  # MA1003 - Mathematical Techniques

 Credit points: 3 Year: 2021 Student Contribution Band: Band 2 Administered by: College of Science and Engineering

To develop knowledge and advanced analytical skills in the fields of differential and integral calculus, differential equations, series, linear algebra and complex numbers through independent and collaborative learning. To equip students with the techniques required for the application of integral and differential calculus, differential equations and linear algebra in disciplines where these concepts are used.

### Learning Outcomes

• communicate mathematical thinking incorporating the concepts and methods presented in the course;
• define hyperbolic functions and describe their properties; define inverse trigonometric and inverse hyperbolic functions and describe their properties;
• solve first order differential equations and second order differential equations with constant coefficients, including non-homogeneous cases and apply these methods to word problems;
• use convergence tests to determine properties of series and power series. Determine power series representations of functions;
• systematically solve a system of linear equations; compute and understand the role of the determinant in a matrix equation; solve a matrix equation using the matrix inverse;
• understand the rectangular, polar and exponential forms of a complex number. Perform the four standard arithmetic operations and find roots using complex numbers. Solve equations involving complex numbers;
• differentiate quantities on curves defined by parametric equations; understand and use the concepts of the differential and linear approximation for functions of a single variable and apply Newtons method to solve nonlinear equations involving a single variable;
• use techniques presented to evaluate integrals analytically. Use the trapezoidal rule and Simpsons rule to evaluate integrals numerically. Apply integrals to determine volumes of solids of revolution, arc length and surface area of revolution.

### Subject Assessment

• Written > Examination (centrally administered) - (60%) -
• Written > Examination - In class - (25%) -
• Written > Test/Quiz 1 - (3%) -
 Prerequisites: MA1000 OR MA1011 OR MA1009 InadmissibleSubjectCombinations: MA1002

## Availabilities

Townsville, Intensive, Study Period 3
Census Date 04-Feb-2021
Face to face teaching 04-Jan-2021 to 15-Feb-2021 (Classes commence Monday 4 January 2021 and conclude on Monday 15 February. Classes will run Monday, Wednesday and Friday during this period.)

The student workload for this 3 credit point subject is approximately 130 hours.

• 84 hours - 12 hours contact per week for 7 weeks
• assessment and self-directed study

Townsville, Internal, Study Period 2
Census Date 26-Aug-2021

The student workload for this 3 credit point subject is approximately 130 hours.

• 39 hours lectures
• 12 hours tutorials
• assessment and self-directed study

Townsville, Internal (Pathway), Study Period 48
Census Date 25-Nov-2021

The student workload for this 3 credit point subject is approximately 130 hours.

• 39 hours lectures
• 12 hours tutorials
• assessment and self-directed study

Cairns, Internal, Study Period 2
Census Date 26-Aug-2021