This course continues on from MATH1013. It emphasizes an understanding of the fundamental results from calculus and linear algebra which can both be applied across a range of fields including the physical and biological sciences, engineering and information technologies, economics and commerce, and can also serve as a base for future mathematics courses. Many applications and connections with other fields will be discussed although not developed in detail.

Topics to be covered include:

Calculus - Integration and techniques of integration. Functions of several variables - visualisation, continuity, partial derivatives and directional derivatives.

Linear Algebra - theory and application of Euclidean vector spaces. Vector spaces: linear independence, bases and dimension; eigenvalues and eigenvectors; orthogonality and least squares.

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of calculus and linear algebra and their role in modern mathematics and applied contexts. These concepts include vector spaces, eigenvalues and eigenvectors, orthogonality and least squares in linear algebra; and integration, sequences and series, functions of several variables, and partial differential equations in calculus.
2. Demonstrate accurate and efficient use of calculus and linear algebra techniques as they relate to the concepts listed above.
3. Demonstrate capacity for mathematical reasoning through explaining concepts from calculus and linear algebra.
4. Apply problem-solving using calculus and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.

Assessment will be based on:

• Tutorials (25%; LO 1-4)
• During Semester tests (25%; LO1-4)
• Final examination (50%; LO 1-4)

48 lectures and ten 2-hour laboratory sessions

A pass in MATH1013 or MATH1115.

MATH1116.