E.2 Advanced Calculus and Differential EquationsHL
HL extensions of Calculus. Derivatives of trigonometric, exponential, and logarithmic functions; chain, product, and quotient rules. Second-derivative test. Integration by substitution and of rational/trig/exponential functions. Volumes of revolution. Vector kinematics. Differential equations — separation of variables, slope fields, Euler's method, phase portraits, second-order numerical solutions.
Derivatives of trig, exp, log; chain, product, quotient rulesHLSign up
Standard derivatives · Chain, product, quotient rules
Second derivative test for max/min classificationHLSign up
Concavity from f′′ · Classifying critical points
Integration of rational, trig, exp; substitutionHLSign up
Standard integrals · u-substitution
Area and volume of revolutionHLSign up
V = π ∫ y² dx (about x-axis) · Volume about y-axis
Kinematics — displacement, velocity, accelerationHLSign up
v = ds/dt, a = dv/dt · Distance vs displacement
Differential equations by separation of variablesHLSign up
Separating dy/dx · General and particular solutions
Slope fieldsHLSign up
Visualising solution families · Reading slope fields
Euler's method for numerical solutionsHLSign up
Step-by-step numerical solution · Step size and accuracy
Phase portraits for coupled differential equationsHLSign up
Coupled DE systems · Eigenvalue analysis · Trajectories in phase space
Numerical solution of second-order differential equationsHLSign up
Reducing to a first-order system · Numerical step-by-step solution