MathTrackX: Differential Calculus

About

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.

What you will learn

• How derivatives relate to the slope of a function

• How to calculate the derivative of polynomials and special functions

• Differentiation rules for evaluating the derivative of non-trivial functions

• The concept and application of ‘the second derivative’

• How to use differentiation to solve problems in basic motion, mechanics and optimisation.

Skills you learn

• Differential Calculus
• Derivatives
• Basic Math
• Calculus

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.

Auto Summary

"MathTrackX: Differential Calculus" is a foundational course designed to equip learners with essential skills and knowledge in differentiation, a core aspect of calculus. This course, a part of the MathTrackX XSeries Program, is meticulously crafted to build a robust mathematical foundation and illustrate the application of these principles in real-world scenarios. Led by experienced educators from the University of Adelaide's School of Mathematics and the Maths Learning Centre, the course delves into the basic concepts and techniques of differentiation. Learners will explore the importance of derivatives in understanding rates of change and how functions respond to varying factors. Spanning 15 weeks, this professional-level course is ideal for anyone seeking to enhance their mathematical proficiency, particularly those pursuing STEM-related careers or undergraduate studies. With a focus on practical application, the course aims to boost your confidence and ability to tackle real-world problems through mathematics. Available through edX, "MathTrackX: Differential Calculus" offers flexible subscription options for a comprehensive and engaging learning experience. Join us and develop the mathematical skills crucial for your academic and professional growth.