Program Overview

MATH1921: Calculus Of One Variable (Advanced)

Overview

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates differential calculus and integral calculus of one variable and the diverse applications of this theory. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems.

Topics Covered

Topics covered in this unit of study include:

• complex numbers
• functions of a single variable
• limits and continuity
• differentiation
• optimisation
• Taylor polynomials
• Taylor's Theorem
• Taylor series
• Riemann sums
• Riemann integrals Additional theoretical topics included in this advanced unit include:
  • the Intermediate Value Theorem
  • Rolle's Theorem
  • the Mean Value Theorem

Unit Details and Rules

Managing Faculty or University School

• Science

Details

• Study level: Undergraduate
• Academic unit: Mathematics and Statistics Academic Operations
• Credit points: 3

Enrolment Rules

• Prerequisites: None
• Corequisites: None
• Prohibitions: MATH1001 or MATH1906 or ENVX1001 or MATH1901 or MATH1021 or MATH1931
• Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent

Learning Outcomes

At the completion of this unit, you should be able to:

1. LO1. apply mathematical logic and rigor to solving problems, and express mathematical ideas coherently using precise mathematical language.
2. LO2. demonstrate fluency in the mathematical manipulation of complex numbers and functions, including concepts of surjectivity, injectivity and inverse functions
3. LO3. understand and be able to use fundamental properties of continuous and differentiable functions including limits, limit laws, intermediate and extreme value theorems as well as mean value theorems and applications
4. LO4. work with Taylor polynomial approximations and Taylor series representations of functions including dealing with remainder estimates
5. LO5. demonstrate an understanding of the definition and computation or estimation of definite, indefinite and improper Riemann integrals including proficiency in using integration methods without too much guidance
6. LO6. understand and be able to use the relationships between integral and differential calculus via the Fundamental Theorem of Calculus
7. LO7. apply concepts of calculus to a variety of contexts and applications

Recommendations

Students are strongly recommended to complete MATH1021 Calculus Of One Variable or MATH1921 Calculus Of One Variable (Advanced) before commencing MATH1023 Multivariable Calculus and Modelling or MATH1923 Multivariable Calculus and Modelling (Adv).