MATH150-sug

MATH150-sug - Introduction to ordinary differential...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Introduction to ordinary differential equations Lecture notes for MATH 150 J. R. Chasnov Department of Mathematics Hong Kong University of Science and Technology ii Contents 0 A short mathematical review 1 0.1 Trigonometric functions . . . . . . . . . . . . . . . . . . . . . . . 1 0.2 Exponential function and natural logarithm . . . . . . . . . . . . 1 0.3 Definition of derivative . . . . . . . . . . . . . . . . . . . . . . . . 2 0.4 Differentiating a combination of functions . . . . . . . . . . . . . 2 0.4.1 The sum or difference rule . . . . . . . . . . . . . . . . . . 2 0.4.2 The product rule . . . . . . . . . . . . . . . . . . . . . . . 2 0.4.3 The quotient rule . . . . . . . . . . . . . . . . . . . . . . . 2 0.4.4 The chain rule . . . . . . . . . . . . . . . . . . . . . . . . 3 0.5 Differentiating elementary functions . . . . . . . . . . . . . . . . 3 0.5.1 Power rule . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.5.2 Trigonometric functions . . . . . . . . . . . . . . . . . . . 3 0.5.3 Exponential and natural logarithm functions . . . . . . . 3 0.6 Definition of integral . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.7 Fundamental theorem of Calculus . . . . . . . . . . . . . . . . . . 4 0.8 Definite and indefinite integrals . . . . . . . . . . . . . . . . . . . 4 0.9 Indefinite integrals of elementary functions . . . . . . . . . . . . . 5 0.10 Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0.11 Integration by parts . . . . . . . . . . . . . . . . . . . . . . . . . 6 0.12 Taylor series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 0.13 Complex numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 Introduction to odes 11 1.1 Definition of an ode . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2 The simplest type of differential equation . . . . . . . . . . . . . 11 2 First-order differential equations 13 2.1 Separable equations . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Linear equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.1 Compound interest . . . . . . . . . . . . . . . . . . . . . . 18 2.3.2 Annual percentage yield (APY) . . . . . . . . . . . . . . . 19 2.3.3 Rule of 72 . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3.4 Compound interest with deposits or withdrawals . . . . . 20 2.3.5 Chemical reaction . . . . . . . . . . . . . . . . . . . . . . 21 2.3.6 Terminal velocity of falling mass . . . . . . . . . . . . . . 23 2.3.7 Escape velocity . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3.8 Logistic equation . . . . . . . . . . . . . . . . . . . . . . . 25 iii 3 Second-order linear differential equations with constant coeffi- cients 27 3.1 The principle of superposition . . . . . . . . . . . . . . . . . . . . 28 3.2 Second-order linear homogeneous ode with constant coefficients . 28 3.2.1 Real, distinct roots . . . . . . . . . . . . . . . . . . . . . .Real, distinct roots ....
View Full Document

This note was uploaded on 01/28/2011 for the course MATH 150 taught by Professor T.qian during the Spring '09 term at HKUST.

Page1 / 75

MATH150-sug - Introduction to ordinary differential...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online