Course
Title : Calculus Nature
of the Course: Theoretical
Course
No. : Math Ed. 431 Credit Hours: 3
Level : B Ed (Minor) Teaching Hours: 48
Semester : Third
1. Course Description
The calculus is at the same time a beginning as well as a
complete package course. It is the course where many of the ideas and
techniques learned in the secondary mathematics are pulled together and
answered in a satisfactory way. It is also the foundation for the study of the
natural and social sciences. So, this is an introduction course that provides a
basic knowledge of calculus and its application. It provides a framework for
modeling system. The concepts differentiation and integration in simple standard
forms are applied as early as possible to the determination of maxima and
minima, of the areas and length of curve, of volume of revolution, to the
solution of the day to day problems.
2. The
General Objectives
The general objectives of this course are as
follows:
•
To familiarize
students with techniques, principles and application of differential calculus.
•
To make students capable
in applying the differential calculus to solve the problems of other branches
of mathematics (natural and social sciences).
•
To make
students efficient in applying the
differential calculus to solve the problems of maxima and minima.
•
To make students trained
in using the differential calculus for study
the properties of tangents and normal of a curve (Cartesian curve only).
•
To enhance
the skills of students in demonstrating an understanding of techniques, and
application of integral calculus.
•
To make students
competent in applying integral calculus to evaluate the area, length of plane
curve and volume of solid of revolution.
•
To develop skills
of students on writing differential equation as alternative form to the
different types of family of curves.
•
To make
students able in applying differential equations to solve physical problems.
3. Specific
Objectives and Contents
On completion of this course students should be able to:
Specific
Objectives
|
Content
|
· Define
limit and continuity of a function
· Find
limits of functions
· Test
the continuity of functions.
|
Unit 1: Limits and Continuity (5)
1.1
Use ᵋ-ᵟ in finding
limit
1.2
Left hand limit
and right hand limit
1.3
Continuity of a
function: Meaning of continuity
|
· Define
differentiation.
· Find
the differential coefficient of some specific function
· Explain
the meaning of successive differentiation.
· Find
the derivatives of some specific functions up to 4th order.
· Find
the partial derivatives of two independent variables.
|
Unit
II: Derivatives
(8)
2.1
Differentiation of implicit and explicit function,
trigonometric, logarithmic, exponential, and parametric function.
2.2
Definition and notation of derivative of function,
of order greater than one.
2.3
Differentiation of some
specific functions up to 4th order.
2.4
Partial derivatives of he
functions of type u= f(x,y)
|
· Find
equation of tangent and normal at any point of a Cartesian curve.
· Find
angle between two curves.
· Find
the length of tangent, normal, subtangent, and subnormal (in Cartesian form).
|
Unit III: Tangent and Normal (5)
3.1
Equation of tangent and normal
3.2
Problems on tangent and
normal
3.3
Angle of intersection of
two curves (Cartesian only)
3.4
Problems on Length of tangent, normal, sub-tangent
and sub-normal
|
· Explain
maxima and minima of a function.
· Apply
rules of maxima and minma to find extreme values of a function.
· Solve
some verbal problems on maxima and minima( relating to the daily life).
|
Unit IV: Maxima and Minima (4)
4.1
Meaning of
Maxima and minima
4.1.1 Global
Maxima/minima
4.1.2 Local
Maxima/minima
4.1.3 Stationary
and Saddle points
4.2
Application of
necessary and sufficient condition of determining extreme values
4.3
Problems on
maxima and minim including some behavioral problems
|
· Integrate
different types of functions (by different methods).
· Apply
standard integrals in solving problems
|
Unit V: Indefinite Integral (4)
5.1
Meaning of integration
5.2
Some standard Integrals
|
· Define
integration as the limit of a sum.
· Explain
the meaning of f(x)dx
· Solve
problems of definite integral using definition.
· Find
the area of plane regions using definite integral.
|
Unit VI: Definite Integral (6)
6.1
Integration as the limit of a sum
6.2
Meaning of ∫f(x)dx
6.3
Properties of definite integral.
6.4
Problems on finding definite integral
6.5
Area of plane regions
|
· Calculate
the area of plane region.
· Calculate
the arc length of plane curve.
· Calculate
volume of solids of revolution.
|
Unit VII: Quadrature, Rectification and
Volume (7)
7.1
Introduction
7.2
Application of definite integral in Cartesian form only
7.2.1 Area
7.2.2 Length
7.2.3 Volume
|
· Form
the family of curves in term of differential equations.
· Solve
equation of first order and first degree linear homogeneous equations.
|
Unit 8: Differential Equations
8.1
Definitions (Order and degree)
8.2
Concepts of ordinary differential equation.
8.3
General and particular solution
8.4
Change of variables
8.5
Homogeneous equations
8.6
Equations reducible to homogeneous form
8.7 Linear Differential
equations of first order
8,8 Exact equation
8.9 Equation reducible to linear
form
8.10 Application of differential
equations
|
4.
Instructional
Techniques
4.1 General Instructional
Techniques
Heavy discussion should take place on the issue that students
have been told throughout the secondary level. There are many paradoxical instances
at secondary level not dealt clearly at good length. Students should be engaged
in that you will find the reason why things work the way they do, what they
mean and when they are to be used. Listening to students led naturally to even
more changes in instruction. So, discussion, lectures, project work will be
general instructional technique of delivery of course.
4.2 Specific Instructional
Technique
Unit
|
Activity and Instructional Techniques
|
Teaching Hours (48)
|
1
|
Experiences
will be shared between groups with a seminar
|
5
|
2
|
The
Demonstration method will be used both giving task to students and
showing
their task
|
8
|
3
|
Project
assignment on some theorems
|
5
|
4
|
Group
discussion with sharing
|
4
|
5
|
Guided
Discussion
|
4
|
6
|
Group
discussion with sharing
|
5
|
7
|
Group
discussion with sharing
|
7
|
8
|
Group
discussion with sharing
|
10
|
5.
Evaluation
5.1 Internal Evaluation 40%
Internal evaluation will be conducted by the subject teacher
based on the following aspects:
1) Attendance 4
points
2) Participation
in learning activities 6
points
3) First
assignment/Mid-term exam 10
points
4) Second assignment/assignment ( 1 or 2) 10 points
Total 30
points
5.2 External Evaluation (Final
Examination) 60%
Examination Division, Dean’s office will conduct final
examination at the end of the semester and the types of questions and scores
allocated for each category of questions are given below:
1) Objective
Type Question (Multiple Choice
) 10 points
2) Short
Answer Question (6 Question
5
points ) 30
points
3) Long
Answer Question (2 Question
10
points ) 20 points
Total 60
points
6.
Recommended
Book and references
Recommended Book
Das, B. C. ; & Mukharjee, B. (1984) Differential Calculus. Calcutta:
U N Dhur and Sons Pvt Ltd.
Reference Books
Maskey, S. M. (2008). Calculus. Kathmandu: Ratna Pustak Bhandar.
Narayan, S. (1998). Differential calculus. Delhi: Shyam Lal Chan
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