# Course Title: Calculus and Analysis 1

## Part A: Course Overview

Course Title: Calculus and Analysis 1

Credit Points: 12.00

### Teaching Period(s)

MATH1141

Bundoora Campus

145H Mathematical & Geospatial Sciences

Face-to-Face

Sem 1 2006,
Sem 1 2007

MATH1142

City Campus

145H Mathematical & Geospatial Sciences

Face-to-Face

Sem 1 2006,
Sem 1 2007,
Sem 1 2008,
Sem 1 2009,
Sem 1 2010,
Sem 1 2011,
Sem 1 2012,
Sem 1 2013,
Sem 1 2014,
Sem 1 2015,
Sem 1 2016

MATH1142

City Campus

171H School of Science

Face-to-Face

Sem 1 2017

Course Coordinator: Dr Stephen Davis

Course Coordinator Phone: +61 3 9925 2278

Course Coordinator Email: stephen.davis@rmit.edu.au

Course Coordinator Location: 8.9.8

Pre-requisite Courses and Assumed Knowledge and Capabilities

To successfully complete this course, you are expected to have capabilities consistent with the completion of VCE Mathematical Methods at Year 12 level. That is, you are expected to be able to correctly perform basic algebraic and arithmetic operations; solve quadratic and other algebraic equations; solve simultaneous linear equations; recognise and apply the concepts of function and inverse of a function; recognise the properties of common elementary functions (e.g. polynomials and trigonometric functions); sketch the common elementary functions; solve mathematical problems involving functions; find the derivative of elementary functions from first principles and combinations of elementary functions using the product, quotient and chain rules; find the anti-derivative (integral) of elementary functions; use integral calculus to determine the area under a curve.

Course Description

This course aims to provide a broad introduction to the fundamental mathematical techniques, including differentiation and integration, and mathematical objects needed by mathematicians and most applied scientists. The course builds on the foundations laid in secondary school mathematics and in turn aims to lay the foundation for more advanced studies in mathematics undertaken in the following semester and beyond. Topic areas include differentiation with applications, functions and their derivatives, integration and its applications, methods of integration, complex numbers, and differential equations.

Objectives/Learning Outcomes/Capability Development

On successful completion of this course, you should be able to:

1.  Apply core mathematical skills such as arithmetic, algebraic manipulation, elementary geometry and trigonometry to a range of problems;
2.  Utilise the techniques of integral and differential calculus to formulate and solve problems involving change and approximation;
3.  Recognise the properties of the common mathematical functions (polynomials, exponentials and hyperbolic functions, logarithms, inverse trigonometric and inverse hyperbolic functions) and their combinations commonly found in engineering applications;
4. Identify the properties of complex numbers and apply them to the solution of algebraic equations.

This course contributes to the following Program Learning Outcomes for BP083 Bachelor of Science (Mathematics) BP245 Bachelor of Science (Statistics) and BH119 Bachelor of Analytics (Hons):

Knowledge and technical competence:
• use the appropriate and relevant, fundamental and applied mathematical and statistical  knowledge, methodologies and modern computational tools.

Problem-solving:
• synthesise and flexibly apply knowledge to characterise, analyse and solve a wide range of problems
• balance the complexity / accuracy of the mathematical / statistical models used and the timeliness of the delivery of the solution

Overview of Learning Activities

Key concepts and their application will be explained and illustrated (with many examples) in lectures and in the online notes (these notes have gaps that are filled in during the lecture). Supervised problem-based practice classes will build your capacity to solve problems and to think critically and analytically and give you feedback on your understanding and academic progress. Recommended exercises from the textbook that accompany each Module will assist you to identify gaps in your basic knowledge of the topics presented in class and provide a focus for your private study.

Students will have 46 hours of formal contact comprising 3 hours per week of face-to-face lectures and 1 hour per week, for ten weeks, of supervised tutorial class. It is also expected that students undertake, on average, 6 hours per week of independent study (for every one hour of lecturing, you are expected to independently study the lecture material for a further 2 hours, including the suggested problems and in-class exercises.)

Overview of Learning Resources

You will be able to access course information and learning materials through myRMIT Studies (also known as Blackboard). myRMIT Studies will give access to important announcements, staff contact details, the teaching schedule, online notes, assessment timelines, review exercises and past exam papers. You are advised to read your student e-mail account daily for important announcements. You should also visit myRMIT Studies at least once a day, as important announcements regarding the course will be often be made there, and all important documents related to the course will be available there.
A library guide is available at: http://rmit.libguides.com/mathstats

Overview of Assessment

☒This course has no hurdle requirements.