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This subject covers the same material as MAST10006 Calculus 2, but to a greater depth including a greater emphasis on mathematical rigour and proof.
Students are introduced the complex exponential function, even and odd functions and functions of two or more variables.
Techniques of differentiation and integration will be extended to these cases. Students will be exposed to a wider class of differential equation models, both first and second order, to describe systems such as population models, electrical circuits and mechanical oscillators.
The subject also introduces sequences and series including the concepts of convergence and divergence. In addition to the intuitive understanding of convergence, students will see the mathematical definition of convergence.
Calculus topics include: limits and continuity of functions of one variable, sequences, series, hyperbolic functions and their inverses, level curves, partial derivatives, chain rules for partial derivatives, directional derivative, tangent planes and extrema for functions of several variables.
Complex exponential topics include: definition, derivative, integral and applications. Integration topics include: techniques of integration and double integrals. Ordinary differential equations topics include: first order (separable, linear via integrating factor) and applications, second order constant coefficient (particular solutions, complementary functions) and applications.
Intended learning outcomes
Students completing this subject should be able to:
- calculate limits of functions of one variable
- determine convergence and divergence of sequences and series
- sketch and manipulate hyperbolic and inverse hyperbolic functions
- evaluate integrals using trigonometric and hyperbolic substitutions, partial fractions, integration by parts and the complex exponential;
- find analytical solutions of first and second order ordinary differential equations, and use these equations to model some physical and biological systems
- calculate partial derivatives and gradients for functions of two or more variables, and use these to find maxima and minima
- be able to construct a simple mathematical proof
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis
- collaborative skills: the ability to work in a team
- time-management skills: the ability to meet regular deadlines while balancing competing commitments
Last updated: 3 July 2021