Calculus 2

This subject has the following teaching availabilities in 2009:

• 620-151 (prior to 2008)
• Calculus 1
• 620-161 (prior to 2008)
• Linear Algebra
  

or permission from the Director of the Mathematics and Statistics Learning Centre.

Students may only gain credit for one of 620-113 (prior to 2008), 620-123 (prior to 2008), 620-143 (prior to 2009), Calculus 2, Accelerated Mathematics 2 (620-158 Mathematics 2 prior to 2009), 620-193 (prior to 2006).

Students who have completed 620-121 (prior to 2008) may not enrol in this subject for credit.

This subject will extend knowledge of calculus from school. Students are introduced to hyperbolic functions and their inverses, the complex exponential and functions of two 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.

Calculus topics include: intuitive idea of limits, continuity and differentiability of functions of one variable, hyperbolic functions and their inverses, implicit differentiation, 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.

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.

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 40 or more in VCE Specialist Mathematics 3/4 will normally not be permitted to enrol in this subject; such students should enrol in Accelerated Mathematics 1 or Accelerated Mathematics 2.