This course continues on from MATH1115, providing an in-depth development of fundamental concepts of calculus and linear algebra, with a particular emphasis on the underlying foundations of mathematics. The use and understanding of proof and abstract ideas, will allow students to develop analytical skills which will form a base for further study in fundamental mathematics as well as providing a foundation for a wide range of quantitative areas such as computer science, engineering, economics, statistics and physics. 

Topics to be covered include:

Analysis - Functions of several variables, partial derivatives, double integrals; infinite series, convergence tests, power series, Taylor series, binomial series, complex power series, vectors, dot product, cross product, planes and lines in 3-space, vector functions, curves and parametrization, Kepler’s laws, functions of several variables, chain rule, gradients and directional derivatives, Quadratic forms, extreme values, Lagrange multipliers;

Algebra – induction, theory and application of Euclidean vector spaces, vector spaces, linear independence, bases and dimension, eigenvalues and eigenvectors, orthogonality and least squares.

Note: This is a HPC. It involves extra material and emphasizes the use and understanding of proof and abstract ideas to a deeper conceptual level than MATH1014.

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

1. Explain the fundamental concepts of analysis and linear algebra and their role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of analysis and linear algebra techniques.
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from analysis and linear algebra.
4. Apply problem-solving using analysis and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.

Assessment will be based on:

• Tutorials (5%; LO 1-4)
• Five assignments (25% in total: LO 1-4)
• Mid-semester test (25%; LO 1-4)
• Final examination (45%; LO 1-4)

48 lectures and 10 hours of laboratory and tutorial sessions

A mark of 60 or more in MATH1021 or MATH1115.

with MATH1002, MATH1004, MATH1014, MATH1012, MATH1022 and ENGN1222