# Mathematics

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# Code(Credit) : ABC01(3-0-1)

## Course Objectives:

1. To understand the concepts matrices, progressions, trigonometry, two dimensional geometry and calculus.
2. To solve linear equations representing physical systems.
3. To understand the importance of calculus and their applications.

## Learning Outcomes:

Upon successful completion of this course, the student will be able:

1. To represent linear systems by matrices and solve them for unknown variables.
2. To evaluate nth terms, trigonometric ratios, locus and to solve differential equations.

## Course Syllabus:

Module I:  Matrices:                                                                                                 5 Hours

Introduction, types of matrices, Scalar multiple of a matrix and multiplication of matrices, Transpose of a matrix, Determinants,

Module II                                                                                                                   5 Hours

Adjoint of a matrix, Inverse, Application of determinants to solve simultaneous equations (Cramer’s Rule)

Module III:  Arithmetic and Geometric Progression:                                            5 Hours

Introduction, Arithmetic Progression, Sum of n terms of an arithmetic progression, Geometric Progression, Sum of n terms of Geometric Progression.

Module IV: Trigonometry:                                                                                       5 Hours

Introduction, Trigonometric ratios and the relations, Trigonometric ratios of compound angles,

(Sin (A+B), Cos (A+B), Tan (A+B) formulae only),   Trigonometric ratios of multiple angle

(Sin 2A, cos2A, tan 2A), Heights and distances.

Module V: Co –ordinate Geometry                                                                         5 Hours

Distances between points-Area of a triangle, Co-ordinates of a point dividing a given segment in a given ratio – locus -equation to a straight line in different forms-Angle between straight lines-point of intersection.

Module VI: DIFFERENTIAL CALCULUS                                                         5 Hours

Simple concepts of functions, limits, Continuity and Differentiation, Differentiation, First order derivatives of elementary functions.

Module VII: INTGRAL CALCULUS:                                                                  5 Hours

Indefinite integrals, Integration as on inverse process of differentiation, integration by substitution, integration by parts, integration of algebraic function.   Definite integrals.

Differential equations: Formation of a differential equation, order and degree, solution of first order differential equations (Variables separable method)

TEXT BOOKS

1. Intermediate first and second year mathematics by Telugu Akademi, A. P State in Institute of Telugu language, Hyderabad. Text Book for A. P ,
2. Intermediate –I A : 3. (3.1, 2, 3.3,3.4, 3.5, 3.7.1)  6 ( 6.1, 6.2, 6.3)
3. Intermediate –I B : 3 : ( 3.1-3.5, 3.8), 8( 8.2,8.3,8.4) , 9 (9.1, 9.2, 9.3, 9.4)
• Intermediate –II B : 6, 7 ( simple problems)  8 (8.1, 8.2(a))

Reference Books,

1. Higher Engineering Mathematics by DR. B. S. Grewal. 44th Edition, 2017.
2. Remedial Mathematics by SahanazBatul, PHI learning private Limited, 2012.
3. Intermediate Mathematics IA, I B, II A and II B, S. Chand Publications 2017.

## Session 1

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## Session 2

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# Code(Credit) : ABC01(1-1-0)

## Course Objectives

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## Learning Outcomes

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## Course Syllabus

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## Session 1

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## Session 2

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