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University of Adelaide

MathTrackX: Differential Calculus

University of Adelaide via edX

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Overview

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.

Taught by

Dr Melissa Humphries, Dr Daniel Stevenson, Dr David Butler, Dr Brendan Harding and Nicholas Crouch

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Reviews

4.8 rating at edX based on 6 ratings

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