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Course map

1. Course Learning Objectives (CLOs) Mapping

At the completion of the course, students will be able to:

  1. Perform differentiation and integration using analytical and numerical methods
  2. Apply optimization techniques in engineering problem-solving
  3. Apply ordinary differential equations and partial differentiation in engineering problem-solving
  4. Understand and apply basic concepts of computer simulation and modeling to analyze engineering systems
  5. Use linear algebra and operations involving matrices to solve simultaneous equations

Each module in the course supports at least one of these CLOs.

2. Modules

Module 0: Course Introduction

Objective: Upon completion of this module, students will be able to describe foundational principles and engineering problem-solving approaches

Module 1: Dimensional Analysis (2 Weeks)

Objective: Upon completion of this module, students will be able to apply dimensional analysis and the Pi theorem to formulate, simplify, and evaluate engineering problems, including the development and interpretation of physical models.

Module 2: Differential Calculus (4 Weeks)

Objective: Upon completion of this module, students will be able to compute derivatives, analyze multivariable functions, and apply differential calculus techniques to optimize and interpret engineering systems, including problems aligned with FE exam–level applications.

Module 3: Integral Calculus (2 Weeks)

Objective: Upon completion of this module, students will be able to evaluate definite and indefinite integrals and apply integration techniques to solve engineering problems involving accumulated quantities and system behavior.

Module 4: Differential Equations (2 Weeks)

Objective: Upon completion of this module, students will be able to formulate, analyze, and solve ordinary and partial differential equations to model engineering systems governed by conservation laws.

Module 5: Computer Simulation and Modeling (2 Weeks)

Objective: Upon completion of this module, students will be able to develop mathematical models of engineering systems and implement analytical and numerical simulation techniques to evaluate system behavior and performance.

Module 6: Linear Algebra (1 Week)

Objective: Upon completion of this module, students will be able to construct and solve systems of linear equations using matrix operations and apply linear algebra techniques to analyze engineering systems.

Module 7: Monte Carlo Simulation (1 Week, Elective)

Objective: Upon completion of this module, students will be able to apply Monte Carlo simulation techniques to quantify uncertainty and evaluate probabilistic outcomes in engineering decision-making.

Module 8: Linear Regression (1 Week, Elective)

Objective: Upon completion of this module, students will be able to apply linear regression techniques to analyze engineering data, assess model performance, and interpret statistical relationships.

Students have to select one of the elective modules.

3. Participation

Each module includes an exit ticket discussion post as part of the participation grade, helping students stay engaged with the course and their peers. Exit tickets are brief, end-of-lesson feedback designed to quickly gauge student understanding, questions, provide instructors with immediate feedback, and start discussion. At the end of each module, students are required to submit a participation log, which tracks their engagement with course materials ensuring active learning.

4. Assessment

Assessment in this course utilizes weekly homework assignments designed to reinforce learning objectives across all modules, ranging from foundational concepts in dimensional analysis and calculus to practical applications in computer simulation and statistical modeling. Critical thinking exercises and optional Excel tutorials that mirror the homework assignments are also incorporated to promote deeper engagement and skill development.

5. Evaluation

The Feedback and Learning Assessment Survey is conducted after each module to evaluate student learning, assess the difficulty and pacing of the content, and gather feedback for course improvements. This survey encourages self-reflection and helps the instructor refine instructional materials, ensuring a well-balanced and engaging learning experience.

6. Course Alignment Table

CLOs Module Assessments Instructional Materials Learning Activities Tools
CLO 1 - Differentiation and Integration Module 2, Module 3 HW3, HW4, HW5, HW6, HW7, HW8 Lecture slides, videos, Excel sheets, Python codes Worked examples, problem-solving tutorials, practical applications Excel, Python
CLO 2 - Optimization Techniques Module 2, Module 8 HW4, HW13, HW12, HW14 Lecture slides, videos, Excel sheets, Python codes Worked examples, problem-solving tutorial, practical applications, Python simulations Excel, Python
CLO 3 - Differential Equations Module 2, Module 3, Module 4 HW2, HW9, HW10, HW11, HW12, HW14 Lecture slides, videos, Excel sheets, Python codes Worked examples, problem-solving tutorials, practical applications, Python simulations Excel, Python
CLO 4 - Computer Simulation & Modeling Module 1, Module 5, Module 7, Module 8 HW1, HW2, HW11, HW12, HW13, HW14 Lecture slides, videos, Excel sheets, Python codes Worked examples, problem-solving tutorials, practical applications, modeling exercises Excel, Python
CLO 5 - Linear Algebra Module 6 HW13, HW14 Lecture slides, videos, Excel sheets, Python codes Worked examples, problem-solving tutorial, practical applications Excel, Python
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