Subject Name : Engineering
Mathematics II
Code / Credit
: EE 150/4 sks
Course status :
Compulsory
Semester / The academic year : II/ Genap 2012-2013
Pre-requisites/Co-requisites : (P) Engineering Mathematics I
Lecturer : Yuliati, S.Si,
MT
Description of Subjects : This
course contains knowledge of problem solving techniques into mathematical
models to solve problems analytically or
using a computer approach.
Competency standards /
Learning Outcomes :
Students are able to:
1. Analyze data and create solutions to problems.
2. Using computer programs and applications.
3. Collaboration and presentations in the classroom.
Reference books :
1. Kreyszig Erwin. 2006. Advanced Engineering Mathematics 9th
Edition. John Wiley & Sons.
2. Dale Varberg & Edwin J Purcell. 2007. Calculus with Analytic Geometry
9th Edition. Prentice Hall International.
3. Jeffrey Alan. 2002. Advanced Engineering Mathematics. Harcourt
Academic Press.
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Week
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Basic competencies / capabilities end to be achieved
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Study materials
(teaching materials)
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Reference
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Learning Model
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Learning Media
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Criteria for Assessment
(Indicator)
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Form of evaluation
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Weight rating
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Subject
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Sub subject
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1
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Students
understand the purpose and objective approach to learning with SCL
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SCL Guidelines
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Explanation of the
implementation of the teaching of the SCL, Rules lectures, assignments, and
assessments
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The
presentation of the lecturer
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lectures +
discussion
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LCD projector, whiteboard.
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-
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1
2
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Students are
able to define multivariable functions, domain of functions of several
variables, graph and level curve, partial derivative, to find limit and continuity, and differential in n-space
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Derivative in
n-Space (2)
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Introduction; Function of multivariable, Domain of functions of
several variables, graph and level curve, partial derivative, to find limit and continuity, and differential in n-space
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(2)
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Informal
presentations and discussion groups
(Lecturer
describes an outline of the material "Derivative in n-Space",
students are given the task of group discussions "create 5 examples of
multivariable functions and partial derivative” , student discussions in
small groups, the results were presented to the class discussion.
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LCD projector, whiteboard, calculator.
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Activity and results
of discussion in each group. Student can solve the multivariable functions problems
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Short test, homework to practice the questions
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5%
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3
4
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Students are
able to find solution of the first
order-ordinary differential equations (ODEs).
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The First Order-
Ordinary Differential Equations (ODEs)
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Basic Concepts. Modeling Geometric Meaning
of y' = f(x, y). Direction Fields, Separable ODEs. Modeling, Exact ODEs, Integrating
Factors, Linear ODEs. Bernoulli Equation, Population Dynamics, Existence and
Uniqueness of Solutions
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(1)
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Informal
presentations and discussion groups
(Lecturer
describes an outline of the material "The First ODEs", students are
given the task of group discussions "create 5 examples of the following discussion about how to
find solutions of ODEs", students in small group discussions, the
discussions presented in the class.
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LCD projector, whiteboard, calculator.
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Activity and
results of discussion in each group.
Student can
solve the ODEs problems
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Short test, homework to practice the questions.
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5%
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5
6
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Students are
able to find solutions of the Second
order-Linear Ordinary Differential Equations (ODEs).
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The Second order-Linear Ordinary Differential
Equations (ODEs).
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Homogeneous Linear ODEs of Second Order, Homogeneous
Linear ODEs with Constant Coefficients, Differential Operators, Modeling:
Free Oscillations. (Mass-Spring System), Euler-Cauchy Equations, Existence
and Uniqueness of Solutions. Wronskian, Nonhomogeneous ODEs, Modeling: Forced
Oscillations. Resonance, Modeling: Electric Circuits, Solution by Variation
of Parameters.
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(1)
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Presentations
and discussion groups (Lecturer describes an outline of the material "
The Second order-Linear Ordinary
Differential Equations (ODEs )", students are given the task of group
discussions " to find solutions of second order ODEs”, student
discussions in small groups, the results were presented to the class
discussion.
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LCD projector, whiteboard, calculator.
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Student’s
Activity and the results of discussion in each group.
Student can
solve the second order ODEs problems
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Short test, homework to practice the questions.
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5%
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7
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Quiz I
Review Material
for preparing Midterm Exam
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·
Materials Quiz on Chapter 15 (2) and Chapter 1&2
(1)
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(Time 2x50minutes)
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(1)
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·
Lecturer give a quiz
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Students are given the task of discussion groups to discuss the
material in accordance with predetermined by the lecturer in this chapter.
·
The results were presented to the class discussion.
·
Lecturer reiterated important points about the material that has
been presented by each group.
• Lecturer
provide conclusions about the material that was presented by the students.
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LCD projector, whiteboard, calculator.
