C-102: Engineering Mathematics – I syllabus for DCE 1st Year C20 regulation APSBTET

Engineering Mathematics – I detailed syllabus for Diploma in Civil Engineering (DCE) for C20 regulation curriculum has been taken from the APSBTET official website and presented for the DCE students. For course code, course name, number of credits for a course and other scheme related information, do visit full semester subjects post given below.

For Diploma in Civil Engineering 1st Year scheme and its subjects, do visit DCE 1st Year C20 regulation scheme. The detailed syllabus of engineering mathematics – i is as follows.

Unit Title

For the complete syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdfs platform to make students’s lives easier.

Course Objectives:

1. To apply the principles of Algebra, Trigonometry and Co-Ordinate Geometry to real-time problems in engineering.
2. To comprehend and apply the concept of Differential Calculus in engineering applications.

Course Outcomes:

1. Identify various functions, resolve partial fractions and solve problems on matrices.
2. Solve problems using the concept of trigonometric functions, their inverses and complex numbers.
3. Find the equations and properties of straight lines, circles and conic sections in coordinate system.
4. Evaluate the limits and derivatives of various functions.
5. Evaluate solutions for engineering problems using differentiation.

Unit I

For the complete syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdfs platform to make students’s lives easier.

Unit II

Trigonometry

1. Trigonometric ratios:Definition of trigonometric ratios of any angle, values of trigonometric ratios at specified values, draw graphs of trigonometric functions, periodicity of trigonometric functions.
2. Compound angles:Formulas of sin(A±B), cos(A±B), tan(A±B),cot(A±B),and related identities with problems.
3. Multiple and sub multiple angles:Formulae for trigonometric ratios of multiple angles 2A, 3A and sub multipleangles A/2 with problems.
4. Transformations of products into sums or differences and vice versa simple problems
5. Inverse trigonometric functions:Definition, domains and ranges-basic properties- problems.
6. Trigonometric equations:Concept of a solution, principal value and general solution of trigonometric equations: sinx =k ,cosx= k, tanx =k, where k is a constant. Solutions of simple quadratic equations, equations involving usage of transformations- problems.
7. Properties of triangles:Relation between sides and angles of a triangle- sine rule, cosine rule, tangent rule and projection rule-area of a triangle- problems.
8. Hyperbolic functions:Definitions of hyperbolic functions, identities of hyperbolic functions, inverse hyperbolic functions and expression of inverse hyperbolic functions in terms of logarithms.
9. Complex Numbers:Definition of a complex number, Modulus and conjugate of a complex number, Arithmetic operations on complex numbers, Modulus- Amplitue (polar) form , Exponential form (Euler form) of a complex number- Problems. DeMoivres theorem.

Unit III

Coordinate Geometry

1. Straight lines: various forms of straight lines, angle between lines, perpendicular distance from a point, distance between parallel lines-examples.
2. Circle: locus of a point, Circle, definition-Circle equation given (i) centre and radius, (ii) two ends of a diameter (iii) centre and a point on the circumference (iv) three non collinear points – general equation of a circle – finding centre, radius.
3. Definition of a conic section, equation of a conic when focus directrix and eccentricity are given. properties of parabola, ellipse and hyperbola in standard forms.

Unit IV

Differential Calculus:

1. Concept of Limit- Definition- Properties of Limits and Standard Limits -Simple Problems-Continuity of a function at a point- Simple Examples only.
2. Concept of derivative- Definition (first principle)- different notations-derivatives of elementary functions- problems. Derivatives of sum, product, quotient, scalar multiplication of functions – problems. Chain rule, derivatives of inverse trigonometric functions, derivative of a function with respect to another function, derivative of parametric functions, derivative of hyperbolic, implicit functions, logarithmic differentiation – problems in each case. Higher order derivatives – examples – functions of several variables – partial differentiation, Eulers theorem-simple problems.

Unit V

For the complete syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdfs platform to make students’s lives easier.

Text Books:

Engineering Mathematics-I, a textbook for first year diploma courses, prepared & prescribed by SBTET, AP.

Reference Books:

1. Shanti Narayan, A Textbook of matrices, S.Chand&Co.
2. Robert E. Moyer & Frank Ayers Jr., Schaums Outline of Trigonometry, 4th Edition, Schaums Series
3. M.Vygodsky, Mathematical Handbook, Mir Publishers, Moscow.

For detailed syllabus of all other subjects of Diploma in Civil Engineering, C20 regulation curriculum do visit DCE 1st Year subject syllabuses for C20 regulation.

For all Diploma in Civil Engineering exam timetable, visit APSBTET DCE all semester exam timetable direct link.