49. Bachelor Express v. CA, supra GR No. 85691 (188 SCRA 216); July 31, 1990; 3
rd
Division- Gutierrez, Jr., J.II.
COMMON CARRIERS
C. Common Carriage of Passengers; (7) Responsibility for acts of strangers and co-passengers
Common Carrier/Petitioner: Bach
Math 123, Weeks 1 & 2:
First-Order Differential Equations
Section 1: Course Structure
In this course, we will study two very important mathematical topics found
throughout the sciences: differential equations and linear algebra. We
will see that, although
Definition 2
Consider a differential equation y
(n) = f(x, y, . . . , y(n1) where y is a
function of x (i.e. y = y(x) and y
(n) denotes the n
th order derivative
with respect to x. Then:
the order of the differential equation is the order of the highesto
2 = x
(c) u
t =
2u
x2
Solution: We have that: (a) is a second-order linear ordinary differential equation; (b) is a first-order nonlinear ordinary differential equation
(nonlinear because of the y
2
!); and (c) is second-order linear partial differential
Section 4: Initial Value Problems
A differential equation can, in general, given rise to multiple solutions.
Given our understanding of differential equations as modeling physical phenomenon, we should be slightly disconcerted. When we throw a projectile
study. We will see at the end of the course that the tools we will learn
when studying linear algebra will frequently appear in the understanding of
differential equations.
We had better stop for a moment and make sure we understand a differential equatio
Definition 4
The initial value problem (IVP) associated with a first-order differential equation is given by
IVP (
y
0 = f(x, y),
y(x0) = y0
where x0, y0 R.
A solution to an IVP corresponds to picking the specific trajectory in the
slope field diagram whi
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Chap 1: Fundaments of Passive Circuit
Analysis
I. Passive elements
II. Circuit analysis
III. Laplace transform
IV. First-order passive circuits
V. Second-order passive circuits
VI. Transfer function
VII.Examples
I. Passive components
Passive components d
mm 123 MIoktErm it 3 SolUtion F16
Show all work
1. Solve any way you want.
(12 points, a.) 5 points, b) 7 points)
. 3 2 .2 3x1+2322=2 o g 12.-
4
is
3 I 3A, cfw_V2, [1 3%, 3V1] maa/1:
3 2 f 2 74 0 7 W2 :f: We. fink
may
'l[ 1 ';1:& x1+$2+933=1
Z I L! xi
San Jos State University
College of Science, Department of Mathematics and Statistics
Math 123 Differential Equations & Linear Algebra, Section 01, Fall 2016
Course and Contact Information
Instructor:
Dan Goldston
Office Location:
MH 315
Telephone:
408-92
Linear Algebra and Differential Equations (Math 123), Spring 2017
Yoshihiro Uchida Hall 124, MW 1:302:45pm (Sec. 01, code 24157)
Instructor: Dr. Daniel Brinkman
Office and phone: MacQuarrie Hall 312; (408) 924-3199
Office hours: MW 12:00-1:10pm + TBD?
E-m
Math 123, Week 5:
Linear Independence, Basis, and Matrix
Spaces
Section 1: Linear Independence
Recall that every row on the left-hand side of the coefficient matrix of a linear
system Ax = b which could be obtained by elementary row operations could
be wr
because the right hand side depends upon y, which is an unknown function of x. That is, we cannot evaluate the integral because it is with
respect to x while the term to be integrated is with respect to y. The
method of direct integration can go no farthe
Classify the following differential equations:
1. y-(4/x) y = sin(x)
a. first-order linear
b. second-order linear <c. first-order non linear
2. y+y^2 = x
a. first-order linear
b. second-order linear
c. first-order non linear <-
3. u/t
a.
b.
c.
=^2u/x2
fir
50. Cangco v. MRR, supra
GR No. 12191 (38 Phil 768); October 14, 1918; Fisher, J
II. COMMON CARRIERS
C. Common Carriage of Passengers; (8) Duty of Passengers; effect of Contributory Negligence
Common Carrier: Manila Railroad Co.
