Vector Operations Exercises
Vector Operations and its Applications
Mathematics 54  Elementary Analysis 2
Institute of Mathematics
University of the PhilippinesDiliman
3 October 2014
Math 54 WFQ2 & WFV2  Vector Operations (03 Oct. 2014)
1/37
Vector Oper
9
Mathematics
Learners Material
Module 5:
Quadrilaterals
This instructional material was collaboratively developed and reviewed by
educators from public and private schools, colleges, and/or universities. We encourage
teachers and other education stakehol
Harold Jarche. The New Work. May 5, 2013. www.jarche.com/2013/05/thenewwork/
Matrix Solutions to Systems
of Linear Equations 4
June 26, 2013
Systems of Linear Equations
Methods for Solving Systems of Linear Equations:

Elimination
Substitution
Guessing
Introduction Parabola Ellipse
Conic Sections
(Parabola and Ellipse
Mathematics 54Elementary Analysis 2
Institute of Mathematics
University of the PhilippinesDiliman
11 February 2015
1 / 28
Introduction Parabola Ellipse
Introduction
A conic section is a p
Polar Coordinates More Polar Curves
Polar Coordinate System
Mathematics 54Elementary Analysis 2
Institute of Mathematics
University of the PhilippinesDiliman
09 September 2015
1 / 32
Polar Coordinates More Polar Curves
Graphs in Polar Coordinates Exercis
METHODS IN OBTAINING
THE DETERMINANT
ChE 106 Mathematical Methods in Chemical Engineering
1st Semester AY 20142015
ChE
106
Mathematical
1st Semester
AY 20142015
Engr.
Kristian
July R. YapMethods in Chemical Engineering
University of the
Philippines
Dil
3
MODULE IV Plotting Functions
OBJECTIVE
At the end of this module, you should be able to:
1. Use the plotting feature (plot) of MATLAB
1. Using subplot
2. Customizing plots
3. Labeling plots
2. Use the builtin plotting functions of MATLAB
1. plot, ploty
Trigonometric Substitution
Trigonometric Substitution
Mathematics 54Elementary Analysis 2
Institute of Mathematics
University of the PhilippinesDiliman
28 January 2015
1 / 22
Trigonometric Substitution
Case 1 Case 2 Case 3 Summary Exercises
Recall: Let a
Structure,
Properties,
Processing,
Performance
and
Characterizatio
n of
Nanofibrou
s AMaterials
creative report by
Group 5
The Big Bang Theory
CooperHofstadter Nanofibrous Materials
large surface area to volume ratio
high porosity
small pore size
diamete
DIRECT METHODS FOR SYSTEMS
OF LINEAR EQUATIONS (Part I)
ChE 106 Mathematical Methods in Chemical Engineering
1st Semester AY 20142015
ChE
106
Mathematical
1st Semester
AY 20142015
Engr.
Kristian
July R. YapMethods in Chemical Engineering
University of
Differential Equations Some Applications Exercises
Introduction Solutions
Differential Equations and Applications
Mathematics 54Elementary Analysis 2
Institute of Mathematics
University of the PhilippinesDiliman
20 August 2015
1 / 26
Differential Equatio
DIRECT METHODS FOR SYSTEMS
OF LINEAR EQUATIONS (Part II)
ChE 106 Mathematical Methods in Chemical Engineering
1st Semester AY 20142015
ChE
106
Mathematical
1st Semester
AY 20142015
Engr.
Kristian
July R. YapMethods in Chemical Engineering
University of
Hyperbola Eccentricity
Conic Sections
(Hyperbola and Eccentricity)
Mathematics 54Elementary Analysis 2
Institute of Mathematics
University of the PhilippinesDiliman
13 February 2015
1 / 24
Hyperbola Eccentricity
ConicsStd Eqns Exercises
Hyperbola
Hyperbo
EXISTENCE & UNIQUENESS OF A SOLUTION
Submatrix
Rank of a Matrix
Theorems on Ranks
Types of Solution to a System of Equations
Submatrix
A submatrix of A = [aij] is any matrix obtained by eliminating
some rows and/or some columns of the original matrix A.
