MATH – 113 APPLIED MATHEMATICS – I

MATH – 113            APPLIED MATHEMATICS – I

        COURSE CONTENTS:

1.            QUADRATIC EQUATIONS

1.1-         STANDARD FORM.

1.2-         SOLUTION.

1.3-         NATURE OF ROOTS.

1.4-         SUM AND PRODUCT OF ROOTS.

1.5-         FORMATION.

2.              ARTHMETIC PROGRESSION AND SERIES

2.1-         SEQUENCE.

2.2-         SERIES.

2.3-         NTH TERM.

2.4-         SUM OF THE FIRST N TERM.

2.5-         MEANS.

3.              GEOMETRIC PROGRESSION AND SERIES

3.1-         NTH TERM.

3.2-         SUM OF THE FIRST N TERM.

3.3-         MEANS.

3.4-         INFINITE GEOMETRIC PROGRESSION.

4.              BINOMIAL THEOREM

4.1-         FACTORIALS.

4.2-         BINOMIAL EXPRESSION.

4.3-         BINOMIAL CO-EFFICIENT.

4.4-         THE GENERAL TERM.

4.5-         THE BINOMIAL SERIES.

5.              PARTIAL FRACTIONS

5.1-         INTRODUCTION.

5.2-         LINEAR DISTINCT FACTORS CASE I.

5.3-         LINEAR REPEATED FACTORS  CASE II.

5.4-         QUADRATIC DISTINCT FACTORS CASE  III.

5.5-         QUADRATIC REPEATED FACTORS CASE  IV.

6.              FUNDAMENTALS OF TRIGONOMETRY

6.1-         ANGLES AND QUADRANTS.

6.2-         MEASUREMENTS OF ANGLES.

6.3-         RELATION BETWEEN SEXAGESIMAL AND CIRCULAR SYSTEM.

6.4-         RELATION BETWEEN LENGTH OF A CIRCULAR ARC AND THE RADIAN MEASURE OF ITS CENTRAL ANGLE.

7.              TRIGONOMATRIC FUNCTIONS AND RATIOS

7.1-         TRIGONOMATRIC FUNCTIONS OF ANY ANGLE.

7.2-         SIGNS OF TRIGONOMATRIC FUNCTIONS.

7.3-         TRIGONOMATRIC RATIOS OF PARTICULAR ANGLES.

7.4-         FUNDAMENTAL IDENTITIES.

8.              GENERAL IDENTITIES

8.1-         THE FUNDAMENTAL LAW.

8.2-         DEDUCTIONS.

8.3-         SUM AND DIFFERENCE FORMULAE.

8.4-         DOUBLE ANFLE IDENTITIES.

8.5-         HALF ANGLE IDENTITIES.

8.6-         CONVERSION OF SUM OR DIFFERENCE TO PRODUCTS.

9.              SOLUTION OF TRIANGLES

9.1-         THE LAW OF SINES.

9.2-         THE LAW OF COSINES.

9.3-         MEASUREMENT OF HIGHTS AND DISTANCES.

10.           MENSURATION OF SOLDS

10.1-      REVIEW OF REGULAR PLANE FIGURES AND SIMPSON’S RULE.

10.2-      PRISMS.

10.3-      CYLINDERS.

10.4-      PYRAMIDS.

10.5-      CONES.

10.6-      FRUSTA.

10.7-      SPHERES.

11.           VECTORS

11.1-      SCALARS AND VECTORS.

11.2-      ADDITION AND SUBTRACTION.

11.3-      THE UNIT VECTORS I, J, K.

11.4-      DIRECTION COSINES.

11.5-      SCALAR OR DOT PRODUCT.

11.6-      DEDUCTIONS.

11.7-      DOT PRODUCT IN TERMS OF ORTHOGONAL COMPONENTS.

11.8-      VECTOR OR CROSS PRODUCT.

11.9-      ANALYTIC EXPRESSION FOR   Ax B.

12.           MATRICES AND DETERMINANTS

12.1-      DEFINITION OF MATRIX.

12.2-      ROWS AND COLUMNS.

12.3-      ORDER OF A MATRIX.

12.4-      ALGEBRA OF MATRICES.

12.5-      DETERMINANTS.

12.6-      PROPERTIES OF DETERMINANTS.

12.7-      SOLUTION OF LINEAR EQUATIONS.

BOOKS

1-        TECHNICAL MATHEMATICS VOL. I,      GHULAM YASIN MIHAS.

2-        POLYTECHNIC MATHEMATICS SERIES VOL. I AND II.     PROF.  RIAZ ALI KHAN.

3-       A TEXT BOOK OF ALGEBRA AND TRIGONOMATRY,     PROF.  SANA ULLAH         BHATTI.

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