric, exponential, logarithmic and hyperbolic functions.
• Differentiation, mean value theorem, Taylor’s theorem.
• Uniform convergence, power series.
• Riemann integral, fundamental theorem of calculus.
• Fourier series.

Recommended Reading

• R. R. Goldberg, Methods of Real Analysis, Wiley (1970).
• K. A. Ross, Elementary Analysis, The Theory of Calculus, Springer (2004).
• T. M. Apostol, Calculus, Blaisdell Publishing Company, 1961.
• S. Shirali and H. L. Vasudeva, Mathematical Analysis, Alpha Science International Ltd. (2006).