Annexure ‘CD-01’

L / T / P/S / SW/FW / TOTAL CREDIT UNITS
3 / - / 0 / 0 / 3

Course Title:Applied Mathematics I

Course Code:MATH114

Credit Units:3

Level: UG

Course Objectives: By end of the semester, students get acquainted with the all the basic concepts of Mathematics which will help them in various disciplines in coming semesters. The applications of this course includes science and engineering problems involving areas, volumes, expansion of functions, solution of system of equations, partial derivative, line integral, surface integral, volume integral and much more.

Pre-requisites:Students must have basic knowledge of matrices, differentiation, integration and vectors.

Course Contents/Syllabus:

Module I Linear Algebra / Weightage%
  • Elementary Row Transformation
  • Reduction of a Matrix to Row Echelon Form
  • Rank of a Matrix
  • Consistency of Linear Simultaneous Equations
  • Gauss Elimination Method, Gauss-Jordan Method
  • Eigen Values and Eigen Vectors of a Matrix
  • Caley-Hamilton Theorem
  • Diagonalization of a Matrix
/ 30%
Module II Multivariable Differential calculus
  • Functions of 2 Variables
  • Limits and continuity
  • Partial differentiation
  • Euler’s Theorem
  • Maxima and Minima of two variables
  • Method of Lagrange Multipliers
  • Taylor Series and Maclaurin Series of two variables
  • Jacobian
/ 25%
Module III Multivariable Integral calculus
  • Multiple Integrals-Double integrals
  • Change of order
  • Applications to areas
  • volumes
  • Triple Integral
/ 20%
Module IV Vector Calculus
  • Gradient, Divergence, Curl
  • Evaluation of Line Integral
  • Green’s Theorem in Plane (without proof)
  • Stoke’s Theorem (without proof)
  • Gauss Divergence Theorem (without proof)
/ 25%

Student Learning Outcomes: After completing this course, students learning outcomes are as follows:

  • Students will be able to recognize, identify, classify and describe the problems like they can classify rows and columns and then to apply different transformations and explain the solutions of systems of equations.
  • It will enable the students to apply the concepts learnt in this course, like differentiation and integration, to calculate, compare and interpret the results obtained in other disciplines and determine whether the solutions are reasonable.
  • It will also help the students to formulate/create the problems themselves and then to organize it to find the solutions like theorems of vector calculus can be applied to find line integral, surface integral and volume integral.
  • Students will be able to find partial derivatives, maxima and minima of two variables, Jacobians and expand the functions using Taylor’s series.
  • They can calculate double, single integrals and can apply concepts to find area and volume.
  • Towards the end students will be able to evaluate and assess the results of various problems in other subjects based on these concepts.

Pedagogy for Course Delivery:

  1. Lot of illustrations, examples will be covered in the classroom to give thorough knowledge of the course.
  2. All the topics covered in the syllabus will be correlated with its applications in real life situations and also in other disciplines.
  3. In order to inculcate problem solving ability in students’ time to time quiz, viva, home assignments and class tests will be conducted during the progress of semester.
  4. Extra sessions for revision will be undertaken.

Lab/ Practicals details, if applicable: NA

List of Experiments: NA

Assessment/ Examination Scheme:

Theory L/T (%) / Lab/Practical/Studio (%) / End Term Examination
30 / NA / 70

Theory Assessment (L&T):

Continuous Assessment/Internal Assessment / End Term Examination
Components (Drop down) / MID TERM / HOME ASSIGNMENT / VIVA / ATTENDANCE
Weightage (%) / 10 / 7 / 8 / 5 / 70

Lab/ Practical/ Studio Assessment: NA

Continuous Assessment/Internal Assessment / End Term Examination
Components (Drop down
Weightage (%)

Text:

  1. Differential Calculus by Shanti Narain
  2. Integral Calculus by Shanti Narain
  3. Linear Algebra- Schaum Outline Series.
  4. Engineering Mathematics by B.S. Grewal.
  5. Differential Equation by A.R. Forsyth
  6. Higher Engineering Mathematics by H.K. Dass