# MAST10006 Calculus 2 Notes | Assignment Help | Syllabus

## Country: Australia

### University: University Of Melbourne

“This topic will broaden your calculus understanding beyond what you learned in school. Students learn about hyperbolic functions and their inverses, as well as the complex exponential and two-variable functions. Differentiation and integration techniques will be used to these situations. Students will learn how to use first and second order differential equation models to explain systems including population models, electrical circuits, and mechanical oscillators. The topic also covers sequences and series, as well as the terms convergence and divergence.

The intuitive idea of 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 are just a few of the topics covered in calculus. Definition, derivative, integral, and applications are all examples of complex exponential subjects. Techniques of integration and double integrals are examples of integration subjects. The first order (separable, linear through integrating factor) and applications, as well as the second order constant coefficient (specific solutions, complementary functions) and applications, are all covered in ordinary differential equations.

Learning outcomes that are expected
Students who have completed this course should be able to:

compute the basic limits of a one-variable function
define sequence and series convergence and divergence;
Hyperbolic and inverse hyperbolic functions are sketched and manipulated.
trigonometric and hyperbolic substitutions, partial fractions, integration by parts, and the complex exponential are all used to assess integrals.
discover analytical solutions to first and second order ordinary differential equations and use them to represent certain basic physical and biological systems
Calculate the partial derivatives and gradients of two-variable functions and use them to locate maxima and minima.
Skills that are universal
Students will have the chance to acquire general abilities that will help them in any future professional path, in addition to acquiring particular skills that will help them in their future jobs in science. These are some of them:

analytical skills: the ability to construct and express logical arguments and work in abstract or general terms to increase the clarity and efficiency of analysis; collaborative skills: the ability to work in a team; problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies; problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies; problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies; problem-solving skills: the ability to engage with unfamiliar problems and identify relevant and time-management abilities: the capacity to fulfill regular deadlines while juggling many obligations.” ”

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