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Students are
able to complete the corresponding quiz questions correctly
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Written tests, open book
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30%
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8/9
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Midterm Exam (UTS)
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30%
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10
11
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Students are
able to extend the ides of a definite integral to double and triple integrals
of functions of two or three
variables. |
Multiple Integral (2)
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Introduction, Double Integrals
over Rectangles, Iterated Integrals, Double Integrals over General Regions, Double Integrals in Polar Coordinates, Applications of Double Integrals, Triple Integrals, Triple Integrals in Cylindrical Coordinates, Triple Integrals in Spherical Coordinates, Change of Variables in Multiple Integrals. |
(2)
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·
Lecturer describes an outline of the material "Multiple
Integral".
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Students are given the task of discussing the matter in accordance
with predetermined by the lecturer in this chapter.
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The results of MATLAB simulation program presented in front of the
class.
·
Lecturer reiterated important points about the subject matter of
each group.
• Lecturer
provide conclusions about the material that was presented by the students.
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LCD projector, whiteboard, calculator.
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Students are
able to solve multiple integral problems using MATLAB
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Task completion multiple integral using MATLAB programming
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40%
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12
13
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Students are
able to find the Laplace transforms and The Inverse Laplace Transforms of the
functions
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Laplace Transforms (1)
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Laplace Transforms:Laplace Transform, Inverse
Transform. Linearity. s-Shifting Transforms of Derivatives and Integrals.
ODEs Unit Step Function. t-Shifting , Short Impulses. Dirac's Delta Function. Partial
Fractions, Convolution. Integral Equations, Differentiation and Integration of Transforms.
Systems of ODEs, Laplace Transform: General
Formulas , Table of Laplace Transforms.
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(1)
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·
Lecturer describes an outline of the material "Laplace
Transforms".
·
Students are given the task of discussing the matter in accordance
with predetermined by the lecturer in this chapter.
·
The results of MATLAB simulation program presented in front of the
class.
·
Lecturer reiterated important points about the subject matter of
each group.
• Lecturer
provide conclusions about the material that was presented by the students.
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LCD projector, whiteboard, calculator.
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Students are
able to solve Laplace transforms and inverse Laplace transforms.
Student can
solve the problems using MATLAB
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Homework, Task completion Laplace transforms and inverse using
MATLAB programming
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40%
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14
15
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Students are
able to solve problems using a variety of Linear Algebra methods
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Linear Algebra: Matrices, Vectors, Determinants (1)
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Linear Algebra: Matrices, Vectors, Determinants: Linear
Systems, Matrices, Vectors: Addition and
Scalar Multiplication, Matrix Multiplication, Linear
Systems of Equations. Gauss Elimination, Linear
Independence. Rank of a Matrix. Vector Space, Solutions of Linear Systems: Existence,
Uniqueness, For Reference: Second- and Third-Order Determinants, Determinants.
Cramers Rule, Inverse of a Matrix. Gauss-Jordan
Elimination, Vector Spaces, Inner Product
Spaces.
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(1)
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·
Lecturer describes an outline of the material "Linear Algebra".
·
Students are given the task of discussing the matter in accordance
with predetermined by the lecturer in this chapter.
·
The results of MATLAB simulation program presented in front of the
class.
·
Lecturer reiterated important points about the subject matter of
each group.
• Lecturer
provide conclusions about the material that was presented by the students.
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LCD projector, whiteboard, calculator.
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Students are
able to solve Linear Algebra problems and to compute using MATLAB
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Homework, Task completion Linear Algebra
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40%
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16
17
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Students are
able to solve Vector Differential Calculus problems.
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Vector Differential Calculus (1)
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Vector Differential Calculus: Grad, Div,
Curl,
Vectors in 2-Space and 3-Space, Inner Product (Dot Product), Vector Product (Cross Product), Vector and
Scalar Functions and Fields. Derivatives, Curves. Arc Length. Curvature. Torsion, Gradient of a Scalar Field. Directional
Derivative, Divergence of a Vector Field, Curl of
a Vector Field.
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(1)
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·
Lecturer describes an outline of the material "Vector
Differential Calculus".
·
Students are given the task of discussing the matter in accordance
with predetermined by the lecturer in this chapter.
·
Lecturer reiterated important points about the subject matter of
each group.
• Lecturer
provide conclusions about the material that was presented by the students.
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LCD projector, whiteboard, calculator.
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Students are
able to solve Vector Differential Calculus problems
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Short test, homework to practice the questions.
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30%
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17
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Quizzes and review materials
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30%
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18 19
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Final Semester Exam (UAS)
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35%
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Prepared by:
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Checked by:
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Approved by:
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Lecturer
(Yuliati, S.Si, MT )
NIK.511.99.0402
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Course Coordinator
(----------------------------------)
NIK.
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Head of Department
(----------------------------------)
NIK.
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Date : 3 February 2013
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Date :
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Date :
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