Calculas

Course Title     : Calculus

Nature of the Course: Theoretical

Course No.         : Math Ed.                            

Credit Hours: 3           

Level                   : B Ed        (Minor)                        

Teaching Hours: 48   

Semester    : Third      

Content

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

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)

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

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

Unit V: Indefinite Integral                                 (4)

5.1    Meaning of integration

          5.2    Some standard Integrals

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

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

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