Tiêu đề MTH132 Mathematics II.pdf ✅

1 Pokhara University Faculty of Science and Technology Course Code: MTH 132 (3 credits) Full Marks: 100 Course Title: Mathematics II (3-3-0) Pass Mark: 45 Nature of the Course: Theory Total Lectures: 48 hours Level: Bachelor Year: I / Semester: II Program: Bachelor of Computer Application 1. Course Description: This course covers fundamental of integrals, application of integration, differential equations, vector Space, complex numbers and function of complex variables, sequence and series and Fourier series which are essential as mathematical foundation for computing. 2. General Objectives: The general objective of this course is to provide the students with basic mathematical skills required to understand Computer Application Courses 3. Methods of Instructions: Lecture, Tutorial, Discussion, Assignments and Practical works. 4. Contents in Detail Specific Objectives Contents Explain  Indefinite  Definite  Improper and  Double integration  Symbolic calculation of integration using any software tools (MATLAB/Mathematica/Oc tave etc.) Unit 1: Fundamental of integrals [10 Hrs] 1.1 Introduction 1.2 Indefinite integrals 1.3 Techniques of integration 1.3.1 Integration by substitution 1.3.2 Integration by parts 1.3.3 Integration by partial fractions 1.4 Definite integrals 1.5 Improper integrals 1.6 Beta and Gamma functions 1.7 Double integral (concept only)  Evaluate area and volume by integration Unit 2: Application of integration [7Hrs] 2.1 Introduction 2.2Application in economics (Determination of total cost and total revenue function) 2.3Area between the curves 2.4 Arc length of curves 2.5 Volume of solid of revolution (Disks and Washers) 2.6 Area of surface of revolution, 2.7 Consumer’s surplus and producer’s surplus  Solve first and second order Unit 3: Differential equations [7 Hrs]
2 differential equations. 3.1 Introduction 3.2 Order and degree of ordinary differential equations. 3.3 Solution of differential equations of first order by 3.3.1 Separation of variables 3.3.2 Homogeneous 3.3.3 Linear 3.3.4 Equation reducible to linear form (Bernoulli’s equation) 3.3.5 Linear and exact differential equations 3.4 Second order homogenous ODE with constant coefficients. 3.5 Second order Non homogenous ODE (Concept only)  Solve the problem related to Vector spaces, subspaces, linear dependent and independent, and Eigen values and Eigen vectors Unit 4: Vector Space [6 Hrs] 4.1 Introduction 4.2 Vector spaces and subspaces with example 4.3 Linear combination of vectors 4.4 Linear dependence and independence of vectors 4.5 Basis and dimension of vector space 4.6 Eigen values and Eigen vectors.  Solve and analyze complex number related problems Unit 5: Complex numbers and Function of complex variables [7Hrs] 5.1 Introduction 5.2 Algebra of the complex numbers 5.3 Geometric representation of complex numbers 5.4 Conjugate and absolute values of complex numbers 5.5 Polar form of complex numbers 5.6 Complex variables and function of complex variables 5.7 Analytic functions 5.8 Necessary and sufficient conditions for f(z) to be analytic (without proof) 5.9 Harmonic functions 5.10 Conformal mappings  Find Sum of series  Expand function in series Unit 6: Sequence and series [6 Hrs] 6.1 Introduction 6.2 Arithmetic and Geometric series 6.3 Sum of finite natural numbers 6.4 Sum of square of first ‘n’ natural numbers 6.5 Sum of cubes of first ‘n’ natural numbers. 6.6 Convergence of geometric series 6.7 Taylor series (one and two variables) 6.8 Maclaurin series.

4 practical evaluation with 80% attendance in the class in order to appear in the Semester End Examination. Failing to get such score will be given NOT QUALIFIED (NQ) to appear the Semester-End Examinations. Students are advised to attend all the classes, formal exam, test, 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. 8. Prescribed Books and References Text Books: 1. Erwin Kreyszig Advance engineering Mathematics, 2. Thomas and Finney Calculus Pearson References: 1. D.R. Bajracharya, R.M. Shrestha &et al, Basic mathematics I, II, Sukunda Pustak Bhawan, Nepal 2. Budnick F.S. Applied Mathematics for Business Economics and the Social sciences MCGraw-Hill Ryerson Limited 3. K.K. Shrestha & R. K. Thagurathi, Applied Mathematics 4. Rudra Pratap Getting Started with MATLAB, Oxford University Press 2010