MathTrackX: Integral Calculus

Overview

This course is part four of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.

This course will cover basic concepts and techniques relating to integration, another fundamental tool of calculus. Integration is key to understanding the accumulation of a quantity given its rate of change.

Guided by experts from the School of Mathematics and the Maths Learning Centre at the University of Adelaide, this course will cover concepts and techniques to provide a foundation for the applications of differentiation in STEM related careers and/or further study at the undergraduate level.

Join us as we provide opportunities to develop your skills and confidence in applying mathematics to solve real world problems.

Syllabus

Week 1: Anti-differentiation

Understand the concept of anti-derivative as the “reverse” of differentiation
Calculate the anti-derivative of polynomials and special functions (including trigonometric and exponential functions).

Week 2: Definite integrals

Understand the concept of definite integration as the (signed) area under the graph of a function and recognise it as the limit of Riemann sums
Apply definite integration to solve a variety of problems relating to the area between curves.

Week 3: The fundamental theorem of calculus

Understand and apply the fundamental theorem of calculus to calculate definite integrals.

Week 4: Applications of integration

Apply integration to solve problems relating to areas between prescribed curves, basic motion/mechanics and initial value problems.

Week 5: Assessment

There is a timed exam.