Euler’s Method: First Order What is Euler’s method? Euler’s method?is a numerical method for finding approximate solutions to differential equations It treats the derivatives in the equation as bei...
Slope Fields What are slope fields? Normally the tangent lines will be drawn for points that form a regularly-spaced grid of?x?and?y?values How can I use slope fields to study the solutions of a di...
Separation of Variables What is separation of variables? Separation of variables?can be used to solve certain types of first order differential equations If the equation is in that form you can use...
Modelling with Differential Equations Why are differential equations used to model real-world situations? A?differential equation?is an equation that contains one or more derivatives Derivatives de...
Differentiation for Kinematics How is differentiation used in kinematics? Displacement,?velocity?and?acceleration?are related by calculus In terms of differentiation and derivatives Worked Example ...
Displacement, Velocity & Acceleration What is kinematics? Kinematics?is the branch of mathematics that models and analyses the?motion?of objects Common words such as?distance, speed?and?acceler...
Volumes of Revolution Around x-axis What is a volume of revolution around the x-axis? The?volume?of?revolution?is the volume of this solid Be careful – the ’front’ and ‘back’ of this solid are flat...
Negative Integrals The area under a curve may appear?fully?or?partially?under the x-axisthis occurs if the negative area(s) is/are greater than the positive area(s), their?sum?will be?negative How ...
Integrating Composite Functions (ax+b) What is a composite function? A?composite?function?involves one function being applied after another A composite function may be described as a “function of a...
