Board of Technical Examinations
| Course Title: ENGINEERING MATHEMATICS – I | Course Code | : 15SC01M | |
| Semester | : I | Core / Elective | : Core |
| Teaching Scheme in Hrs (L:T:P) : 4:0:0 | Credits | : 4 Credits | |
| Type of course | : Lecture + Assignments | Total Contact Hours | : 52 |
| CIE | : 25 Marks | SEE | : 100 Marks |
| Programmes: Common to all Engineering Diploma Programmes | |||
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:
| Topic and Contents | Hours | Marks |
| LINEAR ALGEBRA | ||
| UNIT-1: MATRICES AND DETERMINANTS | 10 | 31 |
|
(a) Matrices: Basic concepts of matrices: Definition, types of matrices and mathematical operations on matrices (addition, subtraction and multiplication of matrices). |
02 |
|
| (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 | |
| (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 |
|
| ALGEBRA | ||
| UNITS-2: VECTORS | 08 | 27 |
|
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. |
|
|
| UNITS-3: PROBABILITY AND LOGARITHMS | 08 | 14 |
|
(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 |
|
| (b) Logarithms: Definition of common and natural logarithms. Laws of logarithms (no proof). Simple problems on laws of logarithms. |
02 | |
| TRIGONOMETRY | ||
| UNIT-4: ALLIED ANGLES AND COMPOUND ANGLES. | 16 | 47 |
| (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 |
|
|
06 | ||
|
08 | ||
| UNIT-5:COMPLEX NUMBERS | 04 | 09 |
| 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. |
|
|
| UNIT-6: INTRODUCTION TO CALCULUS | 06 | 17 |
| 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. |
|
|
| TOTAL | 52 | 145 |
On successful completion of the course, the student will be able to:
1. Find the product of matrices, value of determinants, and inverse of matrix and solve the simultaneous linear equation.
2. Find the product of vectors and their geometrical applications in finding moment of force, work done.
3. Determine probability of various types of events.
4. Solve the problems related to logarithms.
5. Solve the problems on trigonometric functions with angle of any magnitude.
6. Evaluate the limiting value of algebraic and trigonometric functions.
| CO | Course Outcome | PO Mapped | Cognitive Level | Theory Sessions | Allotted marks on cognitive levels |
TOTAL | ||
| R | U | A | ||||||
| CO1 | Find the product of matrices, value of determinants, and inverse of matrix and solve the simultaneous linear equation | 1,2,3 | R/U/A |
10 |
9 |
10 |
12 |
31 |
| CO2 | Find the product of vectors and their geometrical applications in finding moment of force, work done | 1,2,3 | R/U/A |
8 |
6 |
15 |
6 |
27 |
| CO3 | Determine probability of various types of events | 1,2, | R/U/A | 8 | 3 | 5 | 6 | 14 |
| CO4 | Evaluate the integrations of algebraic, trigonometric and exponential function | 1,2,3,10 | R/U/A |
16 |
15 |
20 |
12 |
47 |
| CO5 | Solve the problems related to logarithms. | 1,2 | R/A | 4 | 3 | 0 | 6 | 09 |
| CO6 | Evaluate the limiting value of algebraic and trigonometric functions | 1,2,10 | R/U/A |
6 |
6 |
5 |
6 |
17 |
|
|
| Total Hours of instruction | 52 | Total marks | 145 | |||
R-Remember; U-Understanding; A-Application Course outcomes –Program outcomes mapping strength
| Course | Programme Outcomes | |||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Engineering Mathematics-I | 3 | 3 | 3 | - | - | - | - | - | - | 3 |
Level 3- Highly Addressed, Level 2-Moderately Addressed, Level 1-Low Addressed.
Method is to relate the level of PO with the number of hours devoted to the COs which address the given PO. If >40% of classroom sessions addressing a particular PO, it is considered that PO is addressed at Level 3
If 25 to 40% of classroom sessions addressing a particular PO, it is considered that PO is addressed at Level 2 If 5 to 25% of classroom sessions addressing a particular PO, it is considered that PO is addressed at Level 1
If < 5% of classroom sessions addressing a particular PO, it is considered that PO is considered not-addressed.
Reference:
1. NCERT Mathematics Text books of class XI and XII.
2. Karnataka State PUC mathematics Text Books of I & II PUC by H.K. Dass and Dr.Ramaverma published by S.Chand & Co.Pvt.Ltd.
3. CBSE Class Xi & XII by Khattar&Khattar published PHI Learning Pvt. ltd.,
4. First and Second PUC mathematics Text Books of different authors.
5. www.freebookcentre.net/mathematics/introductory-mathematics -books.html
Course Assessment and Evaluation:
The Course will be delivered through lectures, class room interaction, exercises and self- study cases.
| Method | What | To whom | When/where (Frequency in the course) | Max Marks | Evidence collected | Contributing to course outcomes | |
|
|
*CIE | Internal Assessment Tests |
Student | Three tests (Average of Three tests will be computed). |
20 |
Blue books |
1 to 6 |
|
Assignments | Two Assignments based on CO's (Average marks of Two Assignments shall be rounded off to the next higher digit.) |
5 |
Log of record |
1 to 6 | |||
| Total | 25 |
|
| ||||
|
*SEE | Semester End Examination |
End of the course |
100 | Answer scripts at BTE |
1 to 6 | ||
|
|
Student feedback |
Students | Middle of the course |
-NA- |
Feedback forms | 1 to 3, delivery of the course | |
|
End of Course survey |
End of course |
Questionnaire | 1 to 6, Effectiveness of delivery of instructions and assessment methods | ||||
*CIE – Continuous Internal Evaluation *SEE – Semester End Examination
Note: I.A. test shall be conducted for 20 marks. Average marks of three tests shall be rounded off to the next higher digit.
Composition of Educational Components: Questions for CIE and SEE will be designed to evaluate the various educational components (Bloom's taxonomy) such as:
| Sl. No. | Educational Component | Weightage (%) |
| 1 | Remembering | 25 |
| 2 | Understanding | 40 |
| 3 | Applying the knowledge acquired from the course | 30 |
|
| Analysis and Evaluation | 5 |
