Applied Mathematics in the 4th semester of the Bachelor of Computer Engineering (BE Computer) program at Pokhara University is typically covered under the course Engineering Mathematics IV (Course Code: MTH 212.3). This course is designed to equip students with advanced mathematical tools and techniques essential for solving complex engineering problems, particularly in computer engineering. It builds on foundational concepts from earlier mathematics courses and introduces topics relevant to signal processing, optimization, and computational applications. Below is an overview of the course, its objectives, content, and relevance to computer engineering.

Course Objectives

The primary objectives of Engineering Mathematics IV are:

1. To provide an understanding of complex variables and their applications in engineering.
2. To introduce Fourier and Z-transforms for signal processing and system analysis.
3. To study partial differential equations (e.g., wave and diffusion equations) in various coordinate systems.
4. To equip students with knowledge of linear programming for optimization problems.
5. To develop skills in applying mathematical concepts to real-world computer engineering challenges, such as algorithm design and system modeling.

Syllabus Overview

Based on available information, the syllabus for Engineering Mathematics IV in the 4th semester of BE Computer at Pokhara University includes the following key topics:

1. Complex Variables:
   • Review of the complex number system.
   • Functions of complex variables, Taylor and Laurent series.
   • Singularities, poles, complex integration, and residues.
   • Applications in signal processing and circuit analysis.
2. Fourier Series and Transforms:
   • Review of Fourier series, Fourier integral, and inversion formula.
   • Frequency and phase spectra, Fourier analysis of step and delta functions.
   • Applications in signal processing and communication systems.
3. Z-Transform:
   • Region of convergence and its relation to causality.
   • Properties of Z-transform, single-sided and double-sided transforms.
   • Convolution, product of transforms, and inverse Z-transform.
   • Parseval’s theorem and solutions to difference equations.
   • Applications in digital signal processing and discrete systems.
4. Partial Differential Equations:
   • Wave and diffusion equations in Cartesian, cylindrical, and polar coordinates.
   • Applications in modeling physical systems relevant to computer engineering.
5. Linear Programming:
   • Simplex method, objective functions, and constraint conditions.
   • Converting inequalities to equalities, canonical form, and optimal solutions.
   • Applications in resource allocation, scheduling, and optimization in computing.
6. Curves and Surfaces:
   • Curves in space, tangent lines, tangent planes.
   • Ellipsoids, hyperboloids, paraboloids, and area projections.
   • Applications in computer graphics and geometric modeling.

Course Structure

• Credits: 3 (3 hours of theory, 2 hours of tutorial, 0 hours of practical).
• Evaluation:
  • Theory: 80% (final exam).
  • Sessional: 20% (assignments, quizzes, and tutorials).
• Textbooks:
  • Advanced Engineering Mathematics by Erwin Kreyszig.
  • Engineering Mathematics II by Prof. D. Sharma, Toya Narayan Paudel, Hari Prasad Adhikari (Sukunda Publication, Kathmandu).
  • Additional references may include Mathematics for Economics by T. Yamane and Applied Mathematics for Business, Economics, and the Social Sciences by F.S. Budnick.

Relevance to Computer Engineering

The topics covered in Engineering Mathematics IV are directly applicable to computer engineering:

• Complex Variables and Transforms: Essential for digital signal processing, image processing, and control systems, where Fourier and Z-transforms are used to analyze and design algorithms for audio, video, and communication systems.
• Linear Programming: Used in optimizing algorithms, resource allocation in networks, and scheduling tasks in operating systems.
• Partial Differential Equations: Applied in modeling heat dissipation in hardware, wave propagation in wireless communication, and simulations in computer graphics.
• Curves and Surfaces: Critical for computer graphics, 3D modeling, and game development, where geometric computations are fundamental.

Teaching Methodology

The course is delivered through a combination of lectures and tutorials. Students are expected to engage in problem-solving sessions, assignments, and projects that reinforce theoretical concepts. The emphasis is on applying mathematical techniques to practical engineering problems, ensuring students can translate abstract concepts into computational solutions.

Challenges and Recommendations

• Challenges: Students often find complex variables and transforms abstract and challenging due to their theoretical nature. Linear programming and partial differential equations require strong analytical skills.
• Recommendations:
  • Practice problem-solving regularly using textbooks like Kreyszig’s Advanced Engineering Mathematics.
  • Use software tools like MATLAB or Python to visualize and solve problems involving Fourier transforms, Z-transforms, and linear programming.
  • Refer to lecture notes and tutorials available on platforms like Self Learning University (SLU) or GitHub repositories curated for Pokhara University students.

Solutions Book and Syllabus

Syllabus