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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: Introduce foundational principles and engineering problem-solving approaches

• CLOs Supported: (provides course context, introduce problem-solving approaches used throughout the course, introduce the modeling (CLO 4)
• Assessment: Homework 1, exit ticket

Module 1: Dimensional Analysis (2 Weeks)

Objective: Build foundational engineering problem-solving skills using dimensional analysis

• CLOs Supported: CLO 4 (Modeling- Physical models)
• Assessments: Homework 1, Homework 2, Exit tickets

Module 2: Differential Calculus (4 Weeks)

Objective: Build essential calculus skills for FE exam and engineering applications

• CLOs Supported: CLO 1 (Differentiation and Integration), CLO 2 (Optimization), CLO 3 (Differential Equations)
• Assessments: Homework 3, Homework 4, Homework 5, Homework 6, Exit tickets

Module 3: Integral Calculus (2 Weeks)

Objective: Strengthen integration skills and applications in engineering

• CLOs Supported: CLO 1 (Differentiation and Integration), CLO 3 (Differential Equations)
• Assessments: Homework 7, Homework 8, Exit tickets

Module 4: Differential Equations (2 Weeks)

Objective: Introduce ordinary and partial differential equations for engineering applications

• CLOs Supported: CLO 3 (Differential Equations)
• Assessments: Homework 9, Homework 10, Exit tickets

Module 5: Computer Simulation and Modeling (2 Weeks)

Objective: Introduce numerical modeling techniques for engineering

• CLOs Supported: CLO 2 (Optimization), CLO 3 (Differential Equations), CLO 4 (Computer Simulation and Modeling)
• Assessments: Homework 11, Homework 12, Exit tickets

Module 6: Linear Algebra (1 Week)

Objective: Introduce matrix operations and their applications in engineering

• CLOs Supported: CLO 5 (Linear Algebra)
• Assessments: Homework 13, Exit tickets

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

Objective: Introduce probabilistic modeling for engineering decision-making

• CLOs Supported: CLO 4 (Computer Simulation and Modeling)
• Assessments: Homework 14, Exit tickets

Module 8: Linear Regression (1 Week, Elective)

Objective: Introduce statistical regression techniques in engineering analysis

• CLOs Supported: CLO 2 (Optimization), CLO 4 (Computer Simulation and Modeling)
• Assessments: Homework 14, Exit tickets

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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