MathTrackX: Differential Calculus

Overview

6-week cohort with live MIT Faculty sessions. Learn to scale AI beyond the pilot stage.

This course is part three 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 differentiation; a fundamental tool of calculus. Derivatives are key to the understanding of rates of change, that is the extent to which a function responds to changes in a dependent variable.

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: Introduction to differential calculus

Calculate the derivative of polynomials and functions with real exponents
Use differentiation to solve a variety of problems including the calculation of slopes of curves, tangents to curves, velocity and acceleration of an object and rate of change of a function
Use derivatives and second derivatives to find features of functions, including stationary points and inflection points
Apply the sum, product and quotient rules to find derivatives of simple functions.

Week 2: Differentiation of special functions

Calculate the derivative of standard trigonometric functions, exponential functions and logarithmic functions
Apply standard differentiation rules to functions involving trigonometric functions, exponential functions and logarithmic functions.

Week 3: The chain rule

Recall and apply the chain rule to differentiate composite functions, including those using polynomials, trigonometric functions, exponential functions and logarithmic functions
Use derivative rules and trigonometric functions, exponential functions and logarithmic functions to solve a variety of problems.

Week 4: Applications of differentiation

Recall and apply differentiation rules to products, quotients and compositions of functions, including those using polynomials, trigonometric functions, exponential functions and logarithmic functions
Use derivative rules to derive rules for common special derivatives
Use derivative rules and trigonometric functions, exponential functions and logarithmic functions to solve a variety of problems.

Week 5: Assessment

There is a timed exam.