E
Matrix Solutions to Systems
of Linear Equations 2
June 19, 2013
Outline
1.Row Echelon Form and Reduced Row
Echelon Form
2.Elementary Row Operations
3.Theorems on Row Equivalence
4.Alternative Matrix Inversion Method!
5.Solution to Systems of Linear Equati
Trig Integrals
Techniques of Integration Trigonometric
Integrals
Mathematics 54Elementary Analysis 2
Institute of Mathematics
University of the PhilippinesDiliman
07 August 2015
1 / 26
Trig Integrals
Summary Exercises
Trigonometric Integrals
We will stud
Parametric Equations Calculus of Parametric Equations
Parametric Curves
Mathematics 54Elementary Analysis 2
Institute of Mathematics
University of the PhilippinesDiliman
18 February 2015
1 / 22
Parametric Equations Calculus of Parametric Equations
Exerci
Matrix Solutions to Systems
of Linear Equations 3
June 21, 2013
Outline
1.Matrix Ranks
2.Theorems on Ranks
3.Types of Solutions to Systems
4.Ill and Wellconditioned Matrix
a. Condition Number
b. UniformMatrix Norm
5.Applications to Engineering Problems
Group 5
Nanofibrous Materials
1. Give two general properties of nanofibrous materials and explain each.
large surface area to volume ratio: these makes them more reactive than monolithic materials since they have
larger surface area
high porosity: the v
Name:
Section:
1st Sem AY 201516
Due: 30 September 2015
Mathematics 54 WFR2
HW (Quiz) on R3 and Vectors
This Homework/Quiz is due on Wednesday, 30 September 2015. Print this sheet out (preferably backtoback) and
write all solutions using nonerasable i
ILLILLCONDITIONED SYSTEMS
OF LINEAR EQUATIONS
ChE 106 Mathematical Methods in Chemical Engineering
1st Semester AY 20142015
ChE
106
Mathematical
1st Semester
AY 20142015
Engr.
Kristian
July R. YapMethods in Chemical Engineering
University of the
Phili
ADJOINT & INVERSE
OF MATRICES
ChE 106 Mathematical Methods in Chemical Engineering
1st Semester AY 20142015
ChE
106
Mathematical
1st Semester
AY 20142015
Engr.
Kristian
July R. YapMethods in Chemical Engineering
University of the
Philippines
Diliman
AD
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Mathematics 54 Assignment (Quiz 9) Due: 10 November 2015 (Tuesday discussion class)
Write your answers on a Whole sheet of yellow pad paper. Show all necessary solutions
and box all nal answers. Homeworks submitted beyond 7:15 AM (for 7:00  8:15 AM
discu
ChE APPLICATIONS TO
SYSTEMS OF LINEAR EQUATIONS
ChE 106 Mathematical Methods in Chemical Engineering
1st Semester AY 20142015
ChE
106
Mathematical
1st Semester
AY 20142015
Engr.
Kristian
July R. YapMethods in Chemical Engineering
University of the
Phil
Name:
1st Sem AY 201516
08 September 2015
Mathematics 54 WFR2
Quiz on Conic Sections
This quiz is good for 15 mins. Show complete solutions on the space provided, and box final answers.
A student shall be subject to disciplinary action for any form of ch
Mecaelah S. Palaganas
MatE 10
201420608
XYZ
Reaction Paper on the Documentary
Metals have been used widely by man since ancient ages and have
been an important part in the development of the world. In the past, these
metals were used for cooking, agricul
Mecaelah S. Palaganas
MatE 10
201420608
XYZ
Metals, Polymers, or Ceramics?
Materials science and engineering plays an important role in humans lives. It lets us investigate
the inner world of materials up the atomic level, which gives us a deeper underst