Pokhara University
Faculty of Science and Technology
Course Code: MTH 150
Full Marks: 100
Course title: Algebra and Geometry (3-2-0)
Pass Marks: 45
Nature of the course: Theory
Total Lectures: 45 hours
Level: Bachelor
Program: BE
Course Description
The course covers matrices and determinants, a system of linear equations, rank, vector spaces, eigenvalues, and eigenvectors. It also covers infinite series and Fourier series. Moreover, it covers the geometry of two and three dimensions.
General Objectives
The general objective of the course is to provide sound knowledge of Algebra and Geometry of two and three dimensions.
Methods of Instruction
Lecture, Discussion, Readings, and Class Work
Contents in Detail
Specific Objectives
Unit I: Matrix and Determinants (7 hrs)
- Type of matrices, matrix multiplication, determinant, properties of determinant, orthogonal matrix, inverse of a matrix.
- System of linear equations and Gauss elimination method
- Linear dependence and independence, row rank, column rank, rank of the matrix, consistency condition, Caley-Hamilton theorem and its use in finding the inverse of a matrix
Unit II: Vector Space (6 hrs)
- Vector space, subspace, linear combination of vectors, Basis
- Linear transformation
- Eigenvalues and eigenvectors, some applications of eigenvalues problems
Unit III: Infinite Series (8 hrs)
- Introduction, necessary condition for an infinite series to be convergent, properties, p-series
- Comparison test, ratio test, root test, integral test
- Alternating series, Leibnitz test, absolute convergence, power series, interval of convergence
Unit IV: Fourier Series (6 hrs)
- Periodic function, even and odd functions, Fourier coefficients
- Fourier series of a function with period 2Ï€ and arbitrary period 2L
- Half-range expansions
Unit V: Two-dimensional Geometry (7 hrs)
- Parabola
- Ellipse
- Hyperbola
Unit VI: Three-dimensional Geometry (11 hrs)
- Review of the plane
- Straight lines
- Sphere
List of Tutorials
The following tutorial activities of 30 hours per group of a maximum of 24 students shall be conducted to cover all the required contents of this course. This will enable the students to complete the math problems under the supervision of the subject teacher.
- Problems on matrices and determinants (1 hr)
- To test the consistency and then solve the linear equations (2 hrs)
- Determining the rank of a matrix (1 hr)
- Problems on vector space, linear transformation, eigenvalues, and eigenvectors (3 hrs)
- MATLAB work: Matrix creation, addition, subtraction, multiplication, inverse, rank, solution of linear equations, Eigenvalues and Eigenvector, characteristic equation using the command window (2 hrs)
- To test for the convergence of a series (2 hrs)
- Finding the radius of convergence and the interval of convergence (2 hrs)
- MATLAB work: Creation and summation of series (1 hr)
- Problems on Fourier series (4 hrs)
- To obtain the standard equation of an ellipse and hyperbola (1 hr)
- Problems on parabola, ellipse, and hyperbola (3 hrs)
- MATLAB work: Plotting of 2D (1 hr)
- Problems on straight lines (4 hrs)
- Problems on a sphere (2 hrs)
- MATLAB work: Plotting of 3D (1 hr)
Evaluation System and Students’ Responsibilities
Evaluation System
The internal evaluation of a student may consist of assignments, attendance, term exams, and project works, etc. The internal evaluation scheme for this course is as follows:
| Internal Evaluation | Weight | Marks |
|---|---|---|
| Theory | 50% |
Semester-End examination: 50%
Attendance & Class Participation: 10%
Assignments: 20%
Presentations/Quizzes: 10%
Internal Assessment: 60%
Total Internal: 50
Full Marks: 50 + 50 = 100
Students’ Responsibilities
Each student must secure at least 45% marks in internal assessment evaluation with 80% attendance in the class in order to appear in the Semester End Examination. Failing to get such a score will be given NOT QUALIFIED (NQ) to appear in the Semester-End Examinations. Students are advised to attend all the classes, formal exams, tests, etc., and complete all the assignments within the specified time period. Students are required to complete all the requirements defined for the completion of the course.
Prescribed Books and References
Text Books
- Kreyszig, E. Advanced Engineering Mathematics. New Delhi: John Wiley and Sons Inc.
- Thomas, G. & Finney, R. Calculus and Analytical Geometry. New Delhi: Narosa Publishing House.
- Vittal, P. R. Analytical Geometry 2D and 3D, Delhi: Pearson India.
References
- E.W. Swokoswski, Calculus with Analytic Geometry, Prindle, Weber, and Schmidi
- Shanti Narayan, Analytical Solid Geometry, S. Chand and company
- Chandrika Prasad, Algebra and Theory of Equations, Pothishala Pvt. Ltd.
- Ward Cheney and David Kincaid, Linear Algebra: Theory and applications, Jones and Bartlett Publisher