Calculus 1

This subject has the following teaching availabilities in 2011:

Students may only gain credit for one of:

• MAST10005 Calculus 1
• 620-151 Introduction to Biomedical Mathematics (prior to 2008)
• 620-161 Introductory Mathematics (prior to 2008)

Students who have completed any of the following may not enrol in this subject for credit:

• MAST10006 Calculus 2
• 620-121 Mathematics A Advanced (prior to 2008)
• 620-120 UMEP Maths for High Achieving Students (prior to 2008)
• 620-140 Intermediate Mathematics (prior to 2008)
• 620-141 Mathematics A (prior to 2008)

Students may not enrol in MAST10005 Calculus 1 and MAST10006 Calculus 2 concurrently.

This subject extends students' knowledge of functions and calculus and introduces them to the topics of vectors and complex numbers. Students will be introduced to new functions such as the inverse trigonometric functions and learn how to extend the techniques of differentiation to these. Integration techniques will be applied to solving first order differential equations.

Differential calculus: graphs of functions of one variable, trigonometric functions and their inverses, derivatives of inverse trigonometric functions, implicit differentiation, related rates. Integral calculus: integration by trigonometric and algebraic substitutions and partial fractions with application to areas and volumes. Ordinary differential equations: solution of simple first order differential equations arising from applications such as population modelling. Vectors: dot product, scalar and vector projections, plane curves specified by vector equations. Complex numbers: arithmetic of complex numbers, sketching regions in the complex plane, De Moivre's Theorem, roots of polynomials, the Fundamental Theorem of Algebra.

Students completing this subject should:

• be able to graphically represent and analyse key features of polynomial, circular, inverse circular and reciprocal functions and relations representing circles, simple ellipses and hyperbolas;
• be able to manipulate simple trigonometric identities and compound and double angle formulas for sine, cosine and tangent;
• understand the arithmetic of vectors in two and three dimensions, linear independence, scalar product and application to vector projections and resolutes, plane curves specified parametrically by a vector equation and determination of corresponding cartesian equations;
• extend differentiation techniques to implicit differentiation, derivatives of inverse circular functions, second and higher order derivatives and be able to apply these to curve sketching and related rates problems;
• be able to evaluate integrals using algebraic and trigonometric substitutions, and simple partial fractions;
• be able to apply integration techniques to the calculation of volumes of solids of revolution and the solution of simple ordinary differential equations;
• understand the extension of the real numbers to the set of complex numbers and their arithmetic, including Cartesian representation and polar form.

Ten written assignments due at weekly intervals throughout the semester amounting to a total of up to 50 pages of written work (20%), and a 3-hour written examination conducted during the examination period (80%).

This subject potentially can be taken as a breadth subject component for the following courses:

• Bachelor of Arts
• Bachelor of Commerce
• Bachelor of Environments
• Bachelor of Music

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

• 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; and

• time-management skills: the ability to meet regular deadlines while balancing competing commitments.

This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.

Students with a score of 30 or more in VCE Specialist Mathematics 3/4 will not be permitted to enrol in this subject; such students should enrol in one of

• MAST10005 Calculus 2
• MAST10007 Linear Algebra
• MAST10008 Accelerated Mathematics 1
• MAST10009 Accelerated Mathematics 2