Differential equations and rectilinear motion
Chapter 60 of 20 strong
RESTS ONIdentify the inner and outer functions of a composite, differentiate each, multiply the outer derivative evaluated at the inner function by the inner derivative, and write the result in the requested factorised formFOUNDATIONSTransform differential factors and endpoint order in exact substitutionsCH 5Construct direct, contrapositive and contradiction arguments with justified stepsCH 1State the complete anti-derivative family with one arbitrary additive constant, and verify that the constant disappears under differentiationFOUNDATIONSIntegrate rational functions after division and partial-fraction decompositionCH 5Trace supplied sequential assignments, decisions and loopsFOUNDATIONSConstruct, implement and justify algorithms with explicit domains and termination argumentsFOUNDATIONSDifferentiate displacement with respect to time to obtain velocity and acceleration, and interpret position, velocity and acceleration signs and units for motion in a straight lineFOUNDATIONSSolve the velocity-zero condition for rest times, describe direction of motion from the sign of velocity, compute distance travelled when direction changes, and compare average velocity with average speedFOUNDATIONS
Models, verification and direction fields
Separation and initial values
Logistic growth and applications
Euler numerical methods
Rectilinear kinematics