Calculus 2 (MAST10006)

MAST10006 Calculus 2 is a core mathematics subject providing the foundation for further studies in mathematics, statistics and other quantitative fields. Calculus 2 extends knowledge from secondary school mathematics and MAST10005 Calculus 1, and develops logical thinking and the ability understand and communicate mathematical arguments. Students also learn how to use mathematical concepts in applications and how to interpret the results of mathematical models in context.

Topics include: limits and continuity of functions of one variable; sequences; series; Taylor series and polynomials; hyperbolic functions and their inverses; complex exponential; techniques of integration including hyperbolic and trigonometric substitutions; first order ordinary differential equations including separation of variables method, integrating factor method for linear ODEs, and qualitative analysis; applications of first order differential equations such as population models and mixing problems; second order ordinary differential equations including constant coefficient linear homogeneous and inhomogeneous; applications of second order ordinary differential equations such as springs; functions of two variables including sketching surfaces, limits and continuity, partial derivatives and directional derivatives, tangent planes, chain rule for partial derivatives, stationary points and their classification using the Hessian, and double integrals over rectangular regions.