Comprehensive Mathematics I

Course outline

• The field of real numbers, order, absolute value, the topology of real line.
• The field of complex numbers, absolute value, complex conjugate, the topology of the complex plane, trigonometric and exponential form, de Moivre formula, complex roots, complex logarithms, simple complex functions, and mappings.
• Groups and Rings, simple examples, modular arithmetic.
• Sequences, and series of real numbers.
• Real functions of a real variable, limits, continuity, derivatives, Rolle, Mean value and Taylor theorems.
• The definite and indefinite integral, techniques of integration, the trapezoidal rule, improper integrals.
• 1^st order ordinary differential equations, simple models, direction fields, Euler’s method, applications.