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Course Title: ENGINEERING MATHEMATICS – I |
Course Code |
: 15SC01M |
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Semester |
: I |
Core / Elective |
: Core |
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Teaching Scheme in Hrs (L:T:P) :
4:0:0 |
Credits |
: 4
Credits |
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|
Type of course |
: Lecture
+ Assignments |
Total Contact Hours |
: 52 |
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CIE |
: 25
Marks |
SEE |
: 100
Marks |
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Programmes: Common to all Engineering Diploma Programmes |
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Pre-requisites:
Basics in Algebra, Trigonometry
and Coordinate Geometry in Secondary Education.
Course Objectives:
1.
Apply the concept of matrices and determinants and
their applications to solve the linear equation in engineering field.
2.
Apply the vector algebra in solving the problems of statics and mechanics.
3.
Analyse the civil engineering problems using concepts of probability.
4.
Evaluate the advanced engineering mathematical problems using logarithms.
5.
Apply and evaluate trigonometric concept in vector engineering field.
6.
Create the basic concept of calculus.
Course Content:
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Topic and
Contents |
Hours |
Marks |
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LINEAR
ALGEBRA |
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UNIT-1: MATRICES AND DETERMINANTS |
10 |
31 |
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(a) Matrices: Basic concepts of matrices: Definition,
types of matrices and mathematical operations on matrices (addition,
subtraction and multiplication of matrices). |
02 |
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(b) Determinant: Definition, problems on
finding the determinant value of 2nd and 3rd order.
Problems on finding unknown quantity in a 2nd and 3rd
order determinants using expansion. Solving simultaneous linear equations
using determinant method (Cramer’s rule up to 3rd order). |
04 |
|
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(c) Inverse and applications of matrices: Minors and Cofactors of
elements of matrix. Adjoint and Inverse of matrices of order 2nd
and 3rd order. Elementary row and column operations on matrices.
Characteristic equation and characteristic roots (eigen values) of 2x2
matrix. Statement of Cayley-Hamilton theorem and its verification for 2x2
matrix. Solution of system of linear equations using Gauss Elimination method
(for 3 unknowns only). |
04 |
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ALGEBRA |
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UNITS-2: VECTORS |
08 |
27 |
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Definition of vector.
Representation of vector as a directed line segment. Magnitude of a vector.
Types of vectors. Position vector. Expression of vector by means of position
vectors. Addition and subtraction of vectors in terms of line segment. Vector
in plane and vector in a space in terms of unit vector i, j and k
respectively. Product of vectors. Scalar product and vector product of two
vectors. Geometrical meaning of scalar and vector product. Applications of
dot (scalar) and cross (vector) products. Projection of a vector on another
vector. Area of parallelogram and area of triangle. Work done by force and moment of force. |
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UNITS-3: PROBABILITY AND LOGARITHMS |
08 |
14 |
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(a) Probability: Introduction. Random
experiments: outcomes and sample space. Event: Definition, occurrence of an
event, types of events. Algebra of events- complementary event, the events A
or B, A and B, A but not B, mutually exclusive events, exhaustive events,
defining probability of an event. Addition rule of probability. Conditional
probability: definition, properties of conditional probability, simple problems. |
06 |
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(b)
Logarithms: Definition of common
and natural logarithms. Laws of logarithms (no proof). Simple problems on
laws of logarithms. |
02 |
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TRIGONOMETRY |
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UNIT-4: ALLIED ANGLES AND COMPOUND ANGLES. |
16 |
47 |
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(a) Recapitulation of angle
measurement, trigonometric ratios and standard angles. Allied angles: Meaning
of allied angle. Signs of trigonometric ratios. Trigonometric ratios of
allied angles in terms of 8. Problems
on allied angles. (b)
Compound angles: Geometrical proof of
sin(A+B) and cos(A+B) and hence deduce tan(A+B). Write the formulae for sin(A-B), cos(A-B) and
tan(A-B), problems. Multiple and sub multiple angle formulae for 2A and 3A.
Simple problems. Transformation formulae. Expression for sum or difference of
sine and cosine of angles into product form. Expression for product of sine
and cosine of angles into sum or differences
form. |
02 |
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06 |
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08 |
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UNIT-5:COMPLEX NUMBERS |
04 |
09 |
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Meaning of imaginary number i and its
value. Definition of complex
number
in
the
form
of a + ib. Argand diagram of
complex numbera + ib (Cartesian system). Equality of complex numbers.
Conjugate of complex number. Algebra of complex numbers, modulus of complex
number, principal value of argument of complex number, polar form: Z = r(cos8
+ i sin8) and exponential form Z
= rei8of complex number,
where r is modulus and 8 is principal value of argument of complex number. |
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UNIT-6: INTRODUCTION TO CALCULUS |
06 |
17 |
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Limits: Constants and variables. Definition of function. Types of functions:
Explicit and implicit function, odd and even functions(definition with
example). Concept of x → a.Definition of limit of a function.
Indeterminate forms. Evaluation of limit of functions by factorization,
rationalization. Algebraic limits. Statement of sn–an lim =
nan–1 where n is any rational number. s→a s–a Proof of lim sin 8 =
1 where 8 is in radian. Related 8→0 8 problems. Standard limit (statement only) x x 1. lim a –1 = log a, 2. Lim e –1 = 1 s→0 s e s→0 s n 1 3. lim (1 + 1) = e, 4.lim(1 + n)n = e n→∞ n n→0 Simple problems on standard limits. |
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TOTAL |
52 |
145 |
