MATH – 213 APPLIED MATHEMATICS – II

MATH – 213    APPLIED MATHEMATICS – II

      

COURSE CONTENTS:

1.                   FUNCTION AND LIMITS

1.1.                    CONSTANT AND VARIABLE QUANTITIES.

1.2.                    FUNCTIONS AND THEIR CLASSIFICATION.

1.3.                    THE CONCEPT OF LIMIT AND LIMIT OF A FUNCTION.

1.4.                    FUNDAMENTAL THEOREMS ON LIMIT AND SOME IMPORTANT LIMITS.

2.                   DIFFERENTIATION

2.1.                    INCREMENTS.

2.2.                    DIFFERENTIAL COEFFICIENT OF DIFFERENTIATION BY FIRST PRINCIPLE.

2.3.                    GEOMATERICAL INTERPRETATION OF DIFFERENTIAL COEFFICIENT.

2.4.                    DIFFERENTIAL COEFFICIENT OF Xn, (ax+b) IN AND THREE IMPORTANT RULES.

3.                   DIFFERENTIATION OF ALGEBRIC FUNCTIONS

3.1.                    EXPLICIT FUNCTIONS AND IMPLICIT FUNCTIONS.

3.2.                    PARAMETRIC FORMS.

4.                   DIFFERENTIATION TRIGONOMETRIC FUNCTIONS

4.1.                    DIFFERENTIAL COEFFICIENT OF Sin x, Cos x, Tan x FROM FIRST PRINCIPLE.

4.2.                    DIFFERENTIAL COEFFICIENT OF Cosec x, Sec x, Cot x.

4.3.                    DIFFERENTIATION OF INVERSE TRIGONOMETRIC FUNCTIONS.

5.                   DIFFERENTIATION OF LOGARITHMIC AND EXPONENTIAL FUNCTIONS

5.1.                    DIFFERENTIATION OF In x AND Log ax.

5.2.                    DIFFERENTIATION OF ax AND ex.

6.                   RATE OF CHANGE OF VARIABLE

6.1.                    INREASING AND DECREASING FUNCTIONS.

6.2.                    MAXIMA AND MAXIMA VALUES.

6.3.                    CRITERIA FOR  MAXIMUM AND MINIMUM VALUES.

6.4.                    METHODS OF FINDING MAXIMA AND MAXIMA.

7.                   INTEGRATION

7.1.                    CONCEPT.

7.2.                    FUNDAMENTAL FORMULAS.

7.3.                    IMPORTANT RULES.

8.                   METHODS OF INTEGRATION

8.1.                    INTEGRATION BY SUBTITUTION.

8.2.                    INTEGRATION BY PARTS.

9.                   DEFINITE INTEGRALS

9.1.                    PROPERTIES.

9.2.                    APPLICATION TO AREA.

10.                PLANE ANALYTIC GEOMETRY AND STRAIGHT LINE

10.1.                 CO-ORDINATE SYSTEM.

10.2.                 DISTANCE FORMULA AND RATIO FORMULAS.

10.3.                 INCLINATION AND SLOPE OF A LINE.

10.4.                 THE SLOPE FORMULA.

11.                EQUATIONS OF STRAIGHT LINE

11.1.                 SOME IMPORTANT FORMS.

11.2.                 GENERAL FORM AND ANGLE FORMULA.

11.3.                 PARALLELISM AND PERPENDIOULARITY.

12.                THE EQUATIONS OF CIRCLE

12.1.                 STANDARD FORM OF EQUATION.

12.2.                 CENTRAL FORM OF EQUATION AND GENERAL FORM EQUATION.

12.3.                 RADIUS AND CO-ORDINATES OF THE CENTRE.

BOOKS:

1.             CALCULUS AND ANALYTIC GEOMETRY,  THOMAS FINNY.

2.             TECHNICAL MATHEMATICS VOL. I AND II,  GHULAM YASIN MINHAS.

3.             POLYTECHNIC MATHEMATICS SERIES VOL. I AND II,  PROF. RIAZ ALI KHAN.

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