EECM 3714
Lecture 3: Unit 3
Non-linear equations
Renshaw, Ch. 5, 11, 12
02 March 2022
,OUTLINE - Renshaw, Ch. 5, 11 & 12
• Cubic Functions & polynomials
• Other non-linear functions
• Logarithmic and exponential functions
• Examples
, CUBIC FUNCTIONS, Ch 5, P 153-60
• The cubic function 𝑦 = 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 + 𝑑
• The cubic function contains a term involving 𝑥 3 , 𝑥 2 and 𝑥 and usually yields an S-shaped curv
• If the cubic function cuts x axis three times, the corresponding cubic equation has 3 real r
See Fig 5.4
• If the cubic function cuts x axis once, so one real root (and two complex roots, involving imag
numbers). See Fig 5.4
• If the cubic function has one cut plus a tangency, so 2 real roots with one of them "repeated"
• Unlike quadratic equations, there is no rule or formula for solving for the roots of cubic equat
• These roots can be solved only by trial-and-error methods.
Lecture 3: Unit 3
Non-linear equations
Renshaw, Ch. 5, 11, 12
02 March 2022
,OUTLINE - Renshaw, Ch. 5, 11 & 12
• Cubic Functions & polynomials
• Other non-linear functions
• Logarithmic and exponential functions
• Examples
, CUBIC FUNCTIONS, Ch 5, P 153-60
• The cubic function 𝑦 = 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 + 𝑑
• The cubic function contains a term involving 𝑥 3 , 𝑥 2 and 𝑥 and usually yields an S-shaped curv
• If the cubic function cuts x axis three times, the corresponding cubic equation has 3 real r
See Fig 5.4
• If the cubic function cuts x axis once, so one real root (and two complex roots, involving imag
numbers). See Fig 5.4
• If the cubic function has one cut plus a tangency, so 2 real roots with one of them "repeated"
• Unlike quadratic equations, there is no rule or formula for solving for the roots of cubic equat
• These roots can be solved only by trial-and-error methods.
