Case 1:
The factors of Q(x) are all linear and none is repeated. That is,
Q(x) = (x - a1 )(x - a 2 )
(x - a n )
where no two of the a i are identical. In this case, we write
P(x) A1 A2 = + + Q(x) x - a1 x - a 2 where A1, A 2 , Example: + An x - an (1)
, A
Part III Higher-Order Equations and Power Series Method
124
Methods for solving some special higherorder equations D-operator method (the most important method we would discuss in this part) Reduction of order by substitution Power series method
125
Theo
Part II: Linear Second (Higher) Order Equations with Constant Coefficients
65
Methods We Need to Learn: Linear 2-nd order homogenous equations (basic case)
d2y dy + a1 + a2 y = 0 dx dx 2
Linear 2-nd order non-homogenous equations: Variation of parameters
FE1007: Ordinary Differential Equation
1
Topics discussed in this course Limit and derivative of multi-variable functions Sequence and Series Integral of multi-variable functions Ordinary differential equations (ODEs)
CA and the final examination CA: Up
FE1007 MATHEMATICS 2 MS2900 ESSENTIAL MATHS Part 1 Summary
Lecturer: Dr. Ser Wee Associate Professor Office: S2-B4b-05 Tel: 6790 5951 Email: ewser@ntu.edu.sg
Part 2 Lecturer: Prof. Koh Soo Ngee Course Coordinator: A/Prof. Xiao Gaoxi
1
COURSE OVERVIEW
Fun
FE1007 MATHEMATICS 2 MS2900 ESSENTIAL MATHS Lecture notes : Part 1a
Lecture notes and tutorial questions are also posted at edveNTUre Lecturer: Dr. Ser Wee (EEE) Associate Professor Office: S2-B4b-05 Tel: 6790 5951 Email: ewser@ntu.edu.sg
Course Coordinat