MA1114 Single Variable Calculus II

This course is a review of techniques of integration, applications of integration, infinite series, convergence tests, and Taylor series, parametric equations and polar coordinates and a brief introduction to the arithmetic of complex numbers and DeMoivre’s theorem. Taught at the rate of nine hours per week for five weeks.

Prerequisite

MA1113

Lecture Hours

4

Lab Hours

1

Course Learning Outcomes

• Calculate geometric and physical quantities (such as area, volume, work, average value etc.) by setting up and evaluating a definite integral.

• Apply advanced integration techniques-including substitution, integration by parts, trigonometric substitution, and partial fractions-to evaluate indefinite and definite integrals.
• Determine the convergence or divergence of infinite sequences and series and justify the conclusion using appropriate convergence tests.
• Use power series to represent of functions and determine their interval of convergence.
• Apply Taylor's Theorem to find polynomial approximations of functions and estimate their accuracy and use Taylor series to solve problems across scientific and economic fields.
• Describe curves using Cartesian, parametric and polar coordinates to compute geometric properties like area and arclength.
• Express complex numbers in rectangular, polar and exponential forms to perform fundamental arithmetic operations, including roots and powers.