The student will:
• have a thorough understanding of calculus with emphasis on differentiation and solving first and second order ordinary differential equations.
• be able to perform arithmetic with complex numbers, work with complex valued polynomials and create and interpret Argand diagrams.
• be proficient with vector manipulation and the geometry of 3-d space, including lines and planes.
• understand core mathematical concepts and discourse such as sets, logic and methods of proving.
The course Calculus 1 for AT, TN, and EE begins with differential equations (DEs). Differential equations are essential in mathematical modelling. We shall look at typical first and second order ordinary differential equations and how to solve them.
In order to solve certain types of differential equations, we require complex numbers, so we shall cover the basics of complex numbers and how they are involved with DEs.
We take the Argand plane depiction of Complex numbers and segue into vector analysis. Vectors are of vital importance in any scientific study involving physics or engineering. We shall cover essential vector arithmetic and geometry, including lines and planes.
We complete the course with an overview of limits, continuity and differentiation. These topics first seen in high school benefit from a fresh look, including related ideas such as L’Hospital’s rule.
Throughout the course we shall make repeated references to mathematical languages such as sets, logic and proving. We shall use this mathematical language in contexts related to calculus.