Introduction to differentiation
Learn how to solve differential equations using direct integration, separation of variables, and the integrating factor method. This course also covers applications of differential equations in real-world problems and explores various approaches to finding solutions. Gain the skills to recognize and solve different types of differential equations and understand exponential growth, decay, and population models. Start solving problems involving exponential growth and decay today.
This free course is an introduction to differentiation. Section 1 looks at gradients of graphs and introduces differentiation from first principles. Section 2 looks at finding derivatives of simple functions. Section 3 introduces rates of change by looking at real life situations. Section 4 looks at using the derivative of a function to deduce useful facts for sketching its graph. Section 5 covers the second derivative test, used to determine the nature of stationary points and ends by looking at rates of change, including the real-life situation, using differentiation to find acceleration.
Course learning outcomes
After studying this course, you should be able to:
Understand the idea of differentiation from first principles
Differentiate power functions
Find stationary points of some functions
Determine the nature of some stationary points using either the first or second derivative tests
Understand and work with derivatives as rates of change in mathematical models.