Passenger: Jose Cangco
Jo
53. Villa Rey Transit v. CA
GR No. L-25499 (31 SCRA 510); February 18, 1970;En Banc- Concepcion, C.J., II.
COMMON CARRIERS
D. Damages Recoverable from Common Carriers; (2) Actual or Compensatory
Claim: a complaint was filed against the operator of the bus
51. Cariaga v. LTB Co. & MRR GR No. L-11037 (110 Phil 346); December 29, 1960; En Banc- Dizon J.II. COMMON CARRIERS
D. Damages Recoverable from Common Carriers; (2) Actual or Compensatory
Summarized Facts: this is an action filed by Edgardo Carriaga for t
52. Pan American World Airways, Inc. v IAC GR No. L-70462 (164 SCRA 268); August 11, 1988; 3
rd
Division- Cortes, J.II.
COMMON CARRIERS
D. Damages Recoverable from Common Carriers; (2) Actual or Compensatory
upon payment by Pangan of the regular fare. The
48. Pilapil v. CA
GR No. 52159 (180 SCRA 546); December 22, 989; 2 nd Division- Padilla, J.II.
COMMON CARRIERS
C. Common Carriage of Passengers; (7) Responsibility for Strangers and Co-Passengers
Jose Pilapil, a paying passenger, boarded Alatco Transport
47. Maranan v. Perez
GR No. L-22272 (20 SCRA 412); June 26, 1967; Bengzon, J.P., J.
II. COMMON CARRIERS
C. Common Carriage of Passengers; (6) Responsibility for Acts of Employees
Rogelio Corachea, on 18 October 1960, was a passenger in a taxicab
owned and
54. Philippine Airlines v. CA
GR No. 54470 (185 SCRA 110); May 8, 1990; 1st Division- Grino-Aquino, J.II.
COMMON CARRIERS
D. Damages Recoverable from Common Carriers; (2) Actual or Compensatory
On 23 October 1988, Leovigildo A. Pantejo, then City Fiscal
Open Policy
Development Insurance v IAC G.R. No. 71360
July 16, 1986
J. Cruz
Facts:
A fire occurred in the building of Philippine Union. It sued for recovery of damages from the petitioner
on the basis of an insurance contract between them. The petitioner
No
.
1
Case Title
GR No.
Date
GUINOO
October 15, 2014
CRUZ
3
Fortune Life Insurance v. COA
17566
6
18327
2
21352
5
July 29, 2013
2
Manila Bankers Life Insurance Corp.
v. Aban
Sun Life of Canada v. Kit
January 27, 2015
ELERIA
4
Insular Life v. Khu
April 18
Math 123: Week 4
Applications and Numerical Methods
Section 1: Inflow / Outflow Models
One application of first-order linear differential equations differential equations is modeling the amount (or concentration) of a substance in a wellstirred tank/vesse
Math 123, Spring 2016, Term Test ll
Differential Equations and Linear Algebra
(version 2)
Date: Wednesday, April 20
Time: 1:302:45 p.111.
Instructor: Matthew Johnston '4
Last Name:
First Name:
SJSU Student ID Number
Math 123, Spring 2016, Term Test ll
Differential Equations and Linear Algebra
(version 1)
Date: Wednesday, April 20
Time: 1:302:45 pm.
Instructor: Map-thew Johnston
,1; r
,1"; [5
Last Name;- 1
(7.57 V v V W
_, l-
Fnst- Name: 11, 1
l 5
SJSU Student ngN
Instruetions
Math 133A, Spring 2016, Term Test ll
Ordinary Differential Equations (version 1)
Date: Wednesday, April 13
Time: 12: 00 1: 15 p 111.
Lecture Section: 001
Last Name:
.x
xx
E
Instructor: Matthew D Johnston
x y
First Name: 1
SJSU Student ID
Math 133A, Spring 2016, Term Test ll
Ordinary Differential Equations (version 2)
Date: Wednesday, April 13
Time: 12:001:15 pm.
Lecture Section: 001
Instructor: Matthew D. Johns/ton
Last Name:
First Name:
SJ SU Student ID Numbergy
1 West