MA1003 - Mathematical Techniques

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

• end of semester exam (60%)
• other exams (25%)
• quizzes or tests (3%)
• tutorial quizzes (5%)
• on-line quizzes (7%).

Note: Minor variations might occur due to the continuous Subject quality improvement process, and in case of minor variation(s) in assessment details, the Subject Outline represents the latest